TY - JOUR
T1 - Stochastic safety for Markov chains
AU - Bujorianu, Manuela L.
AU - Wisniewski, Rafael
AU - Boulougouris, Evangelos
N1 - © 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
PY - 2021/4
Y1 - 2021/4
N2 - In this letter, we study the so-called p-safety of a Markov chain. We say that a state is p-safe in a state space S with respect to an unsafe set U if the process stays in the state space and hits the set U with the probability less than p. We show several ways of computing p-safety: by means the Dirichlet problem, the evolution equation, the barrier certificates, and the Martin kernel. The set of barrier certificates forms a cone. We show how to generate barrier certificates from the set of extreme points of a cone base.
AB - In this letter, we study the so-called p-safety of a Markov chain. We say that a state is p-safe in a state space S with respect to an unsafe set U if the process stays in the state space and hits the set U with the probability less than p. We show several ways of computing p-safety: by means the Dirichlet problem, the evolution equation, the barrier certificates, and the Martin kernel. The set of barrier certificates forms a cone. We show how to generate barrier certificates from the set of extreme points of a cone base.
KW - stochastic systems
KW - computational methods
KW - optimization
KW - numerical algorithms
KW - Lyapunov methods
KW - Markov processes
KW - algorithms
U2 - 10.1109/LCSYS.2020.3002475
DO - 10.1109/LCSYS.2020.3002475
M3 - Article
SN - 2475-1456
VL - 5
SP - 427
EP - 432
JO - IEEE Control Systems Letters
JF - IEEE Control Systems Letters
IS - 2
ER -