Probabilistic-constrained optimal control of a class of stochastic hybrid systems

  • Koichi Kobayashi
  • Koichiro Matou
  • Kunihiko Hiraishi


Stochastic hybrid systems have several applications such as biological systems and communication networks, but it is difficult to consider control of general stochastic hybrid systems. In this paper, a class of discrete-time stochastic hybrid systems, in which only discrete dynamics are stochastic, is considered. For this system, a solution method for the optimal control problem with probabilistic constraints is proposed. Probabilistic constraints guarantee that the probability that the continuous state reaches a given unsafe region is less than a given constant. In the propose method, first, continuous state regions, from which the state reaches a given unsafe region, are computed by a backward-reachability graph. Next, mixed integer quadratic programming problems with constraints derived from the backward-reachability graph are solved. The proposed method can be applied to model predictive control.


Backward-reachability graphs optimal control probabilistic constraints stochastic hybrid systems 


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Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Koichi Kobayashi
    • 1
  • Koichiro Matou
    • 1
  • Kunihiko Hiraishi
    • 1
  1. 1.School of Information ScienceJapan Advanced Institute of Science and TechnologyNomi, IshikawaJapan

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