Sufficient Conditions for Robust Probabilistic Reach-Avoid-Stay Specifications using Stochastic Lyapunov-Barrier Functions

Yiming Meng; Jun Liu

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arXiv · 2203.12746

Sufficient Conditions for Robust Probabilistic Reach-Avoid-Stay Specifications using Stochastic Lyapunov-Barrier Functions

Yiming Meng·Jun Liu

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Abstract

Stability and safety are crucial in safety-critical control of dynamical systems. The reach-avoid-stay objectives for deterministic dynamical systems can be effectively handled by formal methods as well as Lyapunov methods with soundness and approximate completeness guarantees. However, for continuous-time stochastic dynamical systems, probabilistic reach-avoid-stay problems are viewed as challenging tasks. Motivated by the recent surge of applications in characterizing safety-critical properties using Lyapunov-barrier functions, we aim to provide a stochastic version for the probabilistic reach-avoid-stay problems in consideration of robustness. To this end, we first establish a connection between stochastic stability with safety constraints and reach-avoid-stay specifications. We then prove that stochastic Lyapunov-barrier functions provide sufficient conditions for the target objectives. We apply Lyapunovbarrier conditions in control synthesis for reach-avoid-stay specifications, and show its effectiveness in a case study.

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BibTeX RIS

Yiming Meng, Jun Liu. 2022-03-23. Sufficient Conditions for Robust Probabilistic Reach-Avoid-Stay Specifications using Stochastic Lyapunov-Barrier Functions. https://arxiv.org/abs/2203.12746

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