Adaptive Neural Tracking Control for Nonstrict-Feedback Nonlinear Systems with Unknown Control Gains via Dynamic Surface Control Method

Abstract

This paper addresses the tracking control problem of nonstrict-feedback systems with unknown control gains. The dynamic surface control method, Nussbaum gain function control technique, and radial basis function neural network are applied for the design of virtual control laws, and adaptive control laws. Then, an adaptive neural tracking control law is proposed in the last step. By using the dynamic surface control method, the “explosion of complexity” problem of conventional backstepping is avoided. Based on the application of the Nussbaum gain function control technique, the unknown control gain problem is well solved. With the help of the radial basis function neural network, the unknown nonlinear dynamics are approximated. Furthermore, through Lyapunov stability analysis, it is proved that the proposed control law can guarantee that all signals in the closed-loop system are bounded and the tracking error can converge to an arbitrarily small domain of zero by adjusting the design parameters. Finally, two examples are provided to illustrate the effectiveness of the proposed control law.