Adaptive state-feedback stabilization of stochastic nonholonomic systems with an unknown time-varying delay and perturbations

Abstract

The problem of adaptive state-feedback stabilization of stochastic nonholonomic systems with an unknown time-varying delay and perturbations is studied in this paper. Without imposing any assumptions on the time-varying delay, an adaptive state-feedback controller is skillfully designed by using the input-state scaling technique and an adaptive backstepping control approach. Then, by adopting the switching strategy to eliminate the phenomenon of uncontrollability, the proposed adaptive state-feedback controller can 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. Finally, the simulation example shows the effectiveness of the proposed scheme.

Adaptive event-triggered control for stochastic nonholonomic systems with unknown virtual control coefficients

“…To solve this difficulty, many effective control strategies have been proposed, mainly including smooth time-varying stabilization, discontinuous time-invariant stabilization, and hybrid stabilization. In recent years, employing the backstepping technique and quartic Lyapunov functions, the stability and controller design issues for stochastic nonholonomic systems have been systematically investigated, and significant research results have been achieved [2,3,4,5]. It is worth mentioning that the virtual control coefficients are not available for some practical physical systems.…”