Switching control for incremental stabilization of nonlinear systems via contraction theory

TL;DR

This paper introduces a switching control method based on contraction theory to incrementally stabilize nonlinear systems efficiently, reducing control effort by activating control only when necessary.

Contribution

It develops a novel switching control strategy using contraction analysis for incremental stabilization of nonlinear systems, with a practical design procedure and illustrative example.

Findings

Sufficient conditions for incremental stability of switched Filippov systems.

A control design method that minimizes control effort by switching only when needed.

Successful demonstration on a representative nonlinear system.

Abstract

In this paper we present a switching control strategy to incrementally stabilize a class of nonlinear dynamical systems. Exploiting recent results on contraction analysis of switched Filippov systems derived using regularization, sufficient conditions are presented to prove incremental stability of the closed-loop system. Furthermore, based on these sufficient conditions, a design procedure is proposed to design a switched control action that is active only where the open-loop system is not sufficiently incrementally stable in order to reduce the required control effort. The design procedure to either locally or globally incrementally stabilize a dynamical system is then illustrated by means of a representative example.