International Workshop on Hybrid Systems: Computation and Control

HSCC 2006: Hybrid Systems: Computation and Control pp 49-63

Reachability Analysis for Controlled Discrete Time Stochastic Hybrid Systems

  • Saurabh Amin
  • Alessandro Abate
  • Maria Prandini
  • John Lygeros
  • Shankar Sastry
Conference paper

DOI: 10.1007/11730637_7

Volume 3927 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Amin S., Abate A., Prandini M., Lygeros J., Sastry S. (2006) Reachability Analysis for Controlled Discrete Time Stochastic Hybrid Systems. In: Hespanha J.P., Tiwari A. (eds) Hybrid Systems: Computation and Control. HSCC 2006. Lecture Notes in Computer Science, vol 3927. Springer, Berlin, Heidelberg

Abstract

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Saurabh Amin
    • 1
  • Alessandro Abate
    • 1
  • Maria Prandini
    • 2
  • John Lygeros
    • 3
  • Shankar Sastry
    • 1
  1. 1.University of California at BerkeleyBerkeleyUSA
  2. 2.Politecnico di MilanoMilanoItaly
  3. 3.University of PatrasPatrasGreece