Maximum hands-off feedback control for finite-time stabilization

This work proposes a way to time-sparsify predesigned stabilizing feedback controls. For this purpose, a finite-time stabilizing sliding-mode feedback control law is considered. For the finite-time stabilizing controller, an on- off switching signal is designed to optimally time-sparsify the feedback control signals. Due to the non-Lipschitz nature of the sliding-mode controller, this requires the use of a non-smooth Pontryagin Maximum Principle. Numerical experiments are presented to verify the theoretical results and illustrate the advantages of the proposed ideas.