Mathematical Problems in Engineering

Mathematical Problems in Engineering / 2000 / Article

Open Access

Volume 5 |Article ID 576758 | https://doi.org/10.1155/S1024123X99001192

Thordur Runolfsson, "Risk-sensitive control of stochastic hybrid systems on infinite time horizon", Mathematical Problems in Engineering, vol. 5, Article ID 576758, 20 pages, 2000. https://doi.org/10.1155/S1024123X99001192

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

Received23 Jul 1999

Abstract

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.

Copyright © 2000 Hindawi Publishing Corporation. 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.


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