Mathematical Problems in Engineering
Volume 5 (2000), Issue 6, Pages 459-478

Risk-sensitive control of stochastic hybrid systems on infinite time horizon

Thordur Runolfsson1,2

1Department of Engineering, University of Iceland, Hjardarhagi 2-6, Reykjavik IS107, Iceland
2EECS Department, The University of Michigan, Ann Arbor 48109-2122, MI, USA

Received 23 July 1999

Copyright © 2000 Thordur Runolfsson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A risk-sensitive optimal control problem is considered for a hybrid system that consists of continuous time diffusion process that depends on a discrete valued mode variable that is modeled as a Markov chain. Optimality conditions are presented and conditions for the existence of optimal controls are derived. It is shown that the optimal risk-sensitive control problem is equivalent to the upper value of an associated stochastic differential game, and insight into the contributions of the noise input and mode variable to the risk sensitivity of the cost functional is given. Furthermore, it is shown that due to the mode variable risk sensitivity, the equivalence relationship that has been observed between risk-sensitive and H control in the nonhybrid case does not hold for stochastic hybrid systems.