Verification and Control for Finite-Time Safety of Stochastic Systems via Barrier Functions
For control engineers and researchers working on safety-critical stochastic systems, this work provides a more precise verification and control method for finite-time safety guarantees.
This paper introduces a state-dependent barrier certificate condition for stochastic systems that yields tighter probability bounds on finite-time safety compared to prior works, and proposes a method for synthesizing polynomial controllers to achieve a specified safety probability. Case studies demonstrate improved performance.
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.