Robust distributed control of quasilinear reaction–diffusion equations via infinite-dimensional sliding modes

Abstract

This paper investigates the problem of robust tracking control for quasilinear reaction–diffusion partial differential equations subject to external unknown perturbations. The considered class of equations is quite general, and includes classical equations such as the heat equation or the Fisher–KPP equation as special cases. Global practical stabilization of the tracking error system is established under mild conditions on the disturbance term using a regularized infinite-dimensional sliding-mode controller. Extensive simulations support and validate the theoretical results.