Global Output Feedback Stabilization of Semilinear Reaction-Diffusion PDEs

TL;DR

This paper develops a finite-dimensional control strategy for globally stabilizing semilinear reaction-diffusion PDEs with sector-bounded nonlinearity, using boundary or distributed actuation and Dirichlet measurements.

Contribution

It introduces a new control design approach based on a linear plant approximation for global stabilization of reaction-diffusion PDEs with sector-bounded nonlinearity.

Findings

Feasibility of stabilization depends on controller order and sector size.

Derived sufficient conditions for exponential stabilization.

Applicable to boundary and distributed control configurations.

Abstract

This paper addresses the topic of global output feedback stabilization of semilinear reaction-diffusion PDEs. The semilinearity is assumed to be confined into a sector condition. We consider two different types of actuation configurations, namely: bounded control operator and right Robin boundary control. The measurement is selected as a left Dirichlet trace. The control strategy is finite dimensional and is designed based on a linear version of the plant. We derive a set of sufficient conditions ensuring the global exponential stabilization of the semilinear reaction-diffusion PDE. These conditions are shown to be feasible provided the order of the controller is large enough and the size of the sector condition in which the semilinearity is confined into is small enough.