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arXiv · 1905.12077

Verification and Control for Finite-Time Safety of Stochastic Systems via Barrier Functions

Cesar Santoyo·Maxence Dutreix·Samuel Coogan
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Abstract

This paper studies the problem of enforcing safety of a stochastic dynamical system over a finite time horizon. We use stochastic barrier functions as a means to quantify the probability that a system exits a given safe region of the state space in finite time. A barrier certificate condition that bounds the infinitesimal generator of the system, and hence bounds the expected value of the barrier function over the time horizon, is recast as a sum-of-squares optimization problem for efficient numerical computation. Unlike prior works, the proposed certificate condition includes a state-dependent bound on the infinitesimal generator, allowing for tighter probability bounds. Moreover, for stochastic systems for which the drift dynamics are affine-in-control, we propose a method for synthesizing polynomial state feedback controllers that achieve a specified probability of safety. Two case studies are presented that benchmark and illustrate the performance of our method.

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Cesar Santoyo, Maxence Dutreix, Samuel Coogan. 2019-05-28. Verification and Control for Finite-Time Safety of Stochastic Systems via Barrier Functions. https://arxiv.org/abs/1905.12077

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