A note on the wave equation controlled with a dynamic saturating boundary control

Mario Gauvrit (1) , Christophe Prieur (2) , Sophie Tarbouriech (3)

1 ENS Paris Saclay - Ecole Normale Supérieure Paris-Saclay
2 GIPSA-INFINITY - GIPSA - Infinite Dimensional Dynamics
3 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande

This paper studies the nonlinear systems obtained by considering a wave equation in closed loop with a nonlinear dynamical boundary controller. The controller is subject to a magnitude limitation and modeled by a linear ordinary differential equation with a saturation map in the input. The well-posedness of the obtained infinite-dimensional system is first studied and then two stability results are given. These two stability results apply for two cascade cases and give sufficient conditions for the asymptotic stability of the equilibrium. The well-posedness is proven by using nonlinear semigroups techniques, whereas the global asymptotic stability results are obtained by Lyapunov-based arguments in infinite-dimensional state space.

Mots clés: Infinite-dimensional systems; saturation; well-posedness; stability

Domaines: Automatique / Robotique

Mario Gauvrit, Christophe Prieur, Sophie Tarbouriech. A note on the wave equation controlled with a dynamic saturating boundary control. NOLCOS 2022 - 12th IFAC Symposium on Nonlinear Control Systems (NOLCOS'22), Jan 2023, Canberra, Australia. pp.108-113, ⟨10.1016/j.ifacol.2023.02.019⟩. ⟨hal-04159866⟩