Adaptive fuzzy tracking control for a class of stochastic nonlinearly parameterized systems with distributed input delay

This paper addresses the problem of adaptive tracking control for a class of stochastic nonlinearly parameterized systems with distributed input delay using fuzzy logic systems (FLS). In this paper, through a state transformation the system can be easily transformed into a system without the distributed input delay, the quadratic functions instead of the quartic functions often utilized in the existing results are used as Lyapunov functions to analyze the stability of systems and the hyperbolic tangent functions are introduced to deal with the Hessian terms. FLS in Mamdani type are used to approximate the unknown nonlinear functions. Then, based on the backstepping technique, the adaptive fuzzy controller is 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. Finally, the example is used to demonstrate the effectiveness of our results proposed in this paper.