It is well-known that hybrid automata are mathematical models for cyber-physical systems. Unfortunately, the most of problems in behavior analysis for stochastic and probabilistic hybrid automata of general form are algorithmically unsolvable. For this reason, much effort has been focused on the development of probabilistic high-level models intended to solve specific problems in behavior analysis for fairly narrow classes of cyber-physical systems. Among them, models based on Markov processes are widely used. An important, and the easiest to analyze, subclass of these models is formed by Markov chains. In the given paper we illustrate the application of the following three classes of such models intended for solving problems of the behavior analysis of cyber-physical systems: models based on iterating random functions on the state space, models based on finite discrete-time Markov chains, and models based on finite continuous-time Markov chains.

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On Some Applications of Markov Chains for Cyber-Physical Systems Analysis

  • Volodymyr G. Skobelev,
  • Volodymyr V. Skobelev

摘要

It is well-known that hybrid automata are mathematical models for cyber-physical systems. Unfortunately, the most of problems in behavior analysis for stochastic and probabilistic hybrid automata of general form are algorithmically unsolvable. For this reason, much effort has been focused on the development of probabilistic high-level models intended to solve specific problems in behavior analysis for fairly narrow classes of cyber-physical systems. Among them, models based on Markov processes are widely used. An important, and the easiest to analyze, subclass of these models is formed by Markov chains. In the given paper we illustrate the application of the following three classes of such models intended for solving problems of the behavior analysis of cyber-physical systems: models based on iterating random functions on the state space, models based on finite discrete-time Markov chains, and models based on finite continuous-time Markov chains.