Adaptive fuzzy tracking control for stochastic nonlinear systems with unknown time-varying delays

- An adaptive fuzzy controller is presented for a class of stochastic nonlinear systems.
- An quadratic function is constructed to give the condition of the stability of systems.
- The scheme guarantees the stability of closed-loop system in the mean square sense.
- The drawback of the quartic moment approach is overcome and the method is simplified.

This paper addresses the problem of adaptive tracking control for a class of stochastic strict-feedback nonlinear time-varying delays systems using fuzzy logic systems (FLS). In this paper, quadratic functions are used as Lyapunov functions to analyze the stability of systems, other than the fourth moment approach proposed by H. Deng and M. Krstic, and the hyperbolic tangent functions are introduced to deal with the Hessian terms. This approach overcomes the drawback of the traditional quadratic moment approach and reduce the complexity of design procedure and controller. Based on the backstepping technique, the appropriate Lyapunov-Krasovskii functionals and the FLS, the adaptive fuzzy controller is well designed. The proposed adaptive fuzzy controller guarantees that all the signals in the closed-loop system are bounded in probability and the tracking error can converge to a small residual set around the origin in the mean square sense.