Abstract
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.
Original language | English |
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Pages (from-to) | 427-432 |
Number of pages | 6 |
Journal | IEEE Control Systems Letters |
Volume | 5 |
Issue number | 2 |
Early online date | 15 Jun 2020 |
DOIs | |
Publication status | Published - Apr 2021 |
Keywords
- stochastic systems
- computational methods
- optimization
- numerical algorithms
- Lyapunov methods
- Markov processes
- algorithms