Hybrid Systems: Computation and Control

Volume 3927 of the series Lecture Notes in Computer Science pp 49-63

Reachability Analysis for Controlled Discrete Time Stochastic Hybrid Systems

  • Saurabh AminAffiliated withUniversity of California at Berkeley
  • , Alessandro AbateAffiliated withUniversity of California at Berkeley
  • , Maria PrandiniAffiliated withPolitecnico di Milano
  • , John LygerosAffiliated withUniversity of Patras
  • , Shankar SastryAffiliated withUniversity of California at Berkeley

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A model for discrete time stochastic hybrid systems whose evolution can be influenced by some control input is proposed in this paper. With reference to the introduced class of systems, a methodology for probabilistic reachability analysis is developed that is relevant to safety verification. This methodology is based on the interpretation of the safety verification problem as an optimal control problem for a certain controlled Markov process. In particular, this allows to characterize through some optimal cost function the set of initial conditions for the system such that safety is guaranteed with sufficiently high probability. The proposed methodology is applied to the problem of regulating the average temperature in a room by a thermostat controlling a heater.