A barrier function approach to finite-time stochastic system verification and control

Published in in submission, 2020

Recommended citation: C. Santoyo, M. Dutreix, S. Coogan "A barrier function approach to finite-time stochastic system verification and control," in submission , 2020 https://csantoyo.github.io/files/barrierfunctionapproach.pdf

This paper studies the problem of enforcing safety of a stochastic dynamical system over a finite-time horizon. We use stochastic control 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 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 upper bound on the evolution of the expectation. We present formulations for both continuous-time and discrete-time systems. Moreover, for 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. Several case studies are presented which benchmark and illustrate the performance of our verification and control method in the continuous-time and discrete-time domains.

Use Google Scholar for full citation. Download paper here