Stochastic safety for Markov chains

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Abstract

In the paper, 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 languageEnglish
Number of pages6
JournalIEEE Control Systems Letters
Early online date15 Jun 2020
DOIs
Publication statusE-pub ahead of print - 15 Jun 2020

Keywords

  • stochastic systems
  • computational methods
  • optimization
  • numerical algorithms
  • Lyapunov methods
  • Markov processes
  • algorithms

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