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

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  • Thordur Runolfsson

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.

Suggested Citation

  • Thordur Runolfsson, 2000. "Risk-sensitive control of stochastic hybrid systems on infinite time horizon," Mathematical Problems in Engineering, Hindawi, vol. 5, pages 1-20, January.
    • Handle: RePEc:hin:jnlmpe:576758
    DOI: 10.1155/S1024123X99001192
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