Stochastic safety for random dynamical systems

Bujorianu, Manuela L. and Wisniewski, Rafał and Boulougouris, Evangelos; (2021) Stochastic safety for random dynamical systems. In: 2021 American Control Conference (ACC). Proceedings of the American Control Conference . IEEE, USA, pp. 1340-1345. ISBN 9781665441971 (

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In the paper, we study the so-called p-safety of a random dynamical system. We generalize the existing results for safety barrier certificates for deterministic dynamical systems and Markov processes. Moreover, we consider the case of random obstacles, modelled as random sets. This leads to the necessity of using integrals with respect to lower and upper distributions. We prove that if there exists at least one barrier certificate then the random dynamical system is safe. The barrier certificates are also defined using such nonlinear distributions. Furthermore, when the family of stochastic Koopman operators has the semigroup property, the barrier certificates are solutions for some type of Dirichlet problems.


Bujorianu, Manuela L., Wisniewski, Rafał and Boulougouris, Evangelos ORCID logoORCID:;