Design of adaptive backstepping dynamic surface control method with RBF neural network for uncertain nonlinear system.

Highlights • Novel Lyapunov functions are constructed to investigate the stability analysis. • The RBF Neural Network can approximate the unknown smooth function. • The dynamic surface control technique is applied to eliminate the "explosion of the complexity". • The adaptive backstepping dynamic surface control is proposed for nonlinear system. Abstract This paper develops an adaptive backstepping dynamic surface control method with RBF Neural Network for a class of nonlinear system under extra disturbances. The considered RBF Neural Network based on adaptive control is applied to approximate the unknown smooth function arbitrarily. The "explosion of the complexity" is eliminated by utilizing the dynamic surface control technique. The Lyapunov function is employed to verify the globally asymptotically stability of the control nonlinear system. Four examples were given to show that the novel control method can not only tracking the expected trajectory very well but also has a better approximation capability for various complex unknown smooth function under disturbances. [ABSTRACT FROM AUTHOR]