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

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Abstract

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.

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Authors and Affiliations

  1. School of Information Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa, 923-1292, Japan

    Koichi Kobayashi, Koichiro Matou & Kunihiko Hiraishi

Authors
  1. Koichi Kobayashi
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  2. Koichiro Matou
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  3. Kunihiko Hiraishi
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Corresponding author

Correspondence to Koichi Kobayashi.

Additional information

Recommended by Editorial Board member Young Soo Suh under the direction of Editor Young Il Lee.

This journal was partially supported by the JSPS Grant-in-Aid for Young Scientists (B) 23760387.

Koichi Kobayashi received his M.E. degree from Hosei University in 2000, and his D.E. degree from Tokyo Institute of Technology in 2007. From 2000 to 2004, he worked at Nippon Steel Corporation. He is currently an Assistant Professor at School of Information Science, Japan Advanced Institute of Science and Technology. His research interests include control of discrete event and hybrid systems. He is a member of the SICE, ISCIE, IEICE, and IEEE.

Koichiro Matou received his master degree from Japan Advanced Institute of Science and Technology in 2011. His research interests include control of hybrid systems.

Kunihiko Hiraishi received his B.E. degree from the Tokyo Institute of Technology in 1983, an M.E. degree in 1985, and a D.E. degree in 1990. He is currently a Professor at School of Information Science, Japan Advanced Institute of Science and Technology. His research interests include discrete event systems and formal verification. He is a member of the IEEE, IEICE, SICE, and IPSJ.

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Kobayashi, K., Matou, K. & Hiraishi, K. Probabilistic-constrained optimal control of a class of stochastic hybrid systems. Int. J. Control Autom. Syst. 10, 897–904 (2012). https://doi.org/10.1007/s12555-012-0505-3

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  • DOI: https://doi.org/10.1007/s12555-012-0505-3

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