Variable Structure Predefined‐Time Stabilization of Second‐Order Systems

Abstract

Abstract A controller that stabilizes second‐order vector systems in predefined‐time is introduced in this paper. That is, for second‐order systems a controller is designed such that the trajectories reach the origin in a time defined in advance. The proposed controller is a variable structure controller that first drive the system trajectories to a linear manifold in predefined time and then drives the system trajectories to a non‐smooth manifold with the predefined‐time stability property, in predefined time also; this is done in order to avoid the differentiability problem that inherently appears when stabilizing high‐order systems in finite time under the block control principle technique. The proposal is applied to the predefined‐time exact tracking of fully actuated mechanical systems. As an example, the proposed solution is applied to a two‐link planar manipulator, and numerical simulations are conducted to show its performance.