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

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  • Dmitrii Lozovanu
  • Stefan Pickl

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. Copyright Springer-Verlag 2006

Suggested Citation

  • Dmitrii Lozovanu & Stefan Pickl, 2006. "An approach for an algorithmic solution of discrete optimal control problems and their game-theoretical extension," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 14(4), pages 357-375, December.
    • Handle: RePEc:spr:cejnor:v:14:y:2006:i:4:p:357-375
    DOI: 10.1007/s10100-006-0010-y
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