Adaptive control-based barrier Lyapunov functions for strict-feedback stochastic nonlinear systems with input saturation and dead zone

The purpose of this paper is to design an adaptive controller for uncertain strict-feedback stochastic nonlinear systems with dead zone and input saturation. A barrier Lyapunov function in asymmetric forms is constructed which can relax the requirements for initial conditions. To simplify the design process of the controller, a dead zone-based model of saturation is implemented and neural networks are used to approximate uncertain nonlinear functions and to construct an observer to cope with difficulties raised by the presence of immeasurable state variables. By applying the backstepping technique, a smooth tracking controller with adaptive law is proposed to ensure all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Furthermore, the tracking error can converge to a small neighbourhood of the origin. The effectiveness of the proposed scheme is presented by simulations on a numerical example.