Control with prescribed performance tracking for input quantized nonlinear systems using self-scrambling gain feedback

Abstract This paper investigates the problem of control with prescribed performance tracking for a class of nonlinear systems in the presence of quantized input. A novel state feedback control scheme by self-scrambling gain is proposed, with the first merit that it is computationally inexpensive, since no linearly-parameterized approximators are used, and the second merit that it is self-adjustable with respect to different levels of tracking errors. Based on a smoothly transformed error variables, the output and virtual tracking errors are guaranteed to converge to some predefined arbitrarily small residual sets regardless of transient and steady bounds. The closed-loop system is proved by rigorously mathematical derivation to be globally stable, and two comparative illustrative examples are given to demonstrate the advantages and effectiveness of the proposed method.