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

TL;DR

This paper develops a finite-dimensional output feedback controller for stabilizing a reaction-diffusion PDE with saturated actuation, providing conditions for stability and domain of attraction estimation.

Contribution

It introduces a new stabilization method using an observer-based controller tailored for reaction-diffusion equations with input saturation.

Findings

Conditions for closed-loop stability are derived.

Feasibility of the conditions increases with observer order.

Lyapunov functionals are used for stability analysis.

Abstract

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.