Novel Adaptive Dynamic Surface Control of Nonlinear systems

A novel adaptive dynamic surface control (DSC) with recursive error surface is proposed for a class of uncertain nonlinear systems in strict-feedback form. The problem of explosion of terms in traditional backstepping design is eliminated by utilizing dynamic surface control. Furthermore, the maximum value of 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 regardless of the number of the NN nodes in whole design procedure. In particular, By designing recursive error surface, the tracking error in the preceding step is considered into the next control law so that the design synthesizes the interaction of the tracking error in each subsystem. The problem for DSC being fragile to the perturbation of its own parameters is avoided. Via constructing new Lyapunov function, the semi-global stability of the close-loop system is proved. Simulation results demonstrate the effectiveness of the control scheme.