Open-loop contraction design

TL;DR

This paper explores how to design input perturbations to make a nonlinear system's trajectory contracting, drawing parallels with feedback stabilization, and demonstrates applications in parameter estimation.

Contribution

It introduces a novel approach to designing contracting input perturbations based on inverse system output variables, linking contraction with feedback stabilization.

Findings

Existence of output variables facilitates contraction design.

Method applies to nonlinear systems for trajectory stabilization.

Relevance demonstrated in parameter estimation scenarios.

Abstract

Given a non-contracting trajectory of a nonlinear system, we consider the question of designing an input perturbation that makes the perturbed trajectory contracting. This paper stresses the analogy of this question with the classical question of feedback stabilization. In particular, it is shown that the existence of an output variable that ensures contraction of the inverse system facilitates the design of a contracting input perturbation. We illustrate the relevance of this question in parameter estimation.