On necessary conditions of tracking control for nonlinear systems via contraction analysis

TL;DR

This paper investigates the necessary conditions for nonlinear systems to achieve universal asymptotic tracking using contraction analysis, linking control contraction metrics and designing a differential controller with practical application to microactuators.

Contribution

It introduces new necessary conditions for tracking control in nonlinear systems and proposes a simple differential controller based on differential detectability.

Findings

Established links to control contraction metrics.

Designed a differential controller via damping injection.

Applied method to electrostatic microactuators.

Abstract

In this paper we address the problem of tracking control of nonlinear systems via contraction analysis. The necessary conditions of the systems which can achieve universal asymptotic tracking are studied under several different cases. We show the links to the well developed control contraction metric, as well as its invariance under dynamic extension. In terms of these conditions, we identify a differentially detectable output, based on which a simple differential controller for trajectory tracking is designed via damping injection. As illustration we apply to electrostatic microactuators.