Kobayashi, K., Matou, K. & Hiraishi, K. Int. J. Control Autom. Syst. (2012) 10: 897. doi:10.1007/s12555-012-0505-3
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 graphsoptimal controlprobabilistic constraintsstochastic hybrid systems