Optimal Constrained Stabilization of Stochastic Time-Delay Systems

Physical systems in the real world are usually constrained due to different considerations. These constraints are closely related to the system safety and stability. In this letter we investigate the optimal stabilization control problem of stochastic time-delay systems under safety constraints. We first follow the Razumikhin approach to propose stochastic control Lyapunov and barrier functions, which result in the closed-form controllers for the stabilization and safety control individually. Next, based on the modification of the quadratic programming, an optimization problem is established to address the stabilization control under safe constraints. The optimal controller is derived explicitly in a switching form to tradeoff the stabilization and safety requirements. Finally, a numerical example is presented to illustrate the proposed control strategy.