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Optimal control of generalized multiobjective games with application to traffic networks modeling

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  • Nguyen Van Hung
  • André A. Keller

Abstract

The purpose of this paper is to study some new results on the existence and convergence of the solutions to controlled systems of generalized multiobjective games, controlled systems of traffic networks, and optimal control problems (OCPs). First, we introduce the controlled systems of generalized multiobjective games and establish the existence of the solutions for these systems using Browder‐type fixed point theorem in the noncompact case and the Ci$C_i$‐quasi‐concavity. Results on the convergence of controlled systems of the solutions for such problems using the auxiliary solution sets and the extended Ci$C_i$‐convexity of the objective functions are studied. Second, we investigate OCPs governed by generalized multiobjective games. The existence and convergence of the solutions to these problems are also obtained. Finally, as a real‐world application, we consider the special case of controlled systems of traffic networks. Many examples are given for the illustration of our results.

Suggested Citation

  • Nguyen Van Hung & André A. Keller, 2023. "Optimal control of generalized multiobjective games with application to traffic networks modeling," Mathematische Nachrichten, Wiley Blackwell, vol. 296(8), pages 3676-3698, August.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:8:p:3676-3698
    DOI: 10.1002/mana.202100486
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