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Asymptotic Behavior of the Value Functions of Discrete-Time Discounted Optimal Control

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  • F. Wirth

    (Universität Bremen)

Abstract

We study deterministic discounted optimal control problems associated with discrete-time systems. It is shown that, for small discount rates, the controllability properties of the underlying system can guarantee the convergence of the discounted value function to the value function of the average yield. An application in the theory of exponential growth rates of discrete inclusions is presented. This application motivates the analysis of infinite-horizon optimal control problems with running yields that are unbounded from below.

Suggested Citation

  • F. Wirth, 2001. "Asymptotic Behavior of the Value Functions of Discrete-Time Discounted Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 110(1), pages 183-210, July.
    • Handle: RePEc:spr:joptap:v:110:y:2001:i:1:d:10.1023_a:1017503815092
    DOI: 10.1023/A:1017503815092
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    References listed on IDEAS

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    1. Fabian Wirth, 1993. "Convergence of the Value Functions of Discounted Infinite Horizon Optimal Control Problems with Low Discount Rates," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 1006-1019, November.
    2. Fritz Colonius, 1989. "Asymptotic Behaviour of Optimal Control Systems with Low Discount Rates," Mathematics of Operations Research, INFORMS, vol. 14(2), pages 309-316, May.
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