Concave K∞ function-based adaptive tracking control of nonlinear second-order system

Abstract

How to simultaneously avoid the chattering and overestimation phenomena in classical adaptive sliding mode control is interesting but challenging. In this paper, we investigate the tracking control issue for a class of nonlinear second-order system with external disturbances, in which the bound of external disturbances exists but is unknown. To solve issue, we introduce the so-called concave $K_{\infty }$ function and design a continuous nonsingular terminal sliding mode controller. We first show that both the sliding variable and tracking error can be regulated into an small vicinity of zero within finite time without overestimating the control gain and the unexpected chattering. We then validate the superiority of the proposed method in terms of dynamics, steady-state performance, and anti-interference capability through conducting simulation experiments on magnetic levitation system.