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An approach for an algorithmic solution of discrete optimal control problems and their game-theoretical extension

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Abstract

We consider time discrete systems which are described by a system of difference equations. The related discrete optimal control problems are introduced. Additionally, a gametheoretic extension is derived, which leads to general multicriteria decision problems. The characterization of their optimal behavior is studied. Given starting and final states define the decision process; applying dynamic programming techniques suitable optimal solutions can be gained. We generalize that approach to a special gametheoretic decision procedure on networks. We characterize Nash equilibria and present sufficient conditions for their existence. A constructive algorithm is derived. The sufficient conditions are exploited to get the algorithmic solution. Its complexity analysis is presented and at the end we conclude with an extension to the complementary case of Pareto optima.

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Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Academy of Sciences, Academy str., 5, Chisinau, 2028, Moldova

    Dmitrii Lozovanu

  2. Institut fur Angewandte Systemwissenschaften und Wirtschaftsinformatik, Fakultät fur Informatik, Universität der Bundeswehr München, Munich, Germany

    Stefan Pickl

Authors
  1. Dmitrii Lozovanu
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  2. Stefan Pickl
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Correspondence to Dmitrii Lozovanu.

Additional information

Dmitrii Lozovanu was Supported by BGP CRDF-MRDA MOM2-3049-CS-03.

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Lozovanu, D., Pickl, S. An approach for an algorithmic solution of discrete optimal control problems and their game-theoretical extension. cent.eur.j.oper.res. 14, 357–375 (2006). https://doi.org/10.1007/s10100-006-0010-y

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  • DOI: https://doi.org/10.1007/s10100-006-0010-y

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