Convergence Time Calculation for Supertwisting Algorithm and Application for Nonaffine Nonlinear Systems

Abstract

In this study, an accurate convergence time of the supertwisting algorithm (STA) is proposed to build up a framework for nonaffine nonlinear systems’ finite-time control. The convergence time of the STA is provided by calculating the solution of a differential equation instead of constructing Lyapunov function. Therefore, precise convergence time is presented instead of estimation of the upper bound of the algorithm’s reaching time. Regardless of affine or nonaffine nonlinear systems, supertwisting control (STC) provides a general solution based on virtual control law skill ensuring the output of the systems converges to the origin point at exact time. Benchmark tests are simulated to demonstrate the effectiveness and efficiency of the algorithm.