Saturating Integral Control for Infinite-Dimensional Linear Systems

Abstract

We propose a saturating integrator based controller for infinite dimensional well-posed linear systems, which prevents the controller state from leaving a desired closed interval. This set usually represents actuator constraints or safety requirements. We use Lyapunov theory to prove closed-loop stability and tracking of a constant reference for a suitable set of feasible references. The performance of the proposed controller is showcased through an application: the boundary control of a string equation with localized viscous damping.