Safe Stabilization for Stochastic Time-Delay Systems
Zhuo-Rui Pan, Wei Ren, Xi‐Ming Sun
Abstract
This article addresses the safe stabilization problem of stochastic nonlinear time-delay systems. Based on the Krasovskii approach, we first propose a stochastic control Lyapunov–Krasovskii functional to guarantee the stabilization objective and a stochastic control barrier-Krasovskii functional to ensure the safety objective. Both functionals are developed, respectively, for each control objectives for the first time. Since the optimization problem is not easy to be resolved for stochastic time-delay systems, we derive a sliding mode-based approach to combine the proposed two functionals and to mediate stabilization and safety objectives, which allows to achieve the stabilization objective under the safety requirement. The proposed approach is illustrated via a numerical example.