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

Published in Conference on Control and Transportation Applications (CCTA), 2019

Recommended citation: C. Santoyo, M. Dutreix, S. Coogan, "Verification and control for finite-time safety of stochastic systems via barrier functions" IEEE Conference on Control Technology and Applications pp. 712–717, 2019.

This paper studies the problem of enforcing safetyof 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 thestate space in finite time. A barrier certificate condition thatbounds the infinitesimal generator of the system, and hencebounds the expected value of the barrier function over the time horizon, is recast as a sum-of-squares optimization problemfor efficient numerical computation. Unlike prior works, theproposed certificate condition includes a state-dependent boundon the infinitesimal generator, allowing for tighter probabilitybounds. Moreover, for stochastic systems for which the driftdynamics are affine-in-control, we propose a method for syn-thesizing polynomial state feedback controllers that achieve aspecified probability of safety. Two case studies are presentedthat benchmark and illustrate the performance of our method.

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