13:40–14:00 — L2S, bâtiment IBM
Title. Analysis and Control of Multi-timescale Modular Directed Heterogeneous Networks
Speaker. Anes Lazri (L2S)
Abstract. We study the collective behavior of heterogeneous nonlinear systems, interconnected over generic directed graphs (with non-symmetric Laplacian), in the scenario that, due to the nature of their interconnections, the agents self-organize in modules. These are subnetworks composed of agents that are densely connected with a strong coupling, while the modules themselves are sparsely interconnected. We establish that beyond certain coupling thresholds, inside each module, the systems synchronize rapidly with a weighted-average dynamical system that evolves more slowly than the individual systems. Then, the average dynamical systems corresponding to each and all the modules synchronize among themselves. Thus, provided that the average dynamics admit the origin as a globally asymptotically stable equilibrium and each system is semi-passive, we establish global asymptotic stability for the overall network. In addition, we explore stabilization techniques that consist in controlling the average dynamics to make the origin globally asymptotically stable.
Bio. Anes Lazri obtained his Engineering degree in control engineering from the National Polytechnic School of Algiers in 2020. He obtained a Master’s degree in Automation, signal, and image processing from Paris Saclay University in 2021. Today, he is preparing his doctoral thesis on analyzing and controlling nonlinear system networks at the same university. His research interests include multi-agent systems and nonlinear control.
14:00–15:00 — L2S, bâtiment IBM
Title. Switched systems with omega-regular switching sequences — Application to switched observer design
Speaker. Antoine Girard (L2S)
Abstract. In this talk, I will present recent results on discrete-time switched linear systems. We consider systems with constrained switching signals where the constraint is given by an omega-regular language. Omega-regular languages allow us to specify fairness properties (e.g. « all modes have to be activated an infinite number of times ») that cannot be captured by usual switching constraints given by dwell-times or graph constraints. By combining automata theoretic techniques and Lyapunov theory, we provide necessary and sufficient conditions for the stability of such switched systems. In the second part of the talk, I will present an application of our framework to observer design of switched systems that are unobservable for arbitrary switching. We establish a systematic and almost universal procedure to design observers for discrete-time switched linear systems. This is joint work with Georges Aazan, Luca Greco and Paolo Mason.
Bio. Antoine Girard is a Senior Researcher at CNRS and a member of the Laboratory of Signals and Systems. He received the Ph.D. degree from Grenoble Institute of Technology, in 2004. From 2004 to 2006, he held postdoctoral positions at University of Pennsylvania and Université Grenoble-Alpes. From 2006 to 2015, he was an Assistant/Associate Professor at the Université Grenoble-Alpes. His main research interests deal with analysis and control of hybrid systems with an emphasis on computational approaches, formal methods and applications to cyber-physical and autonomous systems. Antoine Girard is an IEEE Fellow. In 2015, he was appointed as a junior member of the Institut Universitaire de France (IUF). In 2016, he was awarded an ERC Consolidator Grant. He received the George S. Axelby Outstanding Paper Award from the IEEE Control Systems Society in 2009, the CNRS Bronze Medal in 2014, and the European Control Award in 2018.
