Prescribed-Time Control via Periodic Delayed Feedback-Based Super-Twisting Sliding Mode Algorithm

This article investigates the problem of prescribed-time control via continuous sliding mode control laws. First, within the framework of the periodic delayed feedback approach, two novel super-twisting algorithms are proposed, whose settling times are bounded by a constant independent of the initial conditions and can be arbitrarily prescribed. Next, for a class of high-order uncertain nonlinear systems, a novel disturbance observer and a prescribed-time continuous sliding mode control law are designed based on the first super-twisting algorithm. Furthermore, for a class of perturbed double integrator systems, a novel state observer and a prescribed-time continuous sliding mode control law by output feedback are designed based on the second super-twisting algorithm. Unlike the widely used time-varying high-gain feedback approach in the literature, the control laws designed in this article ensure that the system output converges to zero with the settling time being exactly equal to the prescribed time, even in the presence of both matched and mismatched disturbances, while mitigating sensitivity to measurement noise and avoiding the singularity issues caused by infinite gain. Finally, the effectiveness of the proposed approaches is demonstrated through simulations.