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Distributed Finite-Time and Fixed-Time Nash Equilibrium Seeking for Non-Cooperative Game with Input Saturation

Author

Listed:
  • Dong Wang

    (College of Engineering, China University of Petroleum—Beijing at Karamay, Karamay 834000, China)

  • Zhenzhen Gao

    (College of Engineering, China University of Petroleum—Beijing at Karamay, Karamay 834000, China)

  • Long Sheng

    (College of Engineering, China University of Petroleum—Beijing at Karamay, Karamay 834000, China)

Abstract

In this paper, a modified distributed Nash equilibrium seeking problem with input saturation has been investigated. The payoff function of each player is related to the communication topology, which is closer to the actual scenes. The sigmoid function is utilized to limit the range of the input. Through the network communication between players and the gradient of the players’ payoff functions, the finite-time and fixed-time distributed Nash equilibrium seeking protocols with input saturation are given. Using the Lyapunov stability analysis, it is determined that the action of each player converges to the Nash equilibrium if all the players update their action according to the proposed algorithms. The numerical simulations are also provided to testify the algorithms.

Suggested Citation

  • Dong Wang & Zhenzhen Gao & Long Sheng, 2023. "Distributed Finite-Time and Fixed-Time Nash Equilibrium Seeking for Non-Cooperative Game with Input Saturation," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2295-:d:1147214
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