Adaptive dynamic surface control with prescribed tracking performance for nonlinear systems in pure-feedback form

A novel adaptive dynamic surface control (DSC) with prescribed tracking performance is proposed for a class of uncertain nonlinear systems in pure-feedback form. By combining Nussbaum gain function (NGF) with decoupled backstepping, the problems of unknown control directions and control singularity are simultaneously solved. Furthermore, the norm of the ideal weighting vector in neural network (NN) systems is considered as the estimation parameter, such that only one parameter is adjusted at each recursive step. In particular, by prescribed performance bounds, the prespecified tracking performance, i.e., the convergence rate, the allowed maximum overshoot and the steady state error, can be achieved. Based on decoupled backstepping method and Lyapunov stability theorem, the semi-global stability of the close-loop system is proved. Simulation results demonstrate the effectiveness of the control scheme.