Strict Lyapunov Functions for Time-Optimal Sliding Mode Control Algorithm

Strict Lyapunov functions, with a negative definite derivative, for the time-optimal sliding mode control (TOSMC) algorithm with perturbations, are provided. Here, we present a new nonlinear feedback control technique that combines the classic “bang-bang” time-optimal control (TOC) with methods for sliding-mode control. This approach can achieve robust TOC for double-integral plants under perturbations. A family of switching lines with different slopes is introduced to obtain the desired fast response for those plants with a simple and robust control algorithm. The proposed Lyapunov functions ascertain finite time stability, provide an estimate of the convergence time, and give the upper bound of perturbations for ensuring robustness. Test scenarios demonstrated the system behaviour associated with this proposed TOSMC algorithm.