Utility of the Koopman operator in output regulation of disturbed nonlinear systems

TL;DR

This paper explores how the Koopman operator can be used to address output regulation in nonlinear systems affected by disturbances, proposing a linear controller approach validated through numerical experiments.

Contribution

It demonstrates the equivalence of nonlinear output regulation to bilinear regulation for systems with Koopman representations and introduces a linear feedback controller for the problem.

Findings

Koopman representation enables linearization of certain nonlinear regulation problems.

A linear dynamic output feedback controller can locally solve the nonlinear regulation problem.

Numerical results confirm the effectiveness of the proposed approach.

Abstract

This paper studies the problem of output regulation for a class of nonlinear systems experiencing matched input disturbances. It is assumed that the disturbance signal is generated by an external autonomous dynamical system. First, we show that for a class of nonlinear systems admitting a finite-dimensional Koopman representation, the problem is equivalent to a bilinear output regulation. We then prove that a linear dynamic output feedback controller, inspired by the linear output regulation framework, locally solves the original nonlinear problem. Numerical results validate our analysis.