Adaptive neural network asymptotic tracking control for a class of stochastic nonlinear systems with unknown control gains and full state constraints

This article addresses the issue of adaptive intelligent asymptotic tracking control for a class of stochastic nonlinear systems with unknown control gains and full state constraints. Unlike the existing systems in the literature in which the prior knowledge of the control gains is available for the controller design, the salient feature of our considered system is that the control gains are allowed to be unknown but have a positive sign. By introducing an auxiliary virtual controller and employing the new properties of Numbness functions, the major technique difficulty arising from the unknown control gains is overcome. At the same time, the log ‐type barrier Lyapunov functions are introduced to prevent the violation of the state constraints. What's more, neural networks' universal online approximation ability and gain suppression inequality technology are combined in the frame of adaptive backstepping design, so that a new control method is proposed, which cannot only realize the asymptotic tracking control in probability, but also meet the requirement of the full state constraints imposed on the system. In the end, the simulation results for a practical example demonstrate the effectiveness of the proposed control method.