March 2021

01st of march 2021 - 14h, online seminar

Speaker : Marianne Souaiby (PhD Student supervised by Aneel Tanwani and Didier Henrion)
Title : Stability analysis and ensemble approximations of constrained dynamical systems
Abstract : For a class of constrained dynamical systems, where the evolution of state trajectories is described by nonsmooth differential inclusions, we consider numerical approximation methods for two sets of problems. First, we study stability of such systems using Lyapunov function based methods. By deriving a converse theorem, we specify the class of functions and provide algorithms for computation based on discretization in state space, and sum-of-squares hierarchies. Secondly, we study the evolution of such systems when the initial condition is described by a probability measure over the constraint set. We provide motivation behind our approach and some numerical tools based on polynomial functions to approximate the moments and support of the trajectories. 

Speaker : Mathias Serieye (PhD student supervised by Carolina Albea and Alexandre Seuret)
Title : Stabilization to limit cycles of switching discrete-time affine systems using control Lyapunov functions
Abstract : We study the stabilization of discrete-time switched affine systems using a control Lyapunov approach and a min-switching state-feedback control law. After presenting some preliminaries on cycles and limit cycles, a constructive stabilization theorem is provided and guarantees that the solutions to the closed-loop system converge to a limit cycle. These conditions are expressed in terms of simple linear matrix inequalities, whose underlying necessary conditions relax the usual one in this literature. This method is extended to the case of uncertain systems, for which the notion of limit cycle needs to be adapted. The theoretical results are evaluated on academic examples and demonstrate the potential of the method.