Benoît Legat (Ph.D. student at UCL): Extracting unstable trajectories of switched systems from measures

Everyone is welcome at the seminar with a guest speaker - Benoît Legat, who is a new PhD student of Raphaël Jungers at UCL (http://perso.uclouvain.be/raphael.jungers/content/people). Benoît's Phd topic is "Algebraic optimization and Cyber-Physical control" which is based on using polynomial sums of squares for hybrid
systems control. The motivation behind his visit is to learn about moment techniques (the other side of the coin) from Didier Henrion.

The seminar starts at 3pm in K14 seminar room and it will take 60 minutes including a discussion.

Abstract:  In recent years, the study of the stability of hybrid systems has been the subject of extensive research. Even for switched linear systems, arguably the simplest class of hybrid systems, determining stability is undecidable and approximating the maximal asymptotic growth rate of the norm of a point in the state space is NP-hard. Despite these negative results, the vast range of applications has motivated a wealth of algorithms to approximate this quantity. However, most algorithms aim at producing certificates for the stability of a given switched linear system (e.g. Lyapunov functions) but not much is known on how to exhibit unstable trajectories in case the system is unstable. In this talk, we present a convex optimization problem for certifying the unstability of a switched system using measures as decision variables and we show how to extract unstable trajectories from feasible solutions of this optimization problem. We then show how to use Lasserre moment relaxation to implement this using Semidefinite Programming and show how to extract unstable trajectories from the obtained moments.