Existence and computation of Lyapunov functions for a class of state-constrained systems
Date : 26/04/2023 De 15h00 A 16h00
Lien / Link : https://minesparis-psl-eu.zoom.us/j/97000464677?pwd=R2tRWkZHQnoyc1ppSEdjY1hZRzY1QT09
ID de la réunion / Meeting ID : 97000464677
Mot de passe / Password : 057084
SPEAKER
Aneel Tanwani (LAAS, Toulouse)
https://homepages.laas.fr/atanwani/
TITLE
Existence and computation of Lyapunov functions for a class of state-constrained systems
ABSTRACT
In this talk, we will basically discuss tools for analyzing stability for a class of nonsmooth systems which are particularly used in modeling state trajectories with constraints. The system model consists of a differential equation coupled with a set-valued relation that introduces discontinuities in the vector field at the boundaries of the constraint set. In particular, the set-valued relation is described by the subdifferential of the indicator function of a closed convex cone, which results in a cone-complementarity system. The question of analyzing the stability of such systems is addressed by constructing cone-copositive Lyapunov functions, and we will provide motivation to do so. As a first analytical result, we establish the existence of such functions for the proposed system class with exponentially stable equilibrium. Under some more structure on the system data, we can restrict our search for such functions within the class of homogenous polynomials. We then discuss optimization-based algorithms to solve for the parameters of these Lyapunov functions.
Lien / Link : https://minesparis-psl-eu.zoom.us/j/97000464677?pwd=R2tRWkZHQnoyc1ppSEdjY1hZRzY1QT09
ID de la réunion / Meeting ID : 97000464677
Mot de passe / Password : 057084
SPEAKER
Aneel Tanwani (LAAS, Toulouse)
https://homepages.laas.fr/atanwani/
TITLE
Existence and computation of Lyapunov functions for a class of state-constrained systems
ABSTRACT
In this talk, we will basically discuss tools for analyzing stability for a class of nonsmooth systems which are particularly used in modeling state trajectories with constraints. The system model consists of a differential equation coupled with a set-valued relation that introduces discontinuities in the vector field at the boundaries of the constraint set. In particular, the set-valued relation is described by the subdifferential of the indicator function of a closed convex cone, which results in a cone-complementarity system. The question of analyzing the stability of such systems is addressed by constructing cone-copositive Lyapunov functions, and we will provide motivation to do so. As a first analytical result, we establish the existence of such functions for the proposed system class with exponentially stable equilibrium. Under some more structure on the system data, we can restrict our search for such functions within the class of homogenous polynomials. We then discuss optimization-based algorithms to solve for the parameters of these Lyapunov functions.