State-feedback stabilization for a class of more general high order stochastic nonholonomic systems

This paper studies the problem of state-feedback stabilization control for a class of high order stochastic nonholonomic systems with disturbed virtual control directions and more general nonlinear drifts. By using the backstepping approach, we develop a recursive controller design procedure in the stochastic setting. To get around the stabilization burden associated with nonholonomic systems, a switching control strategy is exploited in this procedure. The tuning function technique is applied in the design to avoid the disadvantage of overparameterization. It is shown that, under some conditions, the designed controller could ensure that the closed-loop system is almost asymptotically stabilized in probability. It is noted that the obtained conclusion can be extended to multi-input systems. A simulation example is provided to illustrate the effectiveness of the proposed approach. Copyright (C) 2011 John Wiley & Sons, Ltd.