Generalized Integral Siding Mode Manifold Design: A Sum of Squares Approach

TL;DR

This paper introduces a novel SOS programming-based method for designing generalized integral sliding mode manifolds and controllers for nonlinear systems with uncertainties, verified through simulations and practical applications.

Contribution

It provides a systematic SOS-based algorithm for designing sliding mode manifolds and controllers, including conditions for successful implementation in uncertain nonlinear systems.

Findings

Effective design of sliding mode manifolds using SOS programming

Successful application to glucose-insulin regulation and unicycle steering

Verification through simulations and real-world examples

Abstract

This paper presents a general form of integral sliding mode manifold, and proposes an algorithmic approach based on Sum of Squares (SOS) programming to design generalized integral sliding mode manifold and controller for nonlinear systems with both matched and unmatched uncertainties. The approach also gives a sufficient condition for successful design of controller and manifold parameters. The result of the paper is then verified by several simulation examples and two practical applications, namely Glucose-insulin regulation problem and the unicycle dynamics steering problem are considered.