Adaptive fuzzy backstepping output feedback tracking control of MIMO stochastic pure-feedback nonlinear systems with input saturation

In this paper, the adaptive fuzzy backstepping output feedback tracking control problem is considered for a class of uncertain stochastic multi-input and multi-output (MIMO) nonlinear systems in pure-feedback form. The stochastic MIMO nonlinear systems under study have unknown nonlinear functions, input saturation and immeasurable states. By using fuzzy logic systems to identify the uncertain nonlinear system, and a smooth function to approximate the input saturation, a fuzzy state observer is designed and the estimations of the immeasurable states are obtained. Based on the backstepping recursive design technique, an adaptive fuzzy output feedback tracking control approach is developed. It is shown that the proposed control approach guarantees that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) in mean-square in the sense of probability, and the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing design parameters appropriately. A simulation example is provided to show the effectiveness of the proposed approach.