State-Feedback Stabilization of Stochastic Nonholonomic Systems with an Unknown Time-Varying Delay

Qinghui Du,Qianqian Cui,Dongkai Zhang

doi:10.1155/2019/7516734

Abstract

This paper investigates the state-feedback stabilization of stochastic nonholonomic systems with an unknown time-varying delay. Without imposing any assumptions on the time-varying delay, a state-feedback controller is skillfully designed by using input-state-scaling technique and backstepping control approach. The switching strategy is proposed to eliminate the phenomenon of uncontrollability and to guarantee that the closed-loop system has an almost surely unique solution for any initial state and the equilibrium of interest is globally asymptotically stable in probability. A simulation example demonstrates the effectiveness of the proposed scheme.

Highlights

Nonholonomic systems represent an important class of control systems, which arises in many mechanical systems such as mobile robots, car-like vehicles, underactuated satellites, and the knife-edge
Without imposing any assumptions on the time-varying delay, an adaptive state-feedback controller was skillfully designed by using adaptive backstepping control technique, and it was proven that the constructed controller can guarantee the closed-loop system to be globally asymptotically stable in probability
(ii) Globally asymptotically stable in probability if it is globally stable in probability and

Summary

Introduction

Nonholonomic systems represent an important class of control systems, which arises in many mechanical systems such as mobile robots, car-like vehicles, underactuated satellites, and the knife-edge. Zhao et al [12] designed a state-feedback controller to stabilize a class of more general high-order stochastic nonholonomic systems. Wu and Wu [19] proposed a robust state-feedback switching controller to stabilize time-delay nonholonomic systems with strongly nonlinear uncertainties by using discontinuous transformation and dynamic feedback approach. Qin and Min [22] studied the adaptive stabilization problem for a class of stochastic nonholonomic systems with time delays. Min et al [24] have studied the problem of globally adaptive control for stochastic nonlinear time-delay systems with perturbations and its application. Without imposing any assumptions on the time-varying delay, an adaptive state-feedback controller was skillfully designed by using adaptive backstepping control technique, and it was proven that the constructed controller can guarantee the closed-loop system to be globally asymptotically stable in probability.

Preliminary Results

State-Feedback Control Design

Switching Control Stability

Simulation Example

Conclusion