Adaptive Exponential Stabilization for a Class of Stochastic Nonholonomic Systems

Xiaoyan Qin

doi:10.1155/2013/658050

Abstract

This paper investigates the adaptive stabilization problem for a class of stochastic nonholonomic systems with strong drifts. By using input-state-scaling technique, backstepping recursive approach, and a parameter separation technique, we design an adaptive state feedback controller. Based on the switching strategy to eliminate the phenomenon of uncontrollability, the proposed controller can guarantee that the states of closed-loop system are global bounded in probability.

Highlights

The nonholonomic systems cannot be stabilized by stationary continuous state feedback, it is controllable, due to Brockett’s theorem [1]
Under Assumption 5, if the proposed adaptive controller (31) together with the above switching control strategy is used in (1), for any initial contidion (x0, x, θ) ∈ Rn, the closed-loop system has an almost surely unique solution on [0, ∞), the solution process is bounded in probability, and P{limt → ∞θ(t) exists and is finite} = 1
We choose the Lyapunov function V = Vn, and ci > εi + ei; from (32) and Lemma 3, we know that the closed-loop system has an almost surely unique solution on [0, ∞), and the solution process is bounded in probability

Summary

Introduction

The nonholonomic systems cannot be stabilized by stationary continuous state feedback, it is controllable, due to Brockett’s theorem [1]. [3] firstly introduced a class of nonholonomic systems with strong nonlinear uncertainties and obtained global exponential regulation. There exists a natural problem that is how to design an adaptive exponential stabilization for a class of nonholonomic systems with stochastic drift and diffusion terms. Inspired by these papers, we will study the exponential regulation problem with nonlinear parameterization for a class of stochastic nonholonomic systems. We use the inputstate-scaling, the backstepping technique, and the switching scheme to design a dynamic state-feedback controller with ∑T ∑ ≠ I; the closed-loop system is globally exponentially regulated to zero in probability.

Problem Statement and Preliminaries

Controller Design and Analysis

Conclusions