New Design to Adaptive Neural Asymptotic Tracking Control for a Class of Uncertain Stochastic Nonlinear Systems With Unknown Input Constraints

ABSTRACT In this paper, we present a new scheme to design an adaptive neural backstepping tracking controller for a class of stochastic nonlinear systems with unknown input constraints including saturation and dead‐zone. The control design is achieved by using certain auxiliary techniques. More specifically, some piecewise injective differential functions are constructed to approximate these nonlinearity constraints with a bounded approximation error. A new dimension reduction inequality related the norm of basis vectors of radial basis functions is established to design the virtual signals. Some negative power exponential functions and the inverse functions of the above injective differentiable functions are introduced to design the adaptive laws and controller, respectively. These techniques can enlarge the nonlinear systems currently studied by backstepping approach and neural networks. Furthermore, it is shown that all the signals in the closed‐loop system are semi‐globally uniformly, ultimately bounded in probability and the tracking error converges to zero. Meanwhile, the effectiveness of the proposed controller is demonstrated in the simulation study.