Safety of stochastic systems: an analytic and computational approach

Rafal Wisniewski, Luminita Bujorianu

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
21 Downloads (Pure)


We refine the concept of stochastic reach avoidance for a general class of Markov processes introducing a threshold of p for the reaching probability. This new problem is called p-safety, and it aims to ensure that the given process reaches a forbidden set before leaving its ‘working’ state space with a probability of less than p. In the situation when an initial probability measure characterizes the initial states, a variant of p-safety is put forward. We call this form of safety weak p-safety. In this work, we characterize both p-safety and weak p-safety and show how to compute them. We employ semi-definite programming to compute p-safety and linear programming to compute weak p-safety. To get to this point, we use certificates of positivity of polynomials translated into the sum of squares and the Bernstein forms.
Original languageEnglish
Article number109839
Number of pages13
Early online date19 Aug 2021
Publication statusPublished - 30 Nov 2021


  • safety analysis
  • moment method
  • polynomial methods
  • optimization problems
  • Markov models
  • stochastic systems


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