A prescribed-performance-based adaptive finite-time tracking control scheme circumventing the dependence on the system initial condition

This paper is concerned with the prescribed finite-time tracking control problem for a class of nonlinear systems with unknown initial condition, state time-varying delays and external disturbances. A new adaptive prescribed finite-time tracking control scheme bypassing system initial condition is proposed via the prescribed performance method. Several nonlinear mapping functions (NMFs) and a new prescribed finite-time performance function (PFTPF) combining finite-time control with prescribed performance control are constructed to obtain the scheme. In this paper, the assumptions on the time-delay terms are removed by means of the designed Lyapunov–Krasovskii functions. In addition, to avoid step impact effect arisen by an overlarge initial control input, a control input with zero initial value is obtained. Aiming at the design of zero initial control input, a new Lyapunov stability criterion form is put forward. Two practical examples are presented to confirm the effectiveness and superiority of the proposed scheme.