Output-Feedback Stabilization for a Class of Linear Parabolic Systems

TL;DR

This paper develops output-feedback stabilization methods for two-component linear parabolic systems using backstepping control and observer design, ensuring exponential stability with solutions to hyperbolic PDEs.

Contribution

It introduces a backstepping-based approach for boundary control and observation of coupled parabolic PDEs, including well-posedness and stability analysis.

Findings

Design of backstepping controllers and observers for parabolic systems

Proof of exponential stability of the closed-loop system

Solution of hyperbolic PDEs for kernel computation

Abstract

We consider output-feedback stabilization problems for a class of two-component linear parabolic systems with boundary actuation and measurement. The state-feedback control laws are obtained using backstepping method and require measurement of the state at each point in the domain. To this end, backstepping observers are designed for both anti-collocated and collocated sensors and actuators. Furthermore, we show the closed-loop systems consisting of the plant, the backstepping control laws, and the observer is exponentially stable. The backstepping method is used to obtain both control and observer kernels. The kernels are the solution of $4\times4$ systems of second-order hyperbolic linear PDEs whose well-posedness is shown.