Local output feedback stabilization of a Reaction-Diffusion equation with saturated actuation

Hugo Lhachemi (1, 2) , Christophe Prieur (3)

1 L2S - Laboratoire des signaux et systèmes
2 CentraleSupélec
3 GIPSA-INFINITY - GIPSA - Infinite Dimensional Dynamics

This paper is concerned with the output feedback stabilization of a reaction-diffusion equation by means of bounded control inputs in the presence of saturations. Using a finite-dimensional controller composed of an observer coupled with a finite-dimensional state-feedback, we derive a set of conditions ensuring the stability of the closed-loop plant while estimating the associated domain of attraction in the presence of saturations. This set of conditions is shown to be always feasible for an order of the observer selected large enough. The stability analysis relies on Lyapunov functionals along with a generalized sector condition classically used to study the stability of linear finite-dimensional plants in the presence of saturations.

Mots clés: Saturated control; domain of attraction; reactiondiffusion equation; output feedback

Domaines: Optimisation et contrôle [math.OC]; Automatique

Hugo Lhachemi, Christophe Prieur. Local output feedback stabilization of a Reaction-Diffusion equation with saturated actuation. IEEE Transactions on Automatic Control, 2023, 68 (1), pp.564 - 571. ⟨10.1109/TAC.2022.3144609⟩. ⟨hal-03540132⟩