Safe Stabilization for Stochastic Time-Delay Systems

TL;DR

This paper introduces a novel approach for safe stabilization of stochastic nonlinear systems with time delays, using combined Lyapunov-Krasovskii and barrier functionals and a sliding mode method.

Contribution

It develops the first stochastic control Lyapunov-Krasovskii and barrier-Krasovskii functionals for stabilization and safety, and proposes a sliding mode approach to integrate these objectives.

Findings

Successfully guarantees stabilization under safety constraints.

Provides a new method for stochastic time-delay systems.

Validated with a numerical example.

Abstract

This paper addresses the safe stabilization problem of stochastic nonlinear time-delay systems. Based on theKrasovskii 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.