Approximation-Based Adaptive Tracking Control for Switched Stochastic Strict-Feedback Nonlinear Time-Delay Systems With Sector-Bounded Quantization Input

Abstract

This paper addresses the adaptive tracking problem for a class of uncertain switched stochastic strict-feedback nonlinear systems with both sector-bounded quantization input and unknown time-varying delays under arbitrary switching. Major design difficulties for such systems, in which all the time-varying delays absolutely depend on the subsystem number, come from finding a common Lyapunov function (CLF) for all subsystems and dealing with the sector-bounded quantization error. The Lyapunov–Razumikhin method is employed to construct a suitable CLF for all subsystems and relax the restrictions on the time-varying delays. Moreover, some new techniques are presented to overcome the difficulty from the sector-bounded quantization error. With the application of backstepping technique, variable separation technique and fuzzy logic system approximation, a common adaptive tracking control scheme containing only one adaptive parameter is proposed for this class of systems. The derived quantized control scheme ensures that the tracking error remains in a small neighborhood of the origin via the appropriate adjustment of design parameters while all the signals in closed loop system are bounded in probability. Finally, two simulation examples are provided to illustrate the feasibility and applicability of the proposed control design.