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

Abstract

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.

Global inverse optimal stabilization of stochastic nonholonomic systems

“…If the control law (20) globally asymptotically stabilizes the system (19) in probability at the origin with respect to V (x), then the control law…”

“…Moreover, nonholonomic constraints, especially the x 0 -subsystem, i.e., the first equation of (1), create an obstacle in control design. By assuming that the x 0 -subsystem is deterministic, there are several works on design of asymptotic stabilizers in probability for stochastic nonholonomic systems, see [19] where unknown noise covariance is considered, and [20] where nonlinear appearance of unknown parameters is treated. These works are based on the input-to-state scaling proposed in [1], and the control design techniques for high order nonholonomic systems in power chained form in [21] and nonlinear systems with nonlinear appearance of unknown parameters in [2].…”

State-feedback stabilization for stochastic high-order nonholonomic systems with Markovian switching

“…However, this problem for stochastic high order nonholonomic systems has not been received much attention. The paper [18] investigated 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. But the controller for stochastic high-order nonholonomic systems with p 0 , .…”

“…(ii) It is considered in this paper to cancel the power order restriction in [18] and just satisfy p i ≥ 1, i = 1 . .…”

Adaptive motion/force control of nonholonomic mechanical systems with affine constraints

“…Although great progress [1][2][3][4][5][6][7][8][9] has been made for nonholonomic systems during the last decades, controller design for these systems still has a challenge to control engineers.…”