Adaptive NN tracking control for pure-feedback stochastic nonlinear systems based on dynamic surface control

This paper focuses on the problem of adaptive neural network (NN) tracking control for a class of pure-feedback stochastic nonlinear systems. Via the dynamic surface control (DSC) technique and neural networks´ approximation capability, a novel adaptive NN control scheme is proposed. Without using the mean value theorem, an affine variable at each step is constructed. By introducing the additional first-order low-pass filter for the actual control input, the algebraic loop problem in pure-feedback stochastic nonlinear systems is solved. It is proved that the proposed controller ensures that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) in probability while the tracking error converges to a small neighborhood of the origin. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.