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prof. Ing. Michael Šebek, DrSc.

Garant a tutor programu Kybernetika a robotika - bakalářský
Tutor programu Kybernetika a robotika - magisterský

Všechny publikace

Distributed Estimation on Sensor Networks With Measurement Uncertainties

  • DOI: 10.1109/TCST.2020.3026815
  • Odkaz: https://doi.org/10.1109/TCST.2020.3026815
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This article brings distributed estimation for large-scale systems. The plant is considered affected by process disturbance, and measurements are corrupted by measurement noise. The proposed approach fuses measurements of differing reliability so that all nodes reach consensus on the plant's state estimate. This architecture is flexible to the addition of new nodes and, to a certain extent, robust to node or communication link failures. In spite of limited observability by each of the nodes, data fusion over the network allows each node to obtain the full estimate of the plant's state. Structured Lyapunov functions are used to prove the convergence of the estimator. Estimation error covariances are analyzed in detail. The proposed distributed observer design is validated by numerical simulations.

Distributed adaptive consensus protocol with decaying gains

  • DOI: 10.1002/rnc.5056
  • Odkaz: https://doi.org/10.1002/rnc.5056
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This article brings a distributed adaptive protocol for consensus and synchronization in multiagent systems on directed communication networks. Agents are modeled as general linear time-invariant systems. The proposed protocol introduces a novel adaptation scheme allowing control coupling gains to decay to their reference values. This approach improves upon existing adaptive consensus protocols which may result in overly large or even unbounded coupling gains. The protocol design in this article does not rely on any centralized information; hence it is distributed. Nevertheless, the price to pay for this is the need to estimate those reference values. Convergence of the overall network dynamics is guaranteed for correctly estimated references; otherwise, the trajectory of the system is only uniformly ultimately bounded. Two estimation algorithms are proposed: one based on the interval-halving method and the other based on a distributed estimation of Laplacian eigenvalues. Numerical simulations validate the proposed approach.

Zone MPC with guaranteed identifiability in presence of predictable disturbances

  • Autoři: Žáčeková, E., Pčolka, M., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Journal of the Franklin Institute. 2020, 357(2), 978-1001. ISSN 0016-0032.
  • Rok: 2020
  • DOI: 10.1016/j.jfranklin.2019.10.016
  • Odkaz: https://doi.org/10.1016/j.jfranklin.2019.10.016
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    In this paper, the task of ensuring sufficiently excited data for the subsequent reidentification of a model used within the model predictive control framework is tackled. It introduces two algorithms that are developed specifically for zone MPC for systems with external disturbances. Both of them work in two steps and build on the original zone MPC solution. The trade-off between the data informativeness and degradation of the control performance is given by a user-defined threshold for the performance degradation. Moreover, a new optimization criterion quantifying data informativeness is introduced. The proposed algorithms are described in detail and their theoretical properties are discussed. Two different verification scenarios are presented, the first one with an artificial example and the second one considering a real-life building climate control task using a high-fidelity testbed model. The results show that they significantly outperform the classic zone MPC in data informativeness while maintaining acceptable zone violation and energy consumption.

Distributed Observer and Controller Design for Spatially Interconnected Systems

  • DOI: 10.1109/TCST.2017.2769019
  • Odkaz: https://doi.org/10.1109/TCST.2017.2769019
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This work tackles the networked distributed observer and controller design problem for spatially interconnected systems. The state observers are designed in a distributed manner based on pinning control precepts. Compared to existing designs, on the one hand, this novel approach adds fault tolerance with respect to communication link failures in the networked system; on the other hand, our approach brings flexibility of integrating additional sensors into the network. A sufficient condition guaranteeing the stability of the closed-loop system is derived. Numerical simulation is given to verify the proposed design.

Structure-preserving low-order modeling approach of laminated composite plates integrated with macro-fiber composite transducers for dynamic applications

  • DOI: 10.1016/j.compstruct.2018.09.062
  • Odkaz: https://doi.org/10.1016/j.compstruct.2018.09.062
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    An Equivalent Substructure Modeling (ESM) approach of laminated composite plates with integrated macro-fiber composite (MFC) transducers is described. The proposed approach generates structure-preserving low-order system models for dynamic applications such as vibration suppression and energy harvesting. The direct piezoelectric effect of MFC transducers is derived from the electrical boundary conditions and it has the same coupling patterns as equivalent forces which describe the inverse piezoelectric effect. Hence, the reversibility of the piezoelectric effect is ensured and the electrical dynamics of the system can be simulated. The dual electromechanical couplings are assigned to a low-order structural model generated by an equivalent substructure concept. A laminated composite plate with integrated MFC transducers is used for validations and the simulated results agree well with experimental data. Two given study cases demonstrated that the ESM approach not only can generate accurate low-order system models but also provides a flexible fashion to design piezoelectric composite systems.

H∞-output regulation of linear heterogeneous multiagent systems over switching graphs

  • DOI: 10.1002/rnc.4108
  • Odkaz: https://doi.org/10.1002/rnc.4108
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    In this paper, we analyze H∞‐output regulation of linear heterogeneous multiagent systems. The agents are subject to modeled and unmodeled disturbances and communicate over a switching graph. We derive a sufficient condition that guarantees H∞ output regulation for the mentioned setup. This sufficient condition places requirements on both the single‐agent systems and the switching graph. The requirement on the single‐agent systems is an H∞‐criterion that should be satisfied by a proper design of the controller. Meanwhile, the switching graph needs to be maximally connected. Moreover, we derive an upper bound for the overall ‐gain of the output synchronization error with respect to the unmodeled disturbances over a fixed communication graph. We illustrate our technical developments by a simulation example.

On the Necessity of Symmetric Positional Coupling for String Stability

  • Autoři: Martinec, D., Herman, I., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: IEEE Transactions on Control of Network Systems. 2018, 5(1), 45-54. ISSN 2325-5870.
  • Rok: 2018
  • DOI: 10.1109/TCNS.2016.2573739
  • Odkaz: https://doi.org/10.1109/TCNS.2016.2573739
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    We consider a distributed system with identical agents, constant-spacing policy and asymmetric bidirectional control, where the asymmetry is due to different controllers, which we describe by transfer functions. By applying the wave transfer function approach, it is shown that, if there are two integrators in the dynamics of agents, then the positional coupling must be symmetric, otherwise the system is string unstable. The main advantage of the transfer function approach is that it allows us to analyse the bidirectional control with an arbitrary complex asymmetry in the controllers, for instance, the control with symmetric positional but asymmetric velocity couplings.

Towards a Smart Car: Hybrid Nonlinear Predictive Controller with Adaptive Horizon

  • DOI: 10.1109/TCST.2017.2747504
  • Odkaz: https://doi.org/10.1109/TCST.2017.2747504
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper focuses on the development of an optimization algorithm for car motion predictive control that addresses both hybrid car dynamics and hybrid minimization criterion. Instead of solving computationally demanding nonlinear mixed-integer programming task or approximating the hybrid dynamics/criterion, the Hamiltonian-switching Hybrid Nonlinear Predictive Control algorithm developed in this paper incorporates the information about hybridity directly into the optimization routine. To decrease the time-complexity, several adaptive prediction horizon approaches are proposed and for some of them, it is shown that they preserve maneuverabilityrelated properties of the car. All developed alternatives are verified on an example of a motion control of a racing car and compared with the approximation-based nonlinear predictive control and a commercial product. Moreover, sensitivity analysis examining robustness of the algorithm is included as well.

A travelling wave approach to a multi-agent system with a path-graph topology

  • DOI: 10.1016/j.sysconle.2016.12.001
  • Odkaz: https://doi.org/10.1016/j.sysconle.2016.12.001
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    The paper presents a novel approach for the analysis and control of a multi-agent system with non-identical agents and a path-graph topology. With the help of irrational wave transfer functions, the approach describes the interaction among the agents from the ‘local’ perspective and identifies travelling waves in the system. It is shown that different dynamics of the agents create a virtual boundary that causes a partial reflection of the travelling waves. Undesired effects due to the reflection of the waves, such as amplification/attenuation, long transients or string instability, can be compensated by the feedback controllers introduced in this paper. We show that the controllers achieve asymptotic and even string stability of the system.

Consensus-based distributed sensor fusion over a network

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper studies the distributed filtering of noisy measurements of one scalar quantity. The considered network is composed of two sets of nodes: sensing nodes which perform the measuring task and non-sensing nodes which mediate between the sensing nodes. Inspired by Bayesian sensor fusion, three consensus-based algorithms are proposed. In the algorithms, graph edge weights in effect are determined based on variances of measurements of all the sensors. Evolution dynamics of the expected values and covariances of the state estimates throughout the network is analyzed. Numerical simulations are given to examine the fusion performance of the proposed scheme. The results are fairly consistent with the analytical solution regarding the statistical properties of the steady-state state estimates in the network.

Distributed adaptive consensus protocol with Laplacian eigenvalues estimation

  • DOI: 10.1109/PC.2017.7976225
  • Odkaz: https://doi.org/10.1109/PC.2017.7976225
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper addresses distributed consensus problem for multi-agent systems with general linear time-invariant dynamics and undirected connected communication graphs. A distributed adaptive consensus protocol is found to solve problems of existing adaptive consensus protocols related to different, generally large and possibly unbounded coupling gains. This protocol guarantees ultimate boundedness under all conditions, however for an asymptotic stability, a proper estimation of reference values for coupling gains is required. Here, we propose an algorithm for the estimation of the coupling gain reference. The algorithm is based on a distributed estimation of the Laplacian eigenvalues. In comparison to the previously proposed algorithm based on the interval halving method, this algorithm offers robustness to change of the network topology. In addition, it decouples the estimation from the consensus protocol, hence it does not influence stability properties of the adaptive consensus protocol.

Equivalent force modeling of macro fiber composite actuators integrated into nonhomogeneous composite plates for dynamic applications

  • DOI: 10.1088/1361-665X/aa7bd0
  • Odkaz: https://doi.org/10.1088/1361-665X/aa7bd0
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Smart structures with integrated macro fiber composite (MFC) piezoelectric transducers have been increasingly investigated in engineering. A simple but elaborate system model of such smart structure not only can predict system dynamics, but also can reduce challenges in application. Therefore, the equivalent force (EF) modeling approach is presented to model the plate-type structures with integrated piezoelectric actuators in a semi-analytical fashion: analytical EF is applied to finite element (FE) structural models. The EF is derived from the bending effort balance between the equivalent loads, and the equivalent loads are developed by introducing the spatial distribution into a generalized Hamilton's principle. The proposed approach is validated by cantilever aluminum beams with integrated MFC actuators and it is consistent with existing alternative approaches from literature. Then, it is validated on a non-homogeneous composite plate for dynamic applications: a laminated composite plate with integrated MFC actuators was manufactured and both an impact test and MFC drive test were elaborately carried out. The modal validation shows the high fidelity of the EF model and the predicted velocity frequency responds functions (FRFs) agree well with experimental measurement. Being applicable to both numerical and analytical modeling approaches, the EF is actually assigned to the out-plane displacement on the structure and distributed along the edges of the actuators. Therefore, it is convenient to use in EF models. The rotational degrees of freedom could also be eliminated in the EF models without losing structure complexity, since they neither link to the electromechanical coupling nor have a significant kinetic contribution to the system.

Generalized output synchronization of heterogeneous linear multi-agent systems

  • DOI: 10.1109/PC.2017.7976179
  • Odkaz: https://doi.org/10.1109/PC.2017.7976179
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper investigates output synchronization of heterogeneous linear time-invariant systems. Agents distributively communicate measured outputs and synchronize on regulated outputs. Necessary structure of single-agents' drift dynamics is used. Relations between single-agent dynamics, measured outputs and regulated outputs are investigated. Cooperative stability conditions reduce to requirements depending separately on single-agents' structure and interconnecting graph topology, allowing for a distributed control design. Sufficient condition is given based on coordinate transformations which reveal the effects of distributed control on single-agents. It is shown that identical subsystem state synchronization and robustness to interconnections guarantee regulated output synchronization.

Scaling in bidirectional platoons with dynamic controllers and proportional asymmetry

  • DOI: 10.1109/TAC.2016.2594169
  • Odkaz: https://doi.org/10.1109/TAC.2016.2594169
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    We consider platoons composed of identical vehicles with an asymmetric nearest-neighbor interaction. We restrict ourselves to intervehicular coupling realized with dynamic arbitrary-order onboard controllers such that the coupling to the immediately preceding vehicle is proportional to the coupling to the immediately following vehicle. Each vehicle is modeled using a transfer function and we impose no restriction on the order of the vehicle. The only requirement on the controller and vehicle model is that the platoon is stable for any number of vehicles. The platoon is described by a transfer function in a convenient product form. We investigate how the H-infinity norm and the steady-state gain of the platoon scale with the number of vehicles. We conclude that if the open-loop transfer function of the vehicle contains two or more integrators and the second smallest eigenvalue of the graph Laplacian is uniformly bounded from below, the norm scales exponentially with the growing distance in the graph. If there is just one integrator in the open loop, we give a condition under which the norm of the transfer function is bounded by its steady-state gain-the platoon is string-stable. Moreover, we argue that in this case it is always possible to design a controller for the extreme asymmetry-the predecessor following strategy.

Bridging the gap between the linear and nonlinear predictive control: Adaptations for efficient building climate control

  • DOI: 10.1016/j.conengprac.2016.01.007
  • Odkaz: https://doi.org/10.1016/j.conengprac.2016.01.007
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    The linear model predictive control which is frequently used for building climate control benefits from the fact that the resulting optimization task is convex (thus easily and quickly solvable). On the other hand, the nonlinear model predictive control enables the use of a more detailed nonlinear model and it takes advantage of the fact that it addresses the optimization task more directly, however, it requires a more computationally complex algorithm for solving the non-convex optimization problem. In this paper, the gap between the linear and the nonlinear one is bridged by introducing a predictive controller with linear time-dependent model. Making use of linear time-dependent model of the building, the newly proposed controller obtains predictions which are closer to reality than those of linear time invariant model, however, the computational complexity is still kept low since the optimization task remains convex. The concept of linear time-dependent predictive controller is verified on a set of numerical experiments performed using a high fidelity model created in a building simulation environment and compared to the previously mentioned alternatives. Furthermore, the model for the nonlinear variant is identified using an adaptation of the existing model predictive control relevant identification method and the optimization algorithm for the nonlinear predictive controller is adapted such that it can handle also restrictions on discrete-valued nature of the manipulated variables. The presented comparisons show that the current adaptations lead to more efficient building climate control.

Decentralized/distributed output feedback H-infinity controller design for vibration reduction of smart structures

  • Autoři: Zhang, X., Desmet, W., Faria, C., Dong, Z., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: PROCEEDINGS OF ISMA2016 INTERNATIONAL CONFERENCE ON NOISE AND VIBRATION ENGINEERING AND USD2016 INTERNATIONAL CONFERENCE ON UNCERTAINTY IN STRUCTURAL DYNAMICS. Katholieke University Leuven, 2016. pp. 289-302. ISBN 978-90-73802-94-0.
  • Rok: 2016
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    In this work, a static output-feedback H-infinity controller is designed to attenuate vibrations for a flexible beam which is mounted with four piezo actuators. LMI-based optimization approach is incorporated for the controller design. Via imposing zero-nonzero constraints, three information structures are investigated: centralized, decentralized and distributed configuration. Numerical simulations are carried out for all three configurations. Scenario in case of components failure is further studied.

Distributed Adaptive Consensus Protocol with Decaying Gains on Directed Graphs

  • DOI: 10.1016/j.ifacol.2016.10.423
  • Odkaz: https://doi.org/10.1016/j.ifacol.2016.10.423
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    In this paper we present a distributed adaptive consensus protocol, that solves the cooperative regulator problem for multi-agent systems with general linear time-invariant dynamics and directed, strongly connected communication graphs. The protocol addresses the problems of recent distributed adaptive consensus protocols with large or unbounded coupling gains. These problems are solved by introducing a novel coupling gain dynamics that allows the coupling gains to synchronize and decay to some estimated value. Unlike the static consensus protocols, which require the knowledge of the smallest real part of the non-zero Laplacian eigenvalues to design the coupling gain, the proposed adaptive consensus protocol does not require any centralized information. It can be therefore implemented on agents in a fully distributed fashion.

Distributed observer and controller design for state-output decomposed systems

  • DOI: 10.1109/CCA.2016.7587871
  • Odkaz: https://doi.org/10.1109/CCA.2016.7587871
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper tackles the networked distributed observer and controller design problem. The observers are designed in a distributed fashion. The computation effort due to high dimension of the whole system is then mitigated. The controllers are designed using linear quadratic regulation theory. A sufficient condition to guarantee the stability of the closed-loop system is derived. A conservative matrix norm bound condition for the controller is provided as well. Numerical simulation is given to verify the design procedure.

Optimal distributed control with application to asymmetric vehicle platoons

  • Autoři: Herman, I., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Proceedings of the IEEE 55th Conference on Decision and Control (CDC). Piscataway, NJ: IEEE, 2016. p. 4340-4345. ISBN 978-1-5090-1837-6.
  • Rok: 2016
  • DOI: 10.1109/CDC.2016.7798927
  • Odkaz: https://doi.org/10.1109/CDC.2016.7798927
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper considers a distributed system of identical agents with arbitrary LTI models. A method for distributed state-feedback design is provided. The proposed solution consists of two steps: first a single-agent controller is derived and then, based on the network topology, the gain of this controller is adjusted. LQ optimality of this controller is proved provided that the Laplacian has only real eigenvalues and is non-defective. The result is subsequently used to design a controller for asymmetric vehicle platoon. We show that the same controller with a fixed gain is the optimal controller for any number of vehicles in the platoon. However, the performance of the optimal controller is still subject to inherent limitations given by the network topology. In some cases, even exponential scaling in the number of vehicles must occur for any controller.

Output H∞ synchronization of heterogeneous linear multi-agent systems via a distributed output-feedback

  • DOI: 10.1109/CDC.2016.7798666
  • Odkaz: https://doi.org/10.1109/CDC.2016.7798666
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper investigates output H∞ synchronization of a group of linear heterogeneous agents. Agents are subject to external unmodeled disturbances and distributively communicate one set of outputs. The aim is to design a distributed controller to achieve synchronization on another set of outputs with an H∞ bound. We obtain an H∞-criterion for each agent that guarantees output synchronization in the absence of the external unmodeled disturbances and output H∞ synchronization in their presence. We derive the overall L2-gain of the output synchronization error with respect to the external unmodeled disturbances. We demonstrate our developments by a simulation example.

Robustness of uncertain discrete linear repetitive processes with H-infinity disturbance attenuation

  • Autoři: Dabkowski, P., Galkowski, K., Rogers, E., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Proceedings of the European Control Conference. Brussels: EUCA, 2016. pp. 2288-2293. ISBN 978-1-5090-2591-6.
  • Rok: 2016
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Repetitive processes are a class of 2D systems that can be used to model physical systems and also there are applications, such as iterative learning control, where using a repetitive processes setting for design has advantages over alternatives. In most cases, it is discrete dynamics that are basis for design and often there will be a need to deal with uncertainty in the process model and the effects of disturbances. This paper develops new algorithms for these tasks that are computed using linear matrix inequalities when the uncertainty is modeled using two standard representations and disturbance attenuation is measured by an H-infinity norm. The extension of these algorithms to control law design is also developed.

Scaling of H-infinity Norm in Symmetric Bidirectional Platoons

  • Autoři: Herman, I., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: IFAC-PapersOnLine proceedings series. Kidlington Oxford OX GB: Elsevier, 2016. p. 91-96. 22. vol. 49. ISSN 2405-8963.
  • Rok: 2016
  • DOI: 10.1016/j.ifacol.2016.10.378
  • Odkaz: https://doi.org/10.1016/j.ifacol.2016.10.378
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    In this paper scaling of H-infinity norm of selected transfer functions in bidirectional vehicle platoons is investigated. The vehicles are identical and use symmetric nearest-neighbor interactions, hence the communication topology is a pinned undirected path graph. The LTI open-loop model of individual vehicles can be of arbitrary order, but it is required to contain two integrators in order to track the movement of the leader. It is shown that for any agent model some transfer functions in the formation scale linearly, while others scale quadratically. The type of scaling depends on the steady-state gain of the transfer function.

Structured Lyapunov functions for synchronization of identical affine-in-control agents—Unified approach

  • DOI: 10.1016/j.jfranklin.2016.06.028
  • Odkaz: https://doi.org/10.1016/j.jfranklin.2016.06.028
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper brings structured Lyapunov functions guaranteeing cooperative state synchronization of identical agents. Versatile synchronizing region methods for identical linear systems motivate the structure of proposed Lyapunov functions. The obtained structured functions are applied to cooperative synchronization problems for affine-in-control nonlinear agents. For irreducible graphs a virtual leader is used to analyze synchronization. For reducible graphs a combination of cooperative tracking and irreducible graph cooperative synchronization is used to address cooperative dynamics by Lyapunov methods. This provides a connection between the synchronizing region analysis, incremental stability and Lyapunov cooperative stability conditions. A class of affine-in-control systems is singled out based on their contraction properties that allow for cooperative stability via the presented Lyapunov designs.

Synchronizing Region Approach for Identical Linear Time-Invariant Agents

Control reconfiguration of full-state linearizable systems by a virtual actuator

  • Autoři: Vey, D., Lunze, J., Žáčeková, E., Pčolka, M., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Proceedings of the 9th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes. Laxenburg: IFAC, 2015. p. 339-344. ISSN 1474-6670.
  • Rok: 2015
  • DOI: 10.1016/j.ifacol.2015.09.550
  • Odkaz: https://doi.org/10.1016/j.ifacol.2015.09.550
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper presents a new method for control reconfiguration of nonlinear, input-affine systems subject to actuator failures. For full-state linearizable systems it is shown that after the occurrence of an actuator failure the linearizing feedback has to be adapted to the failure case. In a second step, the reconfiguration of the re-linearized system can be accomplished by means of a static linear virtual actuator. An interesting observation is the fact that the faulty system stays reconfigurable as long as there is one actuator left in the faulty plant. This paper illustrates the method by considering a fluid process.

Cooperative synchronization control for agents with control delays: A synchronizing region approach

  • DOI: 10.1016/j.jfranklin.2015.02.011
  • Odkaz: https://doi.org/10.1016/j.jfranklin.2015.02.011
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper investigates multi-agent system synchronization in the presence of control signal delays. Agents are assumed to be identical linear time-invariant systems, interacting on a directed graph topology, all having the same control delay. Distributed control of multi-agent systems is complicated by the fact that the communication graph topology interplays with single-agent dynamics. Here a design method based on a synchronizing region is given that decouples the design of local feedback gains from the detailed properties of graph topology. Such extension of the synchronizing region concept to agents with delays is rigorously justified. Delay-dependent synchronizing region is defined and methods are given guaranteeing its estimates. Qualitative properties of delay-dependent synchronizing regions and implications for control design are discussed. It is found that these regions are inherently bounded which restricts the graphs that allow for synchronization under delayed communication. Stronger property of exponential stability with a prescribed convergence rate is presented as a special case.

Distributed static output-feedback control for state synchronization in networks of identical LTI systems

  • DOI: 10.1016/j.automatica.2014.12.015
  • Odkaz: https://doi.org/10.1016/j.automatica.2014.12.015
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper studies state synchronization of multi-agent systems with disturbances using distributed static output-feedback (OPFB) control. The bounded L2 gain synchronization problem using distributed static OPFB is defined and solved. The availability of only output measurements restricts the local controls design, while the communication graph topology restricts global information flow among the agents. It is shown here that these two types of restriction can be dealt with in a symmetric manner and lead to two similar conditions guaranteeing the existence of bounded L2 gain static OPFB. One condition is on the output measurement matrix on a local scale, and the other on the graph Laplacian matrix on a global scale. Under additional conditions a distributed two-player zero-sum game using static OPFB is also solved and leads to distributed Nash equilibrium on the communication graph. As a special case the static OPFB globally optimal control is given. A new class of digraphs satisfying the above condition on the graph Laplacian is studied. The synchronizing region for distributed static OPFB control is exposed and found to be conical, different than the infinite right-half plane synchronizing region for distributed state feedback.

Identification and Energy Efficient Control for a Building: Getting Inspired by MPC

  • DOI: 10.1109/ACC.2015.7170973
  • Odkaz: https://doi.org/10.1109/ACC.2015.7170973
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper deals with identification of a building model based on real-life data and subsequent temperature controller design. For the identification, advanced identification technique - namely MPC Relevant Identification method - is used. This approach has the capability of providing models with better prediction performance compared to the commonly used methods. Regarding the controller part, several alternatives are proposed. First, both linear and nonlinear MPC controlling the zone temperature are designed. Although highly attractive due to promising energetic savings and thermal comfort satisfaction, MPCs demand high computational power. To overcome this issue and preserve the attractive properties of the MPC, two MPC-learned feedback controllers are proposed, one learned from LMPC and the other learned from NMPC. While remaining computationally low-cost, they improve the performance of the classical controllers towards the high-performance MPC standards. The results exploiting data from real operation of an office equipped with air handling unit situated in Lakeshore building, Michigan Tech, are presented and discussed.

MPC for a Class of Nonlinear Systems with Guaranteed Identifiability

  • DOI: 10.1109/CCA.2015.7320627
  • Odkaz: https://doi.org/10.1109/CCA.2015.7320627
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper addresses the problem of model predictive control for a class of nonlinear systems which satisfies per- sistent excitation condition. The conditions under which a non- linear system description can be handled are specified and two algorithms (one optimizing the first input sample and the other considering optimization of an M -sample subsequence of the input profile) solving the persistent excitation condition within a predictive controller for nonlinear systems are developed, both maximizing the smallest eigenvalue of the information matrix increase. The numerical experiments performed on a test-bed system demonstrate that the algorithms are able to successfully improve identifiability of a nonlinear system description while keeping the original controller performance degradation lower than arbitrarily chosen level.

Nonzero Bound on Fiedler Eigenvalue Causes Exponential Growth of H-Infinity Norm of Vehicular Platoon

  • DOI: 10.1109/TAC.2014.2366980
  • Odkaz: https://doi.org/10.1109/TAC.2014.2366980
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    We consider platoons composed of identical vehicles and controlled in a distributed way, that is, each vehicle has its own onboard controller. The regulation errors in spacing to the immediately preceeding and following vehicles are weighted differently by the onboard controller, which thus implements an asymmetric bidirectional control scheme. The weights can vary along the platoon. We prove that such platoons have a nonzero uniform bound on the second smallest eigenvalue of the graph Laplacian matrix— the Fiedler eigenvalue. Furthermore, it is shown that existence of this bound always signals undesirable scaling properties of the platoon. Namely, the H-infinity norm of the transfer function of the platoon grows exponentially with the number of vehicles regardless of the controllers used. Hence the benefits of a uniform gap in the spectrum of a Laplacian with an asymetric distributed controller are paid for by poor scaling as the number of vehicles grows.

On zero-vibration signal shapers and a wave-absorbing controller for a chain of multi-agent dynamical systems

  • DOI: 10.1109/ECC.2015.7330676
  • Odkaz: https://doi.org/10.1109/ECC.2015.7330676
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    The paper brings together two different approaches for control of chain of oscillatory lumped-parameter multi-agent systems. Namely, the multi-mode zero-vibration input shaper and the wave-absorbing controller are recalled and the similarities and links between them are broadly discussed. The special case of identical agents with a double-integrator character is at the focus throughout the paper. The report reveals that the two approaches are closely related in spite of the fact that they differ significantly in all aspects, from motivation through computational algorithms to target implementation. In addition, the presented numerical results, mostly based on numerical simulations at this moment, show that the two methods can be combined together, to take advantage of both an appropriate initial excitation of the system by the input shaper and of increased robustness coming from the wave-absorber feedback architecture. Such a combined control law is based on a special property of the multi-mode zero vibration input shaper - namely the convergence of its impulse response, as the number of agents increases, to a double bell-shaped function.

Quantized Nonlinear Model Predictive Control for a Building

  • DOI: 10.1109/CCA.2015.7320653
  • Odkaz: https://doi.org/10.1109/CCA.2015.7320653
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    In this paper, the task of quantized nonlinear predictive control is addressed. In such case, values of some inputs can be from a continuous interval while for the others, it is required that the optimized values belong to a countable set of discrete values. Instead of very straightforward a posteriori quantization, an alternative algorithm is developed incorpo- rating the quantization aspects directly into the optimization routine. The newly proposed quaNPC algorithm is tested on an example of building temperature control. The results for a broad range of number of quantization steps show that (unlike the naive a posteriori quantization) the quaNPC is able to maintain the control performance close to the performance of the original continuous-valued nonlinear predictive controller and at the same time it significantly decreases the undesirable oscillations of the discrete-valued input.

Stability of a circular system with multiple asymmetric Laplacians

  • Autoři: Herman, I., Martinec, D., Veerman, J.J.P., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Preprints of the 5th IFAC Workshop on Distributed Estimation and Control in Networked Systems. Laxenburg: IFAC, 2015. pp. 162-167. ISSN 1474-6670.
  • Rok: 2015
  • DOI: 10.1016/j.ifacol.2015.10.324
  • Odkaz: https://doi.org/10.1016/j.ifacol.2015.10.324
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    We consider an asymptotic stability of a circular system where the coupling Laplacians are different for each state used for synchronization. It is shown that there must be a symmetric coupling in the output state to guarantee the stability for agents with two integrators in the open loop. Systems with agents having three or more integrators cannot be stabilized by any coupling. In addition, recent works in analysis of a scaling in vehicular platoons relate the asymptotic stability of a circular system to a string stability. Therefore, as confirmed by simulations in the paper, our results have an application also in path graphs.

Travelling waves in a multi-agent system with general graph topology

  • Autoři: Martinec, D., Herman, I., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Preprints of the 5th IFAC Workshop on Distributed Estimation and Control in Networked Systems. Laxenburg: IFAC, 2015. p. 82-87. ISSN 1474-6670.
  • Rok: 2015
  • DOI: 10.1016/j.ifacol.2015.10.311
  • Odkaz: https://doi.org/10.1016/j.ifacol.2015.10.311
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    The paper presents a novel approach for the analysis of a multi-agent system with arbitrary interaction topology and identical agents. The approach is based on an irrational transfer function, the Wave transfer function, that decomposes the interactions between the agents and identifies the travelling waves in the multi-agent system. The approach based on the travelling waves describes the behaviour of the system from the local perspective, which is complementary to the traditional overall approach. The proposed approach allows us, for example, to describe the local effect of the agents that have more than two neighbours.

Economical Nonlinear Model Predictive Control for Building Climate Control

  • DOI: 10.1109/ACC.2014.6858928
  • Odkaz: https://doi.org/10.1109/ACC.2014.6858928
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    In this paper, two alternatives approaches to model predictive control (MPC) are compared and contrasted for the role of zone temperature controller - the commonly used linear formulation (LMPC) and rather unconventional nonlinear formulation (NMPC). The economical focus is reflected by the performance criterion being a combination of the comfort requirements and the monetary cost penalties (price of the consumed hot water and the electricity needed to deliver the water to the building) of the controlled inputs. With this formulation, the optimal controller drives toward minimization of the real price rather than minimization of abstract quantities. It turns out that the NMPC is able to attack the cost minimization directly while retaining a compact optimization formulation as opposed to the suboptimal linear alternative. A considerable part of the superiority of the NMPC can be owed also to the use of a nonlinear model that captures the nonlinear building dynamics much more accurately than the linear models. Thanks to an enhanced search step choice introduced in this paper, the NMPC outperforms both the LMPC and the conventional controller significantly even under severe computational restrictions which demonstrates its strong practical applicability.

From Linear to Nonlinear Model Predictive Control of a Building

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    In the building climate control area, the linear model predictive control (LMPC)| nowadays considered a mature technique - benefits from the fact that the resulting optimization task is convex (thus easily and quickly solvable). On the other hand, while nonlinear model predictive control (NMPC) using a more detailed nonlinear model of a building takes advantage of its more accurate predictions and the fact that it attacks the optimization task more directly, it requires more involved ways of solving the non-convex optimization problem. In this paper, the gap between LMPC and NMPC is bridged by introducing several variants of linear time- varying model predictive controller (LTVMPC). Making use of linear time-varying model of the controlled building, LTVMPC obtains predictions which are closer to reality than those of linear time invariant model while still keeping the optimization task convex and less computationally demanding than in the case of NMPC. The concept of LTVMPC is verified on a set of numerical experiments performed using a high fidelity model created in a building simulation environment and compared to the previously mentioned alternatives (LMPC and NMPC) looking at both the control performance and the computational requirements.

Harmonic instability of asymmetric bidirectional control of a vehicular platoon

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper deals with harmonic instability of asymmetric control of vehicular platoons. The considered platoons are composed of identical linear models of arbitrary order but there must be at least two integrators in the open loop. Each vehicle only responds to the movement of its immediate neighbors—the predecessor and the follower—and these two couplings are nonidentical. We show that for arbitrary asymmetry of intervehicular coupling, there is an exponential growth of the peak in the platoon’s magnitude frequency responses as the number of vehicles grows—a phenomenon called harmonic instability in the literature. Whereas it has been already shown for some particular cases that the beneficial effects of having the Laplacian eigenvalues lower-bounded by a nonzero constant come at the cost of harmonic instability, here we generalize this result to any linear controllers.

On Satisfaction of the Persistent Excitation Condition for the Zone MPC: Numerical Approach

  • Autoři: Žáčeková, E., Pčolka, M., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Proceedings of The 19th World Congress of the International Federation of Automatic Control. Pretoria: IFAC, 2014. pp. 2848-2853. ISSN 1474-6670. ISBN 978-3-902823-62-5.
  • Rok: 2014
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    In recent years, advanced control techniques such as Model Predictive Control based on optimization and making use of a model providing the predictions of the future behavior of the controlled system have been massively developed. These model-based controllers rely heavily on the accuracy of the available model (predictor of the controlled system behavior) which is crucial for their proper functioning. However, as the current operating conditions can be shifted away from those under which the model has been identified, the model sometimes happens to lose its prediction properties and needs to be re-identified. Unlike the theoretical assumptions, the data from the real operation suffer from undesired phenomena accompanying the closed-loop data. In the current paper, we focus on developing an algorithm which would serve as an alternative to the (often costly or even unrealizable) open loop excitation experiment. The requirements such an algorithm should meet are: low computational complexity, low level of original MPC performance degradation and ability to provide sufficiently informative data when necessary. Unlike to the currently available approaches which solve this problem for the classical MPC formulation (tracking error penalization), in this paper we propose an algorithm which works well also for the zone MPC formulation (penalization of output zone violation), however, it is versatile enough and can be extended considering wider variety of the optimization formulations.

Refinement of a bidirectional platooning controller by wave absorption at the leader

  • DOI: 10.1109/ECC.2014.6862263
  • Odkaz: https://doi.org/10.1109/ECC.2014.6862263
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    The paper tailors the so-called wave-based control known in the field of flexible mechanical structures to the problem of distributed control of vehicular platoons. The proposed solution is based on refinement of the popular symmetric bidirectional distributed controller which enables the platoon leader to actively absorb any incoming (backwards running) wave of positional changes in the platoon. In order to accomplish this, the platoon leader only needs to measure the distance to its immediate follower. This minor augmentation results in significant attenuation of undesirable long transients during the platoon manoeuvres like acceleration/deceleration or during the commanded change of the inter-vehicle distances. Numerical simulations show that the wave-absorbing controller works efficiently even for platoons with a very large number of vehicles and outperforms the known platoon control schemes such as predecessor following or bidirectional control algorithm.

Semi-receding Horizon Algorithm for Sufficiently Exciting MPC with Adaptive Search Step

  • DOI: 10.1109/CDC.2014.7040034
  • Odkaz: https://doi.org/10.1109/CDC.2014.7040034
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    In this paper, the task of finding an algorithm providing sufficiently excited data within the MPC framework is tackled. Such algorithm is expected to take action only when the re-identification is needed and it shall be used as the “least costly” closed loop identification experiment for MPC. The already existing approach based on maximization of the smallest eigenvalue of the information matrix increase is revised and an adaptation by introducing a semi-receding horizon principle is performed. Further, the optimization algorithm used for the maximization of the provided information is adapted such that the constraints on the maximal allowed control performance deterioration are handled more carefully and are incorporated directly into the process instead of using them just as a termination condition. The effect of the performed adaptations is inspected using a numerical example. The example shows that the employment of the semi-receding horizon brings major improvement of the identification properties of the obtained data and the proposed adaptive-search step algorithm used for the “informativeness” optimization brings further significant increase of the contained information while the aggravation of the economical and tracking aspects of the control are kept at aceptable level.

Two-Sided Wave-Absorbing Control of a Heterogenous Vehicular Platoon

  • Autoři: Martinec, D., Herman, I., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Proceedings of The 19th World Congress of the International Federation of Automatic Control. Pretoria: IFAC, 2014. pp. 8091-8096. ISSN 1474-6670. ISBN 978-3-902823-62-5.
  • Rok: 2014
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    The paper tailors the so-called wave-absorbing control designed for a homogenous platoon of vehicles to a platoon where dynamics of vehicles differ. The proposed solution is based on the symmetric bidirectional control of the in-platoon vehicles and wave-absorbing control of the platoon ends. This type of control reduces oscillations of vehicle's velocities and significantly decrease the settling time of the platoon by absorbing waves on the platoon ends. The necessary transfer-function-based mathematical apparatus for description of the so-called soft boundary is also presented. Although the soft boundary is a virtual boundary located between the vehicles of different dynamics, it significantly alters the behaviour of the platoon. It is shown how to incorporate model of the soft boundary into the design of the wave-absorbing control such that its effect is minimized. The proposed control scheme is verified on numerous mathematical simulations.

Wave-absorbing vehicular platoon controller

  • DOI: 10.1016/j.ejcon.2014.06.001
  • Odkaz: https://doi.org/10.1016/j.ejcon.2014.06.001
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    The paper tailors the so-called wave-based control, popular in the field of flexible mechanical structures, to the field of distributed control of vehicular platoons. The proposed solution augments the symmetric bidirectional control algorithm with a wave-absorbing controller implemented on the leader, and/or on the rear-end vehicle. The wave-absorbing controller actively absorbs an incoming wave of positional changes in the platoon and thus prevents oscillations of inter-vehicle distances. The proposed controller significantly improves the performance of platoon manoeuvrers such as acceleration/deceleration or changing the distances between vehicles without making the platoon string unstable. Numerical simulations show that the wave-absorbing controller performs efficiently even for platoons with a large number of vehicles, for which other platooning algorithms are inefficient or require wireless communication between vehicles.

Zeros of transfer functions in networked control with higher-order dynamics

  • Autoři: Herman, I., Martinec, D., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Proceedings of The 19th World Congress of the International Federation of Automatic Control. Pretoria: IFAC, 2014. pp. 9177-9182. ISSN 1474-6670. ISBN 978-3-902823-62-5.
  • Rok: 2014
  • DOI: 10.3182/20140824-6-ZA-1003.01248
  • Odkaz: https://doi.org/10.3182/20140824-6-ZA-1003.01248
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper presents some results regarding location of transfer function zeros in general network control systems with dynamics of arbitrary order. The numerator polynomial of the transfer function is derived as a function of single agent dynamics and a Laplacian matrix. The results already known in literature are extended from single integrator and bidirectional formations to general dynamics and general interconnection structures. The location of zeros is related to poles of a slightly modified structure. Therefore, in some cases the zeros must follow the same root-locus-like rules as the poles do and they interlace.

Control of differential linear repetitive processes using strong practical stability and H-infinity disturbance attenuation

  • Autoři: Dabkowski, P., Galkowski, K., Bachelier, O., Rogers, E., prof. Ing. Michael Šebek, DrSc., Kummert, A.
  • Publikace: International Journal of Control. 2013, 86(4), 636-649. ISSN 0020-7179.
  • Rok: 2013
  • DOI: 10.1080/00207179.2012.756148
  • Odkaz: https://doi.org/10.1080/00207179.2012.756148
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Repetitive processes have a 2D systems structure and therefore standard control theory and design algorithms are not applicable. This article develops new algorithms for differential processes to achieve stabilisation together with a prescribed level of disturbance attenuation as measured by an H-norm. There are several physically motivated definitions of stability for repetitive processes and in this article the interest is in strong practical stability.

Equalization of intervehicular distances in platoons on a circular track

  • DOI: 10.1109/PC.2013.6581381
  • Odkaz: https://doi.org/10.1109/PC.2013.6581381
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    We consider a circular track and a platoon of vehicles driving on it. Our goal is to design a distributed (onboard) control system that will keep uniform spacing between any car and its predecessor without knowing the length of the track. Quite naturally the distributed control problem is posed as a double consensus task, wherein individual cars have to agree on the cruising velocity and the gaps between two consecutive cars. We study the feasibility of the consensus and its convergence properties. We prove that the cars will converge to equal distances and the resulting velocity will be the average of the velocity references of individual cars. We also consider the stability of this circularly connected system.

PDdE-based analysis of vehicular platoons with spatio-temporal decoupling

  • Autoři: Herman, I., Martinec, D., doc. Ing. Zdeněk Hurák, Ph.D., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Preprints of the 4th IFAC Workshop on Distributed Estimation and Control in Networked Systems :Estimation and Control of Networked Systems. Laxenburg: IFAC, 2013, pp. 144-151. ISSN 1474-6670. ISBN 978-3-902823-55-7.
  • Rok: 2013
  • DOI: 10.3182/20130925-2-DE-4044.00019
  • Odkaz: https://doi.org/10.3182/20130925-2-DE-4044.00019
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    The paper provides exact analytical solutions of wave-like PDdE-based (partial differential-difference equation) models of several popular vehicular platooning problems with bidirectional distributed control. Efficient evaluation of eigenvalues, eigenfunctions and wave velocities is proposed for a finite vehicular platoon without an approximation by a continuum model. Thanks to the decoupling of spatial and temporal dynamics, closed-loop stability can be analyzed by looking at a characteristic polynomial using a root-locus-like graphical technique. Although the paper only contains discussions for static state feedback controllers (using measurements of inter-vehicular distances and relative velocities), extensiona to higherorder (dynamic) controllers is straighforward and will be included in the extended version of the paper.

Vehicular Platoons: Survey of Control Algorithms and Experiments

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    The paper surveys various spatial strategies for control of vehicular platoons in future automated highway systems. The strategies are described in space /time domain as well as by local and global transfer functions. Their efficiency, applicability as well as other properties are discussed theoretically. They are also verified on a nice simple based on commercially available racing slot cars equipped with an on-board microcontroller-based control system with additional components such as an infrared range sensor and a wireless communication module.

Constant Time Headway Control Policy in Leader Following Vehicular Platoons: 2-D Polynomial Approach

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Constant time headway policy is considered for control of vehicular platoons in future automated highway systems. 2-D polynomial approach is applied, hence dynamics is described using a fraction of two bivariate polynomials. In contrast to some previous works, the platoon here assumes a leader and an infinite number of followers. The usual bilateral z-transform used for doubly infinite vehicular strings is replaced here by a special unilateral z-transform. This naturally brings the boundary conditions into consideration through which the leader vehicle comes into the scene.

Optimization of Predicted Mean Vote Thermal Comfort Index within Model Predictive Control Framework

  • Autoři: Cigler, J., Prívara, S., Váňa, Z., Komárková, D., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Proceedings of the 51st IEEE Conference on Decision and Control. Piscataway: IEEE, 2012. p. 3056-3061. ISSN 0191-2216. ISBN 978-1-4673-2066-5.
  • Rok: 2012
  • DOI: 10.1109/CDC.2012.6427051
  • Odkaz: https://doi.org/10.1109/CDC.2012.6427051
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Recently, Model Predictive Control (MPC) for buildings has undergone an intensive research. Usually, according to the international standards, a static range for the air temperature represents the thermal comfort which is being kept making use of MPC while minimizing the energy consumption. On contrary, this paper deals with the optimization of the trade-off between energy consumption and Predicted Mean Vote (PMV) index which, opposed to the static temperature range, describes user comfort directly. PMV index is a nonlinear function of various quantities, which makes the problem more difficult to solve. The paper will show the main differences in MPC problem formulation, propose a tractable approximation strategy and compare the control performance both to the conventional and typical predictive control strategies. The approximation of PMV computation will be shown to be sufficiently precise and moreover, such a formulation keeps the MPC optimization problem convex. Finally, it will be shown that the proposed PMV based optimal control problem formulation shifts the savings potential of typical MPC by additional 10% while keeping the comfort at a desired level.

Vehicular platooning experiments with racing slot cars

  • DOI: 10.1109/CCA.2012.6402709
  • Odkaz: https://doi.org/10.1109/CCA.2012.6402709
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    The paper reports on an affordable platform for indoor experimental verification of algorithms for distributed control of platoons of vehicles. The platform is based on commercially available racing slot cars (by Carrera) equipped with an on-board 32-bit microcontroller-based control system. The assembled PCB board was provided by Freescale Semiconductor, Rožnov pod Radhošťem, Czech Republic, within their Freescale Race Challenge 2012 competition of individual autonomous slot cars organized for student teams in Czech and Slovak republics. The documentation is freely available online. Some extra components such as an infrared range sensor and a wireless communication module have been added to the original system. The capabilities and potentials of the proposed platform are demonstrated on platooning experiments using two of the most popular platoon control schemes: predecessor following and leader following. Some technical parameters of the platform as well as design experience are shared in the report. It is hoped to encourage other teams to build a similar setup and possibly expose their new distributed control algorithms to an experimental competition.

2-D polynomial approach to control of leader following vehicular platoons

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper formulates the problems of stabilization and asymptotic following in infinite platoons of vehicles within the 2-D polynomial framework, that is, the dynamics of the problem are described using a fraction of two bivariate polynomials. In contrast to some previous works, the platoon here assumes a leader (and an infinite number of followers), therefore the often used bilateral z-transform should not be used here since it assumes a doubly infinite vehicular strings. The unilateral z-transform seems better suited. However, it brings about the need to take the boundary conditions into consideration; among other, the leader vehicle comes into the scene. The necessary formalism is introduced in the paper and used to provide elegant alternative proofs of some well-known facts about the platooning problem.

New Mathematical Tools for Analysis and Control of Platoons of Cars in Future Automated Highway Systems

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper introduces new mathematical tools for stabilization and asymptotic following in infinite platoons of vehicles in future automated highway systems. The platoon description, behavior analysis and control is approached in 2-D polynomial framework, that is, the dynamics of the problem are described using a fraction of two bivariate polynomials. In contrast to some previous works, the platoon here assumes a leader (and an infinite number of followers), therefore the often used bilateral z -transform should not be used here since it was developed for doubly infinite vehicular strings. The unilateral z -transform seems better suited. However, it brings about the need to take the boundary conditions into consideration; among other, the leader vehicle comes into the scene. The necessary formalism is introduced in the paper and used to provide elegant alternative proofs of some well-known facts about the platooning problem.

2D polynomial approach to stability of platoons of vehicles

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper formulates the problems of stability testing and stabilization of an infinite platoon of vehicles within the 2D polynomial framework, that is, the dynamics of the problem is described using a fraction of two bivariate polynomials. Recent computational tools for testing positivity of polynomial matrices are suggested for stability testing and stabilization.

Complete Fast Analytical Solution of the Optimal Odd Single-Phase Multilevel Problem

  • DOI: 10.1109/TIE.2009.2034677
  • Odkaz: https://doi.org/10.1109/TIE.2009.2034677
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    In this paper we focus on computation of optimal switching angles for general multilevel odd symmetry waveforms. We show that this problem is similar to (but more general than) the PWM modulation problem which is an established method of generating PWM waveforms with low base-band distortion. We introduce a new general modulation strategy for multilevel inverters which takes an analytic form and is very fast with the complexity of only O(n log^2 n) arithmetic operations where n is the num. of controlled harmonics. This alg. is based on a transf. of appropriate trigonometric eqs. for each controlled harmonics to a poly. system of eqs. that is further transformed to a special sys. of composite sum of powers. The solution of this sys. is carried out by a modification of the Newton's identity via Pade approx., formal ortho. poly. theory, and properties of symmetric poly. Finally, the optimal switching sequence is obtained by computing zeros of two formal ortho. poly. in one variable.

Subspace Identification of Poorly Excited Industrial Systems

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Most of the industrial applications are MIMO systems, that can be be identified using knowledge of the system's physics or from measured data employing statistical methods. Currently, there is the only class of statistical identification methods capable of handling the issue of vast MIMO systems - subspace identification methods. These methods need data of certain quality. Nevertheless, the combination of statistical methods and physical knowledge of the system could significantly improve system identification. This paper presents a new algorithm which provides remedy to insufficient data quality of certain kind through incorporating of prior information, e.g. known static gain or input-output feedthrough. The presented algorithm naturally extends classical subspace identification algorithms. The performance of the algorithm is shown on a case study and compared to current methods, where the model is used for an MPC control of a large building heating system.

An often missed detail: Formula relating peek sensitivity with gain margin less than one

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    An inequality relating gain margin with sensitivity peek value is presented in numberous basic control textbooks. In fact, this inequality fails to hold as soon as the open-loop Nyquist plot crosses the negative real axis on the left of the critical point. This opposite case is usually ignored by the textbook authors. A simple alternative inequality is derived in the paper to cover the not so popular opposite case. This fills a small gap one often encounters in basic control courses.

Effective solution of a linear system with Chebyshev coefficients

  • DOI: 10.1080/10652460902727938
  • Odkaz: https://doi.org/10.1080/10652460902727938
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper presents an efficient algorithm for a special triangular linear system with Chebyshev coefficients. We present two methods of derivations, the first is based on formulae where the nth power of x is solved as the sum of Chebyshev polynomials and modified for a linear system. The second deduction is more complex and is based on the Gauss-Banachiewicz decomposition for orthogonal polynomials and the theory of hypergeometric functions which are well known in the context of orthogonal polynomials. The proposed procedure involves O(nm) operations only, where n is matrix size of the triangular linear system L and m is number of the nonzero elements of vector b. Memory requirements areO(m), and no recursion formula is needed. The linear system is closely related to the optimal pulse-wide modulation problem.

Roboti vtrhli na ČVUT!

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Roboti jsou tu! Alespoň na Fakultě elektrotechnické jich je všude plno. Snad každý z 250 studentů začínajících nový bakalářský program Kybernetika a robotika s sebou nosí robota nebo alespoň nějakou jeho část. Ale strach mít nemusíte, jsou to roboti přátelští. Pokud nějakého uvidíte, určitě vám to zlepší náladu. A co se to vlastně děje?

Numerical algorithms for polynomial plus/minus factorization

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Two new algorithms are presented in the paper for the plus/minus factorization of a scalar discrete-time polynomial. The first method is based on the discrete Fourier transform theory (DFT) and its relationship to the Z-transform. Involving DFT computational techniques and the famous fast Fourier transform routine brings high computational efficiency and reliability. The method is applied in the case study of H-2-optimal inverse dynamic filter to an audio equipment. The second numerical procedure originates in a symmetric spectral factorization routine, namely the Bauer's method of the 1950s. As a by-product, a recursive LU factorization procedure for Toeplitz matrices is devised that is of more general impact and can be of use in other areas of applied mathematics as well. Performance of the method is demonstrated by an l(1) optimal controller design example. Copyright (c) 2006 John Wiley & Sons, Ltd.

Optimal PWM problem

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Optimal pulse width modulation (PWM) problem, or as sometimes called selected harmonic elimination (SHE) problem, is an established method of generating pulse width modulation waveforms with low baseband distortion. Key issue is to determine the switching times (angles) so as to produce the signal portion (baseband) and not generate specific higher order harmonics. A spectral gap (guard band or zero band) separates the signal portion which has to be identical to the required output signal, from a uncontrolled frequency portion. The required output signal can be recovered by means of a analog low-pass filter (LPF) with cutoff frequency in guard band.

Plane geometry and convexity of polynomial stability regions

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    The set of controllers stabilizing a linear system is generally non-convex in the parameter space. In the case of two-parameter controller design (e.g. PI control or static output feedback with one input and two outputs), we observe however that quite often for benchmark problem instances, the set of stabilizing controllers seems to be convex. In this note we use elementary techniques from real algebraic geometry (resultants and B´ezoutian matrices) to explain this phenomenon. As a byproduct, we derive a convex linear matrix inequality (LMI) formulation of two-parameter fixed-order controller design problem, when possible.

Single-Phase Optimal Odd PWM Problem

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Optimal pulse width modulation (PWM) problem is an established method of generating PWM waveforms with low baseband distortion. In this paper we focused on computation of optimal switching angles of a odd PWM waveform for generating general odd symmetric waveforms. We introduce an exact and fast algorithm with the complexity of only O(n log(2) n) arithmetic operations. This algorithm is based on transformation of appropriate trigonometric equations for each harmonies to a polynomial system of equations that is transferred to a special system of sum of powers. The solution of this system is carried out by modification of Newton's identity via Pade approximation and orthogonal polynomials theory and property of symmetric polynomials. Finally, the optimal switching sequence is obtained by computing the zeros of two orthogonal polynomials in one variable

Solving the optimal PWM problem for odd symmetry waveforms

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Optimal pulse width modulation (PWM) problem is an established method of generating PWM waveforms with low baseband distortion. In this paper we focused on computation of optimal switching angles of a PWM waveform for generating general odd symmetric waveforms with applications in control. We introduce an exact and fast algorithm with the complexity of only O(n^2) arithmetic operations. This algorithm is based on transformation of appropriate trigonometric equations for each harmonics to a polynomial system of equations that is transferred to a special system of power sums. The solution of this system is carried out by modification of Newton's identity via Pade approximation and orthogonal polynomials theory and property of symmetric polynomials. Finally, the optimal switching sequence is obtained by computing the zeros of two orthogonal polynomials in one variable.

Construction of New System of Polynomial Equations for 3-Phase Multilevel Voltage Converter

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    The main aim of this contribution is presentation a new construction method of a new set of polynomial equations leading to the optimal solution of switching angles which minimize the total harmonic distortion (THD) of a three-phase multilevel converter. The number of equations obtained by this method is lower compared to previous methods. It is possible to solve the problem more simply. This method is based on solution of the single-phase PWM problem which is fast and effcient and gives the conjunction between both problems.

New Special System of Polynomial Equations for 3-phase Multilevel Voltage Converter Derived from the PWM Problem for 1-Phase Inverters

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper contains a new construction method of a new set of polynomial equations leading to the optimal solution of switching angles which minimize the total harmonic distortion (THD) of a three-phase multilevel converter. The number of equations obtained by this method is lower compared to previous methods. It is possible to solve the problem more simply. This method is based on solution of the single-phase PWM problem which is fast and effcient and gives the conjunction between both problems.

Numerical Algorithms for Polynomial Plus/Minus Factorization

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Two new algorithms are presented in the paper for the plus/minus factorization of a scalar discrete-time polynomial. The first method is based on the discrete Fourier transform theory (DFT) and its relationship to the Z-transform. Involving DFT computational techniques and the famous fast Fourier transform routine brings high computational efficiency and reliability. The method is applied in the case study of H2-optimal inverse dynamic filter to an audio equipment. The second numerical procedure originates in a symmetric spectral factorization routine, namely the Bauer's method of the 1950s. As a by-product, a recursive LU factorization procedure for Toeplitz matrices is devised that is of more general impact and can be of use in other areas of applied mathematics as well. Performance of the method is demonstrated by an l1 optimal controller design example.

Polynomial Design Methods

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Polynomial methods are design techniques for complex multivariable systems, signals and processes encountered in Control, Communications and Computing ("C3" technologies) that are based on manipulations and equations with polynomials, polynomial matrices and similar objects. Systems are described by input-output relations in fractional form and processed using algebraic methodology and tools. The design procedure is thus reduced to algebraic operations with polynomial matrices and similar algebraic objects, typically to solving algebraic polynomial equations. This approach not only makes it possible to solve many existing control problems in an elegant and unifying manner but it also provides further insight into the structure of the control systems and reveals new relationships between various control problems.

A Linear Programming Approach for Ventilation Control in Tunnels

Anti-Synchronization Chaos Shift Keying Method Based on Generalized Lorenz System

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    In this paper, a modified version of the Chaos Shift Keying scheme for secure encryption and decription of data is proposed. The proposed scheme uses the effect of anti-synchronization, rather than synchronization. More specifically, the classical CSk method determines the correct value of binary signal through checking which unsynchronized system is getting synchronized. On the contrary, our novel method determines wrong value of binary signal through checking which already synchronized system is loosing synchronization. The advantage of the proposed method is two-fold. First, it requires very reasonable amount of data to encrypt and time to decrypt a single bit. Secondly, its security can be investigated and estimated as practically unbreakable.

Conference Report - 16th IFAC World Congress: The Largest Automatic Control Event

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    The 16th World Congress of the International Federation of Automatic Control (IFAC) was held in Prague 2005. Having over 3500 submitted papers and well over 2500 participants from 50 countries from all over the world, it was the largest and the most successful event ever in the field of automatic control.

Minimum Distance to The Range of a Banded Lower Triangular Toeplitz Operator in l1 and Application in L1-Optimal Control

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    The subject of the paper is the best approximation in l1 of a given infnite sequence by sequences in the range of a given banded lower-triangular Toeplitz operator. Necessary and sufficient conditions for the existence of a minimizing solution are established and a numerical algorithm for finding such a solution is designed and theoretically founded. It is also shown that an optimal error sequence is only fnitely nonzero. The relevancy of the problem in systems theory is outlined and numerical examples are presented.

Observer-based chaos synchronization in the generalized chaotic Lorenz systems and its application to secure encryption

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper studies possible application of the observerbased chaos synchronization to secure encryption. Unlike common approaches that use continuous time synchronized chaos for the so-called chaotic masking, the chaos shift keying (CSK) is being used here. CSK uses piece of synchronized chaotic signal to encode directly a given symbol. This paper uses properties of observer-based synchronization to achieve reasonable amount of information per symbol, moreover, specific properties of dependence of this observer-based synchronization on parameters make possible direct encryption of multi-alphabet symbols. Such a breakthrough is enabled by using anti-synchronization effect, rather than the synchronization one. Our method, further referred as the anti-synchronization chaos shift keying (ACSK), is implemented and thoroughly tested on the recently introduced generalized Lorenz system (GLS) family making advantage of its special parametrization.

Application for design of all stabilizing PI, PD and PID controllers

  • Autoři: Urban, P., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Proceedings of the 7th IASTED International Conference on Control and Applications. Calgary: Acta Press, 2005. p. 101-106. ISBN 0-88986-502-7.
  • Rok: 2005
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    In this work we show graphical user interface for finding of all stabilizing - PI, PD, P1D. It is useful tool for quick controller design. This work is application-oriented and therefore it hasn't much theoretical background.

Banded Matrix Solvers and Polynomial Diophantine Equations

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Numerical procedures and programs for linear Diophantine polynomial equations are proposed in this paper based on the banded matrix algorithms and solvers. Both the scalar and matrix cases are covered. The algorithms and programs developed are based on the observation that a set of constant linear equations resulting from the polynomial problem features a special structure. This structure, known as Sylvester, or block Sylvester in the matrix case, can in turn be accommodated in the banded matrix framework. Reliable numerical algorithms and programs for banded matrices are readily available at present, for instance in the well known LAPACK package. Software routines based on dedicated LAPACK band matrix solvers were programmed in the C language and linked to MATLAB, mainly for two reasons: to provide prospective users with an environment most of them are familiar with, and to gain the possibility of direct comparison with related functions of the Polynomial Toolbox for MATLAB.

Hinf Design with Loose Eigenstructure Assignment - A rank-one LMI approach

  • Autoři: Satoh, A., Sugimoto, K., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Transactions of the Society of Instrument and Control Engineers. 2005, 41(4), 291-299. ISSN 0453-4654.
  • Rok: 2005
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This paper proposes a design technique for state-feedback Hinf control with transient response shaping. A "loose" eigenstructure assignment is proposed, in which closed-loop eigenvalues (poles) and eigenvectors are assigned in specified eigenvalue regions and eigenvector cones respectively. This regional eigenstructure assignment problem is reduces to a rank-one LMI problem, and easily combined with Hinf control by means of enhanced LMI characterization.

Model Based Data Verification in a Highway Tunnel

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    A dynamic model of ventilation, traffic and exhaust inside a highway tunnel has been designed and implemented to simulate conditions inside a brand new highway tunnel Mrazovka in Prague, Czech Republic. A simulation has been performed to verify the data collected from the real tunnel. As a result, a statistical analysis of the simulated and real data is possible. Based upon the data analysis, a simulation program performance is judged as well. For the relevant data sets, an identification of possible measurement errors occurring at the sensors inside the tunnel is performed.

On Rational Bezout Equation

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    In this paper the rational Bezout equation is studied. A relationship between the rational Bezout equation and a specific interconnection of linear systems is established and then a numerical procedure for finding a particular solution of the concerned equation is derived. The devised algorithm is applicable to problems of small-to-medium size as demonstrated by numerical experiments.

Rational Bezout Equation and Interconnection of Linear Systems

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    The Bezout equation over the rings of proper stable rational functions and matrices is studied in this paper. First, a relationship between the rational Bezout equation and a combined serial/parallel interconnection of linear systems is established. The controllability and observability properties that this scheme has to full in order the Bezout equation to be satisfied yield a numerical procedure for finding a particular solution of the concerned equation. This routine is usable for problems of small-to-medium size as demonstrated by numerical experiments.

Real-Time H2 and H_inf Control of a Gyroscope Using a Polynomial Approach

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    In this paper H2 and H_inf control techniques ara applied to the real-time control of a gyroscope with two degrees of freedom. The controllers are designed based on a polynomial approach and using routines from the Polynomial Toolbox for MATLAB. Real-time results are presented, showing a good performance of the controllers.

Robust Pole Placement for Second-Order Systems: an LMI Approach

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Based on recently developed sufficient conditions for stability of polynomial matrices, an LMI technique is described to perform robust pole placement by proportional-derivative feedback on second-order linear systems affected by polytopic or norm-bounded uncertainty. As illustrated by several numerical examples, at the core of the approach is the choice of a nominal, or central quadratic polynomial matrix.

Soudobý návrh regulátoru pro teleskop VLT pomocí optimalizace Hinf

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Pro návrh regulátoru polohy obřího teleskopu VLT, který provozuje mezinárodní organizace ESO na hoře Cerro Paranal v chilské poušti Atacama, byly použity moderní výpočetní metody robustního a optimálního řízení. Tyto metody jsou založeny na minimalizaci normy Hinf přenosu systému, což je úloha lehce řešitelná běžnými sadami programů pro návrh řízení.

Unstable = Unsafe. What Is the Cost of Stabilization of an Unstable Plant

  • Autoři: prof. Ing. Michael Šebek, DrSc.,
  • Publikace: 15th International Conference on Process Control 05. Bratislava: Slovak University of Technology, 2005, ISBN 80-227-2235-9.
  • Rok: 2005

Web-based MATHEMATICA Platform for Systems and Control Education

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    MATHEMATICA benefits from its high-level user interface, graphical abilities, as well as numerical and symbolic computational power and dedicated packages for control systems analysis and design (Control Systems Professional and Advanced Numerical Methods). In addition, MATHEMATICA provides a webbased platform for publication of results and presenting usercallable routines (webMATHEMATICA). In the Czech Republic a project financed by the Ministry of Education and called PUMA (Power User Mathematic Array) has been started recently, focused on creation of webaccessible software tools to support education at technical universities. The authors have been involved in these efforts and would like to contribute by creating a web site based on webMATHEMATICA dedicated to numerical and symbolic computations for systems and controls. This paper is the first report on this topic. The work is in rapid progress now and the paper summarizes the authors' plans and first results.

Dynamická simulace chování vzduchotechniky tunelu Blanka

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Následující článek pojednává o tvorbě simulačního modelu soustavy vzduchotechnik a okolního prostředí připravovaného tunelu Špejchar - Pelc-Tyrolka. V rámci provedených prací byl navržen komplexní systém simulace vzduchotechniky orientovaný na návrh systému řízení technologie tunelu. Tento návrh také umožní specifikování struktury regulace a optimalizaci provozních parametrů chování vzduchotechniky. Součástí navrhovaného řešení je také systém dynamické simulace dopravy, který také umožňuje studium emisního zatížení okolního prostředí. Simulace byla provedena pomocí produktu Matlab 7.0. Použitá kombinace simulačních a softwarových řešení vytvořila dobrý precedens pro použití v této oblasti a splnila všechny požadavky.

Effective computations with 2-variable polynomial matrices in Mathematica

Effective computations with 2-variable polynomial matrices in Mathematica

Fixed-order robust controller design with the Polynomial Toolbox 3.0

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    With the help of numerical examples, this paper describes new fixed-order robust controller design functions implemented in version 3.0 of the Polynomial Toolbox for Matlab. The functions use convex optimization over linear matrix inequalities (LMIs) solved with the SeDuMi solver.

Function Electrically Stimulation of the Calf Muscle Using Matlab and Polynomial Toolbox

  • Autoři: Urban, P., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: MATLAB 2004 - Sborník příspěvků 12. ročníku konference. Praha: VŠCHT, 2004, pp. 587-591. ISBN 80-7080-550-1.
  • Rok: 2004
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This work is concerned with the design of robust control systems for the control of ankle movements generated by the electrical stimulation of the human calf muscle. We try to design robust controllers using functions of Polynomial Toolbox 3.0 and SeDuMi. This work is made in cooperation with Centre for Rehabilitation Engineering in University of Glasgow.

Graphical User Interface for Design of ALL Stabilizing PI, PD and PID Controllers

  • Autoři: Urban, P., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Proceedings of the 6th International Scientific-Technical Conference on Process COntrol (Říp 2004). Pardubice: Univerzita Pardubice, 2004, pp. 270. ISBN 80-7194-662-1.
  • Rok: 2004
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    This work deal with robust control in the field of robust control design of low order dynamic controllers like PI, PD and PID. We present graphical user interface for finding of all stabilizing controllers using the Hermite stability criterion. Presented version of the interface is the last and tool development is currently open. This report is application-oriented.

Graphical User Interface for Finding of All Stabilizing PI, PD and PID Controllers

  • Autoři: Urban, P., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Proceedings of 2nd IFAC Symposium on System, Structure and Control, SSSC 2004. Laxenburg: IFAC, 2004, pp. 258-262.
  • Rok: 2004
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    In this note we present graphical user interface for finding of all stabilizing controllers using the Hermite stability criterion. Using this interface can engineer simple design PI, PD and PID controllers. Presented version of the interface is the last and tool development is currently open. This report is application-oriented.

New algorithms for doubly comprime faktorization based on ordered real Schur form

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    A new algorithm for the doubly coprime factorization over the ring of stable proper rational matrices is presented in this report. The method is based on the statespace description of the involved rational functions and relies on previously published algorithms for pole assignment and for the left-to-right matrix fraction conversion by Varga [3], [2]. Numerical properties are demonstrated by means of examples and numerical experiments.

Numerical properties of a polynomial algorithm for solving scalar rational Bezout identity

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Numerical properties of a computational algorithm for the scalar Bezout identity in the ring of proper stable rational functions is studied in this paper. The method has been implemented in the MATLAB 6.5 computational environment using the pre-release version 3.0 of the Polynomnial Toolbox and exposed to extensive numerical testing. The results are summarized and some useful guidelines for using this well known algorithm are given.

Overcoming non-convexity in polynomial robust control design

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    When developing efficient and reliable computer-aided control system design (CACSD) tools for low-order robust control systems analysis and synthesis, the main issue faced by theoreticians and practitioners is the non-convexity of the stability domain in the space of polynomial coefficients, or equivalently, in the space of design parameters. In this paper, we survey some of the recently developed techniques to overcome this non-convexity, underlining their respective pros and cons. We also enumerate some related open research problems which, in our opinion, deserve particular attention.

Using LAPACK Solvers for Structured Matrices within Matlab

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Linear polynomial equations, also called Diophantine in the systems and control literature, are often needed to design a dynamic feedback controller or compensator. Solving these equations numerically leads to special Toeplitz type sets of linear equations. To solve them, one can naturally call the general purpose solvers build in the standard MATLAB distribution. Another, and potentially more effective way, is to employ dedicated routines of the well known LAPACK library that exploit the structure of the problem to save computational time and memory requirements. This paper describes the experience of the authors with this approach.

Algebraic Approach to I1-Optimal Control: SISO case

Controller Design Using Polynomial Matrix Description

Ellipsoidal Approximation of the Stability Domain of a Polynomial

FFT Based Algorithm for Polynomial Plus-minus Factorization

Graphical User Interface for Design Stabilizing Controllers

MathML for Data Exchange

MATHML for Data Exchange

MATLAB Function for Polynomial Plus/Minus Factorization Based on Band Structured Matrix Decomposition

MATLAB Implementation of an FFT Based Algorithm for Polynomial Plus/Minus Factorization

New Algorithm for Plus-Minus Factorization

New Algorithm for Polynomial Plus-Minus Factorization Based on Band Structured Matrix Decomposition

New Package for effective Polynomial Computation in Mathematica

New Package for Effective Polynomial Computation in Mathematica

Polynomial and matrix Fraction Dessription

Polynomial Approach to the Design of Wiener Filters - Algorithms, Software

  • Autoři: Fajt, J., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Proceedings of Process Control '03. Bratislava: Slovak University of Technology, 2003, pp. 66-1-66-5. ISBN 80-227-1902-1.
  • Rok: 2003

Polynomial Matrix Fraction as Models Linear Systems: Theory and Software Tools

Polynomial Methods and LMI Optimization: New Robust Control Functions for the Polynomial Toolbox 3.0

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Polynomial Methods and LMI Optimization: New Robust Control Functions for the Polynomial Toolbox 3.0

Positive Polynomials and Robust Stabilization with Fixed-Order Controllers

Robust Control Design for Parametric Uncertainties via Polynomial Toolbox for Matlab

Robust Control of a Laboratory Servomechanism

  • Autoři: Urban, P., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Principia Cybernetica 03. Liberec: Technická univerzita, 2003, pp. 153-158. ISBN 80-7083-733-0.
  • Rok: 2003

Robust Pole Placement for Second-Order Systems: An LMI Approach

Symbolic Solution of Spectral Factorization for Robust Control

  • Autoři: Klimentová, A., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Proceedings of Process Control '03. Bratislava: Slovak University of Technology, 2003, pp. 84-1-84-3. ISBN 80-227-1902-1.
  • Rok: 2003

Visualizing Pseudospectra for Polynomial Eigenvalue Problems

Algorithm for Computing l1 Norm of a Polynomial Matrix Fraction

Algorithm for Computing the Induced Gain of LTI System

An Algorithm for Statistic Output Feedback Simultaneous Stabilization of Scalar Plants

  • Autoři: Henrion, D., prof. Ing. Michael Šebek, DrSc., Kučera, V.
  • Publikace: Preprints of the 15th Triennial World Congress of the International Federation of Automatic Control. Oxford: Elsevier, 2002. pp. 542-546.
  • Rok: 2002
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    An Algorithm for Statistic Output Feedback Simultaneous Stabilization of Scalar Plants

Applying the Polynomial Toolbox for Matlab in Mobile Communication Problems

Complex Polynomial Matrices in Signals and Control

Complez Polynomials in Communications: Motivation Algorithms, Software

Discrete-Time Symmetric Polynomial Equations with Complex coefficients

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Discrete-time symmetric polynomial equations with complex coefficients are studied in the scalar and matrix case. New theoretical results axe derived and several algorithms are proposed and evaluated. Polynomial reduction algorithms are first described to study theoretical properties of the equations. Sylvester matrix algorithms are then developed to solve numerically the equations. The algorithms are implemented in the Polynomial Toolbox for MATLAB.

Effective Polynomial Computations in Mathematica

Evaluation of Algorithms for Computing the Covariance Function of a Multivariable ARMA Process

  • Autoři: Söderström, T., prof. Ing. Michael Šebek, DrSc., Ježek, J., Kučera, V., Henrion, D.
  • Publikace: European Journal of Control. 2002, 8(4), 23-26. ISSN 0947-3580.
  • Rok: 2002

Implementation of Polynomial Algebra Via Spectra

MathML in Polynomial Toolbox for Matlab

MathML in Polynomial Toolbox for Matlab

Návrh l1 optimalního regulátoru

New Results on FFT-based Methods for Polynomial Matrices

On Computing the l1 Norm of a Polynomial matrix Fraction

Polynomial Spectral Factorization with Complex Coeficients

Rank-one LMI Approach to Robust Stbility of Polynomial Matrices

Řešení symbolických polynomiálních rovnic

Robust Control of a Laboratory Servomechanism

The Use of Polynomial Toolbox for Matlab for Filter Design

An Evaluation of Algorithms for Computing the Covariance Function of a Multivariable ARMA Process

  • Autoři: Söderström, T., prof. Ing. Michael Šebek, DrSc., Ježek, J., Kučera, V.
  • Publikace: Proceedings of the European Control Conference, ECC'01. ???: APCA - Associacao Portuguesa de Controlo Automático, 2001. pp. 2-5. ISBN 972-752-047-2.
  • Rok: 2001

An LMI Condition for Robust Stability of Polynomial Matrix Polytopes

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    A new condition for robust stability of polynomial matrix polytopes is presented which is based on LMI

D-stability of polynomial matrices

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Necessary and sufficient conditions are formulated for the zeros of an arbitrary polynomial matrix to belong to a given region D of the complex plane. The conditions stem from a general optimization methodology mixing quadratic and semidefinite programming, LFRs and rank-one LMIs. They are expressed as an LMI feasibility problem that can be tackled with widespread powerful interior-point methods. Most importantly, the D-stability conditions can be combined with other LMI conditions arising in robust stability analysis.

Ellipsoidal Approximation of the Stability Domain of a Polynomial

  • Autoři: Henrion, D., Peaucelle, D., Arcelier, D., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Proceedings of the European Control Conference, ECC'01. ???: APCA - Associacao Portuguesa de Controlo Automático, 2001. pp. 98-103. ISBN 972-752-047-2.
  • Rok: 2001

Fast Fourier Transform and Linear Polynomial Matrix Equations

Linear Polynomial Matrix Equations and FFT

LMIs for Robust Stabilization of Systems with Ellipsoidal Uncertainty

  • Autoři: Henrion, D., prof. Ing. Michael Šebek, DrSc., Kučera, V.
  • Publikace: 13th International Conference of Process Control 01. Slovenská technická univerzita v Bratislave, 2001, ISBN 80-227-1542-5.
  • Rok: 2001

New Algorithm for Spectral Factorization and Its Practical Application

On Computing the H-infinity Norm of a Polynomial Matrix Fraction

On Robust Stability of Complex Polynomials

Polynomial Matrices and Recursive QR Factorization

  • Autoři: Sugimoto, K., prof. Ing. Michael Šebek, DrSc., Henrion, D.
  • Publikace: Proceedings of the European Control Conference, ECC'01. ???: APCA - Associacao Portuguesa de Controlo Automático, 2001. pp. 69-72. ISBN 972-752-047-2.
  • Rok: 2001

Polynomial Toolbox for Matlab and Complex Polynomials in Communications

Polynomial Toolbox in Control Education

Rank-One LMI Approach to Robust Stability of Polynomial Matrices

Rank-one LMI Approach to Stability of 2-D Polynomial Matrices

Robust Control Analysis and Design with Polynomial

Some Algorithms Used in the Polynomial Toolbox for Matlab

Stability of Sampled-data Systems with Uncertain Delays

An algorithm for polynomial matrix factor extraction

An LMI Condition for Robust Stability of Polynomial Matrix Polytopes

  • Autoři: Henrion, D., Arcelier, D., Paucelle, D., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Preprints of 3rd IFAC Symposium on Robust Control Design (ROCOND 2000). Oxford: Elsevier Science, 2000. p. 13-18. ISBN 0-08-043249-2.
  • Rok: 2000

D-Stability of Polynomial Matrices

  • Autoři: Henrion, D., Bachelier, O., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: UKACC International Conference on Control 2000. Cambridge: Cambridge University Press, 2000, pp. 1-5.
  • Rok: 2000

Extraction of Infinite Zeros of Polynomial Matrices

  • Autoři: Henrion, D., León, R., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Proceedings of the 39th IEEE Conference on Decision and Control. Sydney: IEEE, 2000. pp. 4221-4227.
  • Rok: 2000

Fast Fourier Transform and Robustness Analysis with Respect to Parametric uncertainties

Improved Polynomial Matrix Determinant Computation

  • Autoři: prof. Ing. Michael Šebek, DrSc., Henrion, D.
  • Publikace: Proceedings of 8th IEEE Mediterranean Conference on Control & Automation. University of Patras, 2000. pp. 19-21.
  • Rok: 2000

LMIs and Polynomial Methods in Control: Illustrative Examples

  • Autoři: Henrion, D., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Preprints of the IFAC/IEEE Symposium on Advances in Control Education, ACE'2000. Sydney: IEEE, 2000, pp. 1056-1062.
  • Rok: 2000

Numerical Algorithms for Polynomial Matrices

Polynomial Design Methods and a Signal Processing Application

Polynomial Toolbox 2.5 and Systems with Parametric Uncertainties

Polynomial Toolbox and Control Education

Robust Control with Polynomial Toolbox 2: Families with Structured Uncertainties

  • Autoři: prof. Ing. Michael Šebek, DrSc., Pejchová, S., Henrion, D.
  • Publikace: Proceedings - the 4-th International Scientific-Technical Conference Process Control 2000. Pardubice: Univerzita Pardubice, 2000, pp. 109. ISBN 80-7194-271-5.
  • Rok: 2000

Robust Stability Analysis via Polynomial Toolbox 2.5: Complicated Parametric Uncertainties

  • Autoři: prof. Ing. Michael Šebek, DrSc., Čelikovský, S., Ruiz, J., Henrion, D.
  • Publikace: Proceedings of the IASTED International Conference, Control and Applications (CA2000). Anaheim: Acta Press, 2000, pp. 149-153. ISBN 0-88986-288-5.
  • Rok: 2000

Spectral Factorization by Means of Discrete Fourier Transform

Stabilization of Affine Polynomial Families: an LMI Approach

An Algorithm for Polynomial Matrix Factor Extraction

  • Autoři: Henrion, D., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: 38th IEEE Conference on Decision and Control - Conference Proceedings. Piscataway: IEEE, 1999, pp. 1875-1880. ISBN 0-7803-5253-X.
  • Rok: 1999

Control Design via Polynomial Toolbox for Matlab Version 2.0

  • Autoři: prof. Ing. Michael Šebek, DrSc., Kwakernaak, H., Henrion, D., Strijbos, R.
  • Publikace: Conference Proceedings of European Control Conference ECC99 (on CD). Aachen: Rubicon - Agentur für digitale Medien, 1999, pp. 1547-1551.
  • Rok: 1999

Control of Systems with Parametric Uncertainties via Polynomial Toolbox 2.0

  • Autoři: prof. Ing. Michael Šebek, DrSc., Pejchová, S.
  • Publikace: EUROCAST '99. Vienna: TU Wien, Institute for Handling Device and Robotics (IHRT), 1999, pp. 201-204.
  • Rok: 1999

Efficient Algorithms for Discrete-Time Symmetric Polynomial Equations with Complex Coefficients

  • Autoři: Ježek, J., Henrion, D., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: 14 th World Congress of IFAC. London: Elsevier Science, 1999, pp. 159-164. ISBN 0-08-042755-3.
  • Rok: 1999

Improved Polynomial Matrix Determinant Computation

  • Autoři: Henrion, D., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: IEEE Transactions on Circuits and Systems. 1999, 46(10), 1307-1308. ISSN 1057-7122.
  • Rok: 1999
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Improved Polynomial Matrix Determinant Computation based on interpolation and FFT

Links Between Robusst and Quadratic Stability of Uncertain Discrete-Time Polynomials

  • Autoři: Henrion, D., prof. Ing. Michael Šebek, DrSc., Kučera, V.
  • Publikace: 7th IEEE Mediterranean Conference on Control and Automation. Tirat Carmel: OriGraph, 1999, pp. 2078-2086.
  • Rok: 1999

New Algorithm for Polynomial Matrix determinant Based on FFT

Numerical and Symbolic Computation of Polynomial Matrix Determinant

Numerical Operations Among Rational Matrices: Standard Techniques and Interpolation

Polynomial Toolbox 2.0 and Simulink

Polynomial Toolbox 2.0 Robust Control of Systems with Parametric Uncertainties

  • Autoři: prof. Ing. Michael Šebek, DrSc.,
  • Publikace: MATLAB '99. Praha: VŠCHT - Ústav fyziky a měřicí techniky, 1999, pp. 189-193. ISBN 80-7080-354-1.
  • Rok: 1999

Polynomial Toolbox and State Feedback Control

  • Autoři: Kučera, V., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: IEEE Internation Symposium on Computer Aided Control System Design. New York: IEEE Press, 1999, pp. 380-385. ISBN 0-7803-5449-4.
  • Rok: 1999

Rank-one LMI Approach to Simultaneous Stabilization of Linear Systems

  • Autoři: Henrion, D., Tarbouriech, S., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Conference Proceedings of European Control Conference ECC99 (on CD). Aachen: Rubicon - Agentur für digitale Medien, 1999, pp. 1-14.
  • Rok: 1999

Rank-one LMI Approach to Simultaneous Stabilization of Linear Systems

Reliable Numerical Methods for Polynomial Matrix Triangularization

Reliable numerical methods for polynomial matrix triangularization

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Numerical procedures are proposed for triangularizing polynomial matrices over the field of polynomial fractions and over the ring of polynomials. They are based on two standard polynomial techniques: Sylvester matrices and interpolation, In contrast to other triangularization methods, the algorithms described in this paper only rely on well-worked numerically reliable tools. They can also be used for greatest common divisor extraction, polynomial rank evaluation, or polynomial null-space computation.

Robust Control with Parametric Uncertainties Using Polynomial Toolbox for Matlab

  • Autoři: prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Proceedings from the Conference on Wiener's Cybernetics. Gran Canaria: Universita de las Palmas, 1999, pp. 189-192.
  • Rok: 1999

State Regulation and Estimation Via Polynomial Toolbox

  • Autoři: Kučera, V., prof. Ing. Michael Šebek, DrSc., Henrion, D.
  • Publikace: Proceedings of the 1st Europoly Workshop - Polynomial Systems Theory & Applications. Praha: Europoly-the European Network of Excellence no. CP97-7010, 1999, pp. 7-17.
  • Rok: 1999

Algebraic approach to robust controller design: A geometric interpretation

Efficient numerical method for the discrete-time symmetric matrix polynomial equation

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    New efficient numerical method for solution of the discrete-time symmetric matrix polynomial equation

Numerical methods for polynomial matrix rank evaluation

Recent Progress in Polynomial Methods and Polynomial Toolbox for Matlab Version 2.0

  • Autoři: prof. Ing. Michael Šebek, DrSc., Kwakernaak, H., Henrion, D., Pejchová, S.
  • Publikace: Proceedings of the 37th IEEE Conference on Decision&Control. Piscataway: IEEE, 1998, pp. 3661-3668. ISBN 0-7803-4394-8.
  • Rok: 1998
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    Recent Progress in Polynomial Methods and Polynomial Toolbox for Matlab Version 2.0

Symmetric matrix polynomial equation: Interpolation results

Two-sided Polynomial Equations in 2-D for Control Problems in Space-time Systems

Hurwitz matrix for polynomial matrices

  • Autoři: Kraus, J.F., Mansour, M., prof. Ing. Michael Šebek, DrSc.,
  • Publikace: INTERNATIONAL SERIES OF NUMERICAL MATHEMATICS. Heidelberg: Birkhäuser Verlag AG, 1996. p. 67-74. ISBN 0-8176-5474-7.
  • Rok: 1996
  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    The aim of this paper is to get a generalized Hurwitz matrix for polynomial matrices. In order to achieve that, we first obtain a relation between the Hurwiz matrix for a polynomial and the Lyapunov equation. Here Rie show how the Hurwitz matrix appears in the solution of the Lyapunov equation using the companion matrix realization and the Kronecker formulation of Lyapunov equation. Using this result we show how the generalized Hurwitz matrix for polynomial matrices can be constructed.

Polynomial control toolbox

  • Autoři: prof. Ing. Michael Šebek, DrSc., Strijbos, R.C.
  • Publikace: Proceedings of the 4th IEEE Mediterranean Symposium on New Directions in Control and Automation. 1996, pp. 488-491.
  • Rok: 1996

POLYNOMIAL OPERATIONS - NUMERICAL PERFORMANCE IN MATRIX DIOPHANTINE EQUATION

  • Pracoviště: Katedra řídicí techniky
  • Anotace:
    In the absence of any theoretical work on polynomial operations, the paper suggests possible evaluation of particular numerical algorithms to solve linear equation in polynomial matrices and draws some: preliminary conclusions with respect to the use of polynomial operations.

H2 Control Problems

  • Autoři: prof. Ing. Michael Šebek, DrSc., Hunt, K.J., Kučera, V.
  • Publikace: Polynomical Methods in optimal control and filtering. London: Peter Peregrinus LTD., 1993. p. 29-56. ISBN 0-86341-295-5.
  • Rok: 1993

J-Spectral Factorisation

  • Autoři: prof. Ing. Michael Šebek, DrSc.,
  • Publikace: Polynomical Methods in optimal control and filtering. London: Peter Peregrinus LTD., 1993. p. 278-305. ISBN 0-86341-295-5.
  • Rok: 1993

Za stránku zodpovídá: Ing. Mgr. Radovan Suk