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

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 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.

Use Google Scholar for full citation. Download paper here