On the Robustness of a Modified Super-Twisting Algorithm With Prescribed-Time Convergence

Abstract

This paper addresses the robustness of a novel two-stage super-twisting algorithm designed to converge within a prescribed time interval despite disturbances and model uncertainties. Initially, we introduce a method for tuning parameters that guarantees the algorithm’s analytic solution will reach the origin precisely at a prescribed instant, assuming an unperturbed scenario. We then enhance this method to maintain prescribed-time convergence, even when faced with unknown bounded disturbances. The algorithm’s performance is demonstrated through a numerical simulation of a state estimation problem for a perturbed damped pendulum. The results show that the estimation errors converge robustly to the origin at the prescribed time and remain there afterward.

Keywords

• Prescribed-time convergence
• robust estimation
• super-twisting algorithm