Approximation Methods for Geometric Regulation

TL;DR

This paper reviews the development of approximate geometric regulation methods, highlighting the evolution from theoretical regulator equations to the practical regularized controller, with recent extensions to delay equations.

Contribution

It provides a comprehensive overview of the progression from theoretical to practical control strategies, including new formulations for delay systems.

Findings

Development of regularized dynamic regulator equations

Iterative scheme for accurate tracking and disturbance rejection

Extension of methods to delay equations

Abstract

In these notes we collect some results from several of the authors' works in order to make available a single source and show how the approximate geometric methods for regulation have been developed, and how the control design strategy has evolved from the theoretical methods, involving the regulator equations, to what we now call the regularized controller. In between these two extremes we developed, in a series of works, a fairly rigorous analysis of the regularization scheme leading to the regularized dynamic regulator equations and an iterative scheme that produces very accurate tracking and disturbance rejection control laws. In our most recent work we have extended dynamic regulator equations to what we now refer to as the regularized controller. This new formulation has only recently being applied to examples including linear and nonlinear delay equations.