Output regulation of infinite-dimensional nonlinear systems: a forwarding approach for contraction semigroups

TL;DR

This paper presents a forwarding control approach for robust output regulation of nonlinear infinite-dimensional systems governed by contraction semigroups, ensuring stability and output tracking under perturbations.

Contribution

It introduces a forwarding-based feedback law for nonlinear contraction semigroup systems, providing conditions for local and global stability in output regulation.

Findings

Sufficient conditions for local exponential stability with small perturbations.

Global asymptotic stability under additional assumptions.

Application examples demonstrating the approach's effectiveness.

Abstract

This paper deals with the problem of robust output regulation of systems governed by nonlinear contraction semigroups. After adding an integral action to the system, we design a feedback law based on the so-called forwarding approach. For small constant perturbations, we give sufficient conditions for the existence of a locally exponentially stable equilibrium at which the output coincides with the reference. Under additional assumptions, global asymptotic stability is achieved. All these conditions are investigated in the case of semilinear systems, and examples of application are given.