Robust adaptive prescribed performance dynamic surface control for uncertain nonlinear pure-feedback systems

Abstract

A robust adaptive prescribed performance dynamic surface control design procedure for a class of nonlinear pure-feedback systems with both unknown vector parameters and unmodeled dynamics is presented. The unmodeled dynamics lie within some bounded functions, which are assumed to be partially known. A state transformation and an auxiliary system are proposed to avoid using the cumbersome formula to handle the non-affine structure. A radical-type Lyapunov function and L function are designed to ensure the prescribed performance of the pure-feedback system. Bounded value of finding the partial derivative of the non-affine function is avoided by designing special virtual controllers in using dynamic surface control. As illustrated by examples, the proposed adaptive prescribed performance dynamic surface control scheme is shown to guarantee the semi-global uniformly ultimately bounded, and the dynamic performance and steady-state performance of the tracking error depend on the prescribed performance functions.