Adaptive neural control for a general class of pure-feedback stochastic nonlinear systems

In this paper, the problem of the adaptive neural control is considered for a class of pure-feedback stochastic nonlinear systems. Based on the radial basis function (RBF) neural networks' universal approximation property, an adaptive neural controller is developed via backstepping technique. It is shown that the proposed controller can guarantee that all the signals in the closed-loop system are bounded in the sense of mean quartic value. Compared with the existing results on adaptive control of stochastic pure-feedback nonlinear systems, the main novelty of this note is that a systematic design procedure is presented for a class of pure-feedback stochastic nonlinear systems with a more general form of the diffusion term. Simulation results are presented to demonstrate the effectiveness of the proposed scheme.