Control of Hybrid Systems

Workshop, Technical University of Cluj-Napoca
Date and time: 30 October 2015, 15:00-17:00 hours
Location: Room P23, Memorandumului 28, Cluj-Napoca

Hybrid systems combine continuous and discrete behaviors, and they are relevant in addressing many problems in engineering. Consequently, they are one of the focus points of current research in control and system theory, and many advances have recently been made. This workshop considers the problem of control in hybrid systems, and brings together four talks on different cutting-edge topics within this area, presented by leading and experienced researchers in the field. Each talk is 30 minutes long, out of which 5 minutes are reserved for questions.

Talk 1: A short introduction to event-triggered control

by Romain Postoyan, researcher, Centre de Recherche en Automatique de Nancy, Universite de Lorraine & CNRS, France
Time: 15:00-15:30.

Abstract: Control systems are nowadays often implemented on digital platforms, which have limited communication, computation and energy resources. Classical controller implementation with periodic sampling no longer seems to be the most appropriate option in this context. Indeed, while sampling periodically facilitates the analysis and the implementation, the induced resource usage is often too big and not in agreement with the system's needs. An alternative consists in transmitting data and in executing the controller only whenever a state-dependent criterion is verified, in which case we talk of event-triggered control. A triggering law is synthesized according to the control objective. Whenever the latter is satisfied the sensors data and the control input are updated: we close the feedback loop. The purpose of this talk is to present event-triggered control and to review some of the fundamental works of the domain from a hybrid dynamical system perspective. We will then mention the interest of adding extra variables to define the transmission criterion.

Biography: Romain Postoyan received the M.Sc. degree in Electrical and Control Engineering from ENSEEIHT (France) in 2005. He obtained the M.Sc. by Research in Control Theory & Application from Coventry University (United Kingdom) in 2006 and the Ph.D. in Control Theory from Universite Paris-Sud (France) in 2009. In 2010, he was a research assistant at the University of Melbourne (Australia). Since 2011, he is a CNRS researcher at the Centre de Recherche en Automatique de Nancy (France).

Talk 2: On switched singularly perturbed systems

by Jamal Daafouz, Professor, Centre de Recherche en Automatique de Nancy, Universite de Lorraine & CNRS, France
Time: 15:30-16:00.

Abstract: In this talk we will introduce the problem of stability analysis and control design of switched singularly perturbed system. The problem is motivated by an industrial application related to steering control of hot strip mills which has been studied in collaboration with ArcelorMittal. The main features with respect to classical two-time-scale systems will be highlighted. We present both stability analysis using Lyapunov functions and control design with H2 and H-infinity performances. We end this talk by pointing out some open problems in this area.

Biography: Jamal Daafouz received the Ph.D. degree in automatic control from the INSA Toulouse, in 1997. In 1998, he joined the Institut National Polytechnique de Lorraine (INPL) as an assistant professor and the Research Centre of Automatic Control (CRAN UMR 7039 CNRS). In 2005, he got the French Habilitation degree from INPL and he was engaged as a professor of automatic control at Universite de Lorraine in Nancy, France. From 2010 to 2015, he was an IUF (Institut Universitaire de France) junior member. He serves as an Associate Editor at the Conference Editorial Board of the IEEE Control Systems Society and for the journals: Automatica, IEEE Transactions on Automatic Control and European Journal of Control. His research interests include hybrid and switched systems, networked control systems, robust control and applications in secure communications, metallurgy and energy management.

Talk 3: Synchronization in networks of linear singularly perturbed systems

by Constantin Morarescu, Associate Professor, Centre de Recherche en Automatique de Nancy, Universite de Lorraine & CNRS, France
Time: 16:00-16:30.

Abstract: Many real systems are characterized by two features. The first one is that they are obtained by interconnecting a bunch of simpler subsystems that have to synchronize in order to reach a global goal. The second one is that each subsystem presents dynamics that evolves on different time-scales. Taking into account the two features leads to the problem of synchronization in networks of singularly perturbed systems. In this work we are providing a preliminary study that considers the problem where each subsystem is linear and the network topology is represented by a connected undirected graph that is fixed in time. We show that we can proceed to a time-scale separation of the overall network dynamics and design the controls that synchronize the slow dynamics and the fast ones. Applying the joint control actions to the network of singularly perturbed systems we obtain an approximation of the synchronization behavior imposed for each scale. The methodology requires a variable transformation to overcome the fact that we are dealing with non-standard singularly perturbed systems. One example illustrates the synchronization behavior of linear singularly perturbed systems.

Biography: Irinel-Constantin Morarescu is currently Associate Professor at Universite de Lorraine and researcher at the Research Centre of Automatic Control (CRAN UMR 7039 CNRS) in Nancy, France. He received the B.S. and the M.S. degrees in Mathematics from University of Bucharest, Romania, in 1997 and 1999, respectively. In 2006 he received the Ph.D. degree in Mathematics and Technology of Information and Systems from University of Bucharest and University of Technology of Compiegne, respectively. His works concern stability and control of time-delay systems, tracking control for nonsmooth mechanical systems, consensus and synchronization problems.

Talk 4: Model predictive control for discrete-event and hybrid systems using optimistic optimization

by Jia Xu, PhD candidate, Delft Center for Systems and Control, Delft University of Technology, the Netherlands
Time: 16:30-17:00.

Abstract: This presentation will focus on model predictive control (MPC) for two types of systems, max-plus linear discrete-event systems and continuous piecewise affine hybrid systems. A class of discrete-event systems that can be described by a model that is "linear" in the max-plus algebra is called max-plus linear systems. The MPC problem for max-plus linear systems usually leads to a nonsmooth nonconvex optimization problem. An alternative approach is to transform the given problem into a mixed integer linear programming problem; however, the computational complexity increases in the worst case exponentially in the prediction horizon. We focus on applying optimistic optimization to solve the resulting MPC optimization problem, where the complexity is exponential in the control horizon instead of the prediction horizon. Hence, optimistic optimization is more efficient when the control horizon is small and the prediction horizon is large. The MPC problem for continuous piecewise affine systems results in the optimization of continuous piecewise affine functions. We propose to use optimistic optimization to solve the given problem. Compared with the mixed integer linear programming method, the optimistic optimization approach is efficient for the optimization of continuous piecewise affine functions with a large number of polyhedral subregions.

Biography: Jia Xu received the BSc degree in Statistics in 2009, at Shandong University, Weihai, China. She was a graduate student from 2009 to 2012 in the Department of Mathematics and in the Department of Control Science and Engineering of Tongji University, Shanghai, China. She is currently a PhD candidate at the Delft Center for Systems and Control of Delft University of Technology in Delft, The Netherlands. Her current research interests include control of discrete-event and hybrid systems, and optimistic optimization.