Output regulation for coupled linear parabolic PIDEs

Abstract

This paper presents a backstepping-based solution of the output regulation problem for coupled parabolic partial integro-differential equations (PIDEs) with spatially-varying coefficients and distinct diffusion coefficients. The considered setup assumes in-domain as well as boundary disturbances, while the output to be controlled can be defined distributed in-domain, pointwise in-domain or at the boundaries and need not be measured. By assuming a finite-dimensional signal model, which may also be non-diagonalizable, a systematic solution of the output regulation problem is presented by making use of observer-based feedforward control. Existence conditions for the corresponding regulator are formulated in terms of the plant transfer behaviour. For the resulting closed-loop system, exponential stability with a prescribed decay rate is verified. The regulator design for two unstable coupled parabolic PIDEs demonstrates the results of the paper.