Article

International Journal of Control, Automation and Systems

, Volume 10, Issue 5, pp 897-904

First online:

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

  • Koichi KobayashiAffiliated withSchool of Information Science, Japan Advanced Institute of Science and Technology Email author 
  • , Koichiro MatouAffiliated withSchool of Information Science, Japan Advanced Institute of Science and Technology
  • , Kunihiko HiraishiAffiliated withSchool of Information Science, Japan Advanced Institute of Science and Technology

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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.

Keywords

Backward-reachability graphs optimal control probabilistic constraints stochastic hybrid systems