Adaptive neural network control of stochastic strict feedback nonlinear systems

The Lyapunov function of integral type is first introduced into a class of stochastic strict-feedback nonlinear systems with unknown virtual control gain functions. By utilizing the approximation capability of neural networks, backstepping technique and Young´s inequality, a simple and effective adaptive neural network state feedback controller is constructed to ensure that the system is semi-global bounded in probability. Under some conditions, by the Lyapunov method, it is shown that all signals in the closed-loop system are bounded in probability. Simulation results are given to illustrate the effectiveness of the proposed control scheme.