TY - JOUR
T1 - Stochastic Safety for Markov Chains
AU - Bujorianu, Luminita Manuela
AU - Wisniewski, Rafal
AU - Boulougouris, Evangelos
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 - Lyapunov methods
KW - Markov processes
KW - Stochastic systems
KW - computational methods
KW - numerical algorithms
KW - optimization algorithms
UR - http://www.scopus.com/inward/record.url?scp=85093923355&partnerID=8YFLogxK
U2 - 10.1109/LCSYS.2020.3002475
DO - 10.1109/LCSYS.2020.3002475
M3 - Journal article
SN - 2475-1456
VL - 5
SP - 427
EP - 432
JO - IEEE Control Systems Letters
JF - IEEE Control Systems Letters
IS - 2
M1 - 9116937
ER -