Integral action feedback design for conservative abstract systems in the presence of input nonlinearities

Ling Ma (1, 2) , Vincent Andrieu (3, 4) , Daniele Astolfi (4, 1) , Mathieu Bajodek (1, 5) , Cheng-Zhong Xu (3) , Xuyang Lou (2)

1 LAGEPP - Laboratoire d'automatique, de génie des procédés et de génie pharmaceutique
2 School of IoT Engineering, Jiangnan University,
3 LAGEP - Laboratoire d'automatique et de génie des procédés
4 CNRS - Centre National de la Recherche Scientifique
5 CPE - École Supérieure de Chimie Physique Électronique de Lyon

In this article, we present a stabilization feedback law with integral action for conservative abstract linear systems subjected to actuator nonlinearity. Based on the designed control law, we first prove the well-posedness and global asymptotic stability of the origin of the closed-loop system by constructing a weak Lyapunov functional. Secondly, as an illustration, we apply the results to a wave equation coupled with an ordinary differential equation (ODE) at the boundary. Finally, we give the simulation results to illustrate the effectiveness of our method.

Mots clés: Stabilization; integral action; nonlinear semigroups; abstract control systems.

Domaines: Optimisation et contrôle [math.OC]

Ling Ma, Vincent Andrieu, Daniele Astolfi, Mathieu Bajodek, Cheng-Zhong Xu, et al.. Integral action feedback design for conservative abstract systems in the presence of input nonlinearities. 2023. ⟨hal-04577332⟩