doc. Kristian Hengster-Movric, Ph.D.

This paper brings a novel scalable control design methodology for Large-Scale Systems. Such systems are considered as multi-agent systems with inherent interactions between neighboring agents. The presented design methodology uses single-agent dynamics and their interaction topology, rather than relying on the model of the entire system. The dimension of the design problem therefore remains the same with growing number of agents. This allows a feasible control design even for large systems. Moreover, the proposed design is based on simple Linear Matrix Inequalities, efficiently solvable using standard computational tools. Numerical results validate the proposed approach.

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.

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.

Differential graphical games have been introduced in the literature to solve state synchronization problem for linear homogeneous agents. When the agents are heterogeneous, the previous notion of graphical games cannot be used anymore and a new definition is required. In this paper, we define a novel concept of differential graphical games for linear heterogeneous agents subject to external unmodeled disturbances, which contain the previously introduced graphical game for homogeneous agents as a special case. Using our new formulation, we can solve both the output regulation and H-infinity output regulation problems. Our graphical game framework yields coupled Hamilton-Jacobi-Bellman equations, which are, in general, impossible to solve analytically. Therefore, we propose a new actor-critic algorithm to solve these coupled equations numerically in real time. Moreover, we find an explicit upper bound for the overall L2-gain of the output synchronization error with respect to disturbance. We demonstrate our developments by a simulation example.

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.

This paper aims to bridge the gap between control engineering and vibration engineering. We developed three distributed schemes over directed communication graph topology, specifically for vibration reduction of flexible structures. Under the distributed schemes, vibrations are attenuated through agents consisting of distributed observers and controllers. Compared to traditional methods, the developed approaches can reduce the communication overhead and the computational complexity when a large number of actuators and sensors are deployed. Moreover, two of the developed schemes enjoy the flexibility in reconfiguration of communication graph topology and integration of redundant agents. Furthermore, numerical simulations are presented to demonstrate the effectiveness of the developed schemes in vibration reduction of flexible structures.

This paper offers a novel approach at flutter suppression problem on morphing wing and relates to current research of morphing aircraft. The active flutter suppression task is formulated as a state synchronization in a network of identical Linear Time-Invariant (LTI) systems. These systems consist of wing segments which can be actuated separately. Finite Element Method (FEM) approach and unsteady aerodynamics represented by Theodorsen function are used for flexible morphing wing modeling. An example of distributed Linear-Quadratic Regulator (LQR) state synchronization is shown in this paper. Comparison in time-domain, frequency-domain, and flutter speeds has been done for the system with distributed LQR and the original system.

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.

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.

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.

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.

In this paper, we propose a novel approach to obtain a reliable and simple mathematical model of dielectrophoretic force for model-based feedback micromanipulation. Any such model is expected to sufficiently accurately relate the voltages (electric potentials) applied to the electrodes to the resulting forces exerted on microparticles at given locations in the workspace. This model also has to be computationally simple enough to be used in real time as required by model-based feedback control. Most existing models involve solving two- or three-dimensional mixed boundary value problems. As such, they are usually analytically intractable and have to be solved numerically instead. A numerical solution is, however, infeasible in real time, hence such models are not suitable for feedback control. We present a novel approximation of the boundary value data for which a closed-form analytical solution is feasible; we solve a mixed boundary value problem numerically off-line only once, and based on this solution, we approximate the mixed boundary conditions by Dirichlet boundary conditions. This way, we get an approximated boundary value problem allowing the application of the analytical framework of Green's functions. The thus obtained closed-form analytical solution is amenable to real-time use and closely matches the numerical solution of the original exact problem.

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.

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.

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.

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.

The use of versatile synchronizing region methodology for synchronization of identical multi-agent systems; state-of-the-art and perspectives.

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.

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.

Heavy computational burden is imposed on centralized controllers when dampening vibration for large-scale flexible structures. For homogeneous flexible structures, the structure of controllers shall be investigated to simplify the control loop design. In this work, firstly a linear-quadratic regulator (LQR) is designed for a normalized infinite-dimensional beam model under a clamped-clamped boundary condition, to demonstrate the decentralization property of the controller. A finite element model (FEM) based on Euler-Bernoulli beam theory is then considered, an LQR is designed with distributed actuators and isolated point-actuators respectively, providing all the states can be measured. Control simulations have shown a decentralization property in both cases, which motivates a decentralized controller inherited from the LQR design. Simulation results have shown that the performance of decentralized controller and the LQR is comparable.

This paper surveys some recent results in identical system state synchronization. Design methods are given for distributed synchronization control of continuous and discretetime multi-agent systems on directed communication graphs. The graph properties complicate the design of synchronization controllers due to an interplay between the eigenvalues of the graph Laplacian matrix and the required stabilizing gains. Methods given herein are based on computation of the local control gains using Riccati design. Conditions are given for synchronization relying on relation of the graph Laplacian eigenvalues to a region in the complex plane that depends on agent dynamics and Riccati solutions. Distributed observers for agents networked on a directed graph are also investigated. Cooperative observer design guaranteeing convergence of estimates of all agents to their actual states is proposed. It is shown that the discrete-time synchronizing region is inherently bounded, so that the conditions for observer convergence and state synchronization are stricter than results for their continuous-time counterparts. If outputs only are available for control the distributed static output-feedback (OPFB) control can be used. The synchronizing region for static OPFB control is exposed and found to be conical, different than the infinite righthalf plane synchronizing region for distributed state-feedback. Furthermore, the multi-agent system synchronization with control signal delays is presented. Agents are assumed to have the same control delay. Delay-dependent synchronizing region is defined and methods are given guaranteeing its estimates.