Approximation-based direct adaptive tracking control for a class of uncertain pure-feedback stochastic nonlinear systems

This paper considers the problem of fuzzy-based direct adaptive tracking control for pure-feedback stochastic nonlinear systems. Fuzzy logic systems are used to approximate the packaged unknown nonlinearities, and then a novel direct adaptive controller is constructed via backstepping technique. The proposed controller guarantees that all the signals in the closed-loop system are bounded in probability and the tracking error converges to a small neighborhood around the origin in the sense of mean quartic value. The main advantages lie in that the proposed controller is simpler and only one adaptive parameter need to be updated online. Simulation example further illustrate the effectiveness of the proposed approach.