Robust Stabilization of Nonlinear Systems with Uncertain Varying Control Coefficient

Zaiyue Yang,C W Chan,Yiwen Wang

doi:10.1155/2014/875372

Abstract

This paper investigates the stabilization problem for a class of nonlinear systems, whose control coefficient is uncertain and varies continuously in value and sign. The study emphasizes the development of a robust control that consists of a modified Nussbaum function to tackle the uncertain varying control coefficient. By such a method, the finite-time escape phenomenon has been prevented when the control coefficient is crossing zero and varying its sign. The proposed control guarantees the asymptotic stabilization of the system and boundedness of all closed-loop signals. The control performance is illustrated by a numerical simulation.

Highlights

The control design for nonlinear uncertain systems has been the research focus in the community for decades [1,2,3]
This paper investigates the stabilization problem for a class of nonlinear systems, whose control coefficient is uncertain and varies continuously in value and sign
In order to complete more complicated control tasks, the Nussbaum function has been combined with other control techniques, such as robust control [8, 12], adaptive control [15,16,17], learning control [6, 11], and backstepping design [8, 15, 16]

Summary

Introduction

The control design for nonlinear uncertain systems has been the research focus in the community for decades [1,2,3]. The general case of signvarying uncertain control coefficient has received much less attention and has not been fully solved yet This problem is technically more challenging and cannot be directly handled by the conventional Nussbaum function. Mathematical Problems in Engineering besides assuming the known bounds of the control coefficient and its varying speed, it requires the control coefficient to be a common term between the unknown dynamics and the control These assumptions make their method specific instead of general, and they need to be relaxed. We propose a new Nussbaum function, which does not require such assumptions of [7] and is able to track the rapidly varying sign of control coefficient.

System Description

Controller Design

Convergence Analysis

Simulation

Conclusion