Direct Adaptive Fuzzy Tracking Control of Non-affine Stochastic Nonlinear Time-Delay Systems

In this research, the problem of direct adaptive fuzzy control based on state feedback for a class of non-affine stochastic nonlinear systems with time delay is considered. Fuzzy logic systems (FLSs) and mean value theorem are utilized to overcome the design difficulties appeared in the unknown nonlinearities and non-affine structure, respectively. With the utilization of adaptive control and backstepping design framework, a direct adaptive fuzzy control method is developed. Through Lyapunov analysis, the presented controller can guarantee that the variables in the closed-loop system are all bounded in the fourth-moment, in the mean time, the output signal can track the given reference signal by appropriately selecting the design parameters. Simulation results are provided to illustrate the correctness of the theoretical results.