Adaptive backstepping control for a class of strict feedback nonlinear systems using radial basis neural network

This paper addresses the problem of designing robust output tracking control for strict-feedback nonlinear systems with unknown nonlinear functions and unknown virtual coefficient nonlinear functions using radial basis neural networks. By defining desired control, a smooth and singularity-free adaptive controller is firstly designed for a first-order plant. Then, an extension is made to high-order nonlinear systems using neural network approximation, adaptive backstepping techniques and robust control. No upper bounds of unknown virtual coefficient functions are required in this paper. The effects of approximation error and unknown upper bounds of virtual coefficient functions are counteracted by adaptive robust terms. It is shown that under the proposed adaptive control the tracking error of the controlled system converges to a small neighborhood around zero. Simulation examples are given to illustrate the effectiveness of the proposed scheme.