Adaptive continuous twisting algorithm

Abstract

In this paper, an adaptive continuous twisting algorithm (ACTA) is presented. For double integrator, ACTA produces a continuous control signal ensuring finite time convergence of the states to zero. Moreover, the control signal generated by ACTA compensates the Lipschitz perturbation in finite time, i.e. its value converges to the opposite value of the perturbation. ACTA also keeps its convergence properties, even in the case that the upper bound of the derivative of the perturbation exists, but it is unknown.