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Distributed Nash equilibrium seeking with order-reduced dynamics based on consensus exact penalty

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Abstract

In this paper, we consider a networked game with coupled constraints and focus on variational Nash equilibrium seeking. For distributed algorithm design, we eliminate the coupled constraints by employing local Lagrangian functions and construct exact penalty terms to attain multipliers’ optimal consensus, which yields a set of equilibrium conditions without any coupled constraint and consensus constraint. Moreover, these conditions are only based on strategy and multiplier variables, without auxiliary variables. Then, we present a distributed order-reduced dynamics that updates the strategy and multiplier variables with guaranteed convergence. Compared with many other distributed algorithms, our algorithm contains no auxiliary variable, and therefore, it can save computation and communication.

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Authors and Affiliations

  1. The Department of Control Science and Engineering, Tongji University, Shanghai, 201804, China

    Shu Liang, Shuyu Liu, Yiguang Hong & Jie Chen

  2. Shanghai Research Institute for Intelligent Autonomous Systems, Shanghai, 201210, China

    Shu Liang, Shuyu Liu, Yiguang Hong & Jie Chen

Authors
  1. Shu Liang
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  2. Shuyu Liu
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  3. Yiguang Hong
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  4. Jie Chen
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Corresponding author

Correspondence to Yiguang Hong.

Additional information

This work was supported in part by the National Key Research and Development Program of China under grant 2022YFA1004700, and in part by the Natural Science Foundation of China under grant 72171171, and in part by Shanghai Municipal Science and Technology Major Project under grant 2021SHZDZX0100.

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Liang, S., Liu, S., Hong, Y. et al. Distributed Nash equilibrium seeking with order-reduced dynamics based on consensus exact penalty. Control Theory Technol. 21, 363–373 (2023). https://doi.org/10.1007/s11768-023-00166-7

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  • DOI: https://doi.org/10.1007/s11768-023-00166-7

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