Backstepping design of robust state feedback regulators for parabolic PIDEs with in-domain outputs

Abstract

Abstract This paper considers the robust output regulation problem for boundary controlled parabolic partial integro-differential equations (PIDEs) of Volterra type, where the output to be controlled is an in-domain distributed or pointwise output. By assuming a finite-dimensional model for the exogenous signals a constructive solution is presented by making use of the backstepping approach. For this, a new backstepping-based stabilization of parabolic PIDE-ODE cascades with an in-domain coupling is proposed. It is shown that the solvability of the output regulation problem can be checked by utilizing the nominal plant transfer behaviour. Robust output regulation is verified for model uncertainties, that do not lead to an unstable closed-loop system. The regulator design for a coupled parabolic/hyperbolic system illustrates the presented results.