Verification and control for finite-time safety of stochastic systems via barrier functions

C. Santoyo, M. Dutreix, S. Coogan
IEEE Conference on Control Technology and Applications, 2019


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.