Optimal Tuning of the Saturated Super-Twisting Algorithm

The saturated super-twisting algorithm is a sliding-mode control law for robust control in the presence of a saturated control input. It can in principle reject arbitrary bounded and Lipschitz continuous perturbations, and features a control signal that is continuous except for a single jump discontinuity. Its tuning requires the choice of a Lyapunov function from a family of quadratic functions. This choice determines the maximum amplitude of perturbations that are guaranteed to be rejected and the magnitude of the control signal’s discontinuity. This contribution proposes a procedure for choosing an optimal Lyapunov function that permits to maximize the available perturbation amplitude and minimize the discontinuity’s magnitude.