NN-based adaptive stabilization for a class of stochastic nonlinear systems

The output tracking problem is considered for a class of stochastic nonlinear systems with unknown control coefficients in this paper. By combining the radial basis function neural network (RBF NN) approximation method with backstepping technique, an adaptive state-feedback controller is successfully constructed to guarantee the solution process to be bounded in probability. In addition, the tracking error signal is 4th-moment semi-globally uniformly ultimately bounded, which can also be regulated into a small neighborhood of the origin in probability. Finally, a simulation example demonstrates the effectiveness of the proposed scheme.