Nonsmooth stabilization and its computational aspects

TL;DR

This paper surveys key nonsmooth stabilization techniques for nonlinear systems, highlighting their theoretical foundations, practical tools, and computational challenges, especially when smooth control Lyapunov functions are unavailable.

Contribution

It provides a comprehensive overview of nonsmooth stabilization methods, including sliding-mode control and nonsmooth backstepping, with practical examples and computational insights.

Findings

Nonsmooth methods are essential when smooth Lyapunov functions do not exist.

The paper discusses computational issues in implementing nonsmooth control strategies.

Examples illustrate the application of nonsmooth stabilization techniques.

Abstract

This work has the goal of briefly surveying some key stabilization techniques for general nonlinear systems, for which, as it is well known, a smooth control Lyapunov function may fail to exist. A general overview of the situation with smooth and nonsmooth stabilization is provided, followed by a concise summary of basic tools and techniques, including general stabilization, sliding-mode control and nonsmooth backstepping. Their presentation is accompanied with examples. The survey is concluded with some remarks on computational aspects related to determination of sampling times and control actions.