Probabilistic-Constrained Optimal Control of a Class of Stochastic Hybrid Systems

• Published in: International journal of control, automation, and systems Vol. 10; no. 5; pp. 897 - 904
• Main Authors: Kobayashi, Koichi, Matou, Koichiro, Hiraishi, Kunihiko
• Format: Journal Article
• Language: Korean
• Published: 2012
• Subjects: stochastic hybrid systems; optimal control; Backward-reachability graphs; probabilistic constraints
• ISSN: 1598-6446; 2005-4092

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.