prof. Ing. Michael Šebek, DrSc.

Tasks and methodology: • adopt and tailor the latest results on optimal and robust control theory and come up with novel effective feedback control solutions for distributed active damping of flexible structures. • Adopt and tailor the latest results on optimal and robust control theory like non-convex non-smooth optimization approach for direct fixed order designs • Study the applications of functionals and measure theory to nonlinear optimal and robust control) • Come up with novel effective feedback control solutions for distributed active damping of flexible structures. • Validate developed concepts by means of high-fidelity simulations and the case studies. http://dce.fel.cvut.cz/katedra/prof-ing-michael-sebek-drsc http://dce.fel.cvut.cz/katedra/kristian-hengster-movric-phd

Cooperation phenomena in distributed systems are receiving increasing attention from diverse disciplines such as physics, biology, computer science and control engineering. Since the early seminal works e.g. [1], and subsequent foundational papers [2],[3], distributed control of multi-agent systems is a well established discipline, with applications in formation control, multi-point surveillance, sensor fusion, power systems, to name just a few. A crucial class of distributed control problems that emerged over time is consensus and synchronization. The research goals for this topic are investigations into necessary and sufficient conditions on systems and their interactions guaranteeing synchronization or consensus on general functions of system's states. Interaction with environment can be taken into account. Issues of cooperative stability, optimality and robustness are of prime interest. The expected research outcomes are development and application of control theoretic and differential geometric (topological) techniques to distributed control of multi-agent systems.References: [1]Tsitsiklis J. Problems in Decentralized Decision Making and Computation, Ph.D. dissertation, Dept. Elect. Eng. and Comput. Sci., MIT, Cambridge, MA, 1984. [2]Jadbabaie A, Lin J., Morse A. Coordination of groups of mobile autonomous agents using nearest neighbour rules. IEEE Transactions on Automatic Control 2003; 48 (6): 988–1001. DOI: 10.1109/TAC.2003.812781 [3]Fax J, Murray RM. Information Flow and Cooperative Control of Vehicle Formations. IEEE Transactions on Automatic Control 2004; 49 (9): 1465-1476. DOI: 10.1109/TAC.2004.834433 [4]Wieland, P., Sepulchre, R., llgower, F. An internal model principle is necessary and sufficient for linear output synchronization, Automatica 47 (2011), pp. 1068-1074. [5]Chopra, N., Spong, M. Pasivity-based Control of Multi-agent Systems, [6]Qu, Zhihua, Cooperative Control of Dynamical Systems, Springer, 2008. http://dce.fel.cvut.cz/katedra/prof

This doctoral research project will focus on several advanced issues in modeling, analysis, estimation and control for micromanipulation for bioanalytical instrumentation. Practical electrokinetic applications will be (re)considered from the perspective of advanced control theory that rely on physical phenomena such as such as dielectrophoresis, electroosmosis, magnetophoresis and alike. In these applications the manipulation is realized through spatially continuous force fields which are derived from physical fields of diverse origin such as electric and magnetic through an array of actuators (arrays of electrodes or coils). Hence, both the spatially continuous and spatially discrete dynamics appears in the model (fields and arrays). Both theoretical analysis and practical experimentation are expected, with an emphasis on communication and collaboration with other engineering and scientific disciplines such as microsystems, biochemistry and even medicine. As a modeling framework, Green's functions will be used which will allow transfer-function-like approaches to analysis and control design. As a computational framework, the state-of-the-art techniques of numerical optimization will be investigated and tailored to the structure of the problems in micromanipulation through arrays of actuators with a special focus on real-time implementations of the algorithms. Literature [1] J. Zemánek, T. Michálek, and Z. Hurák, “Feedback control for noise-aided parallel micromanipulation of several particles using dielectrophoresis,” ELECTROPHORESIS, vol. 36, no. 13, pp. 1451–1458, July 2015.

Today’s manufacturing systems require flexibility with respect to the changes of the production needed to fulfill the market and/or customer demands. Such changes may occur quite often and thus a model-based design of the controllers is necessary. The controllers are typically distributed among the machines that contribute to the production of the desired product. The current trend is to make the machine as autonomous as possible and negotiation-based control schemes are considered for the production system to achieve optimum performance. The optimality criteria may differ and may be represented by e.g. production throughput, time needed to change the machine setup, energy consumption, dependability etc. Such an agent-based approach, whereas the machines are the agents, has been getting a research objective again because the complexity of the systems has been increasing and a centralized optimization approach cannot cover all aspects of the systems. This thesis will focus on combining formal methods of synthesis of discrete event systems from the point of view of the supervisory control (see [1]), which in most cases are not fully observable (see [2]). The current approaches to deal with the distributed nature of the control systems will be studied (see e.g. [3], [4]) also with respect to unreliable resources (see [5]). The primary objective of the research will be to come up with enhancements that combine the exact analytical and synthetical methods with agent-based heuristics. The newly developed methods will allow giving the performance bounds of the resulting system under the assumption of the design flexibility and autonomy of the subsystems. An important aspect of the thesis is the requirement on applicability of the results especially with respect to the existing industrial controllers and engineering systems. Literatura: [1] Komenda J., Masopust, T. Computation of controllable and coobservable sublanguages in decentralized supervisory control via communication. Discrete Event Dynamic Systems: Theory and Applications 27 (4), 2017, 585-608. [2] Komenda, J., Lahaye, S., Boimond, J.-L. (Max,+)-automata with partial observations. 14th IFAC Workshop on Discrete Event Systems WODES 2018, Pages 192-197. [3] Yufeng Chen. Optimal supervisory control of flexible manufacturing systems. Computer science. Conservatoire national des arts et metiers - CNAM, 2015. English. NNT: 2015CNAM0990. [4] Zgorzelski, M., Lunze, J. A new approach to tracking control of networked discrete-event systems. 14th IFAC Workshop on Discrete Event Systems WODES 2018. Pages 448-455 [5] W. Sulistyono and M. Lawley, "Robust supervisory control for manufacturing systems with unreliable resources," Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292), Washington, DC, USA, 2002, pp. 199-204 vol.1.

This doctoral research project will focus on several hot research topics in the area of distributed control of distributed systems with the mathematical optimization unifying all these research threads. The practical incentives for the proposed research come from the domain of distributed manipulation by shaping force fields of diverse physical origin (electrical, magnetic, fluidic, thermal, …) but also from the domain of networked control of multiagent systems. The optimization concepts that are intended to be explored are the (joint) field of values of matrices (also known as numerical range of matrices) and semidefinite programming, both with a focus on real-time implementation and distributed computation. On the modeling side, Green's function framework will be invoked to provide transfer-function-like (hence localized) models of spatially distributed systems. Analysis of limits of achievable control performance as well as scaling of the control schemes with the size of the array of actuators is to be performed. Experimental validation of the results through one of several laboratory setups that are available in the lab (such as dielectrophoresis and magnetophoresis) is anticipated. Literature: [1] P. J. Psarrakos and M. J. Tsatsomeros, “On the relation between the numerical range and the joint numerical range of matrix polynomials.,” ELA. The Electronic Journal of Linear Algebra [electronic only], vol. 6, pp. 20–30, 2000.

• The modelling fits two purposes: predicting the behavior of the structure, and a model for control. • Small validation experiments will be incorporated in the modelling phase. To use the physical model for control, it needs to be converted to a suitable form. • The methods rely on specific assumptions on the type of equations and/or the structure of the equations. For this purpose, the researcher will study control and combine the knowledge with model reduction methodologies for first principles models. • In addition the researcher will help to implement the controller, designed by the other researcher on a large evaluation model. Both will also work together on an experimental use case.. http://dce.fel.cvut.cz/katedra/prof-ing-michael-sebek-drsc http://dce.fel.cvut.cz/katedra/doc-ing-martin-hromcik-phd