Distributed Finite-Time and Fixed-Time Nash Equilibrium Seeking for Non-Cooperative Game with Input Saturation
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. Thr...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/10/2295 |
| _version_ | 1797599262098325504 |
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| author | Dong Wang Zhenzhen Gao Long Sheng |
| author_facet | Dong Wang Zhenzhen Gao Long Sheng |
| author_sort | Dong Wang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T03:31:42Z |
| format | Article |
| id | doaj.art-d81aa8286db74fe9a50aabff759f3f46 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T03:31:42Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d81aa8286db74fe9a50aabff759f3f462023-11-18T02:18:52ZengMDPI AGMathematics2227-73902023-05-011110229510.3390/math11102295Distributed Finite-Time and Fixed-Time Nash Equilibrium Seeking for Non-Cooperative Game with Input SaturationDong Wang0Zhenzhen Gao1Long Sheng2College of Engineering, China University of Petroleum—Beijing at Karamay, Karamay 834000, ChinaCollege of Engineering, China University of Petroleum—Beijing at Karamay, Karamay 834000, ChinaCollege of Engineering, China University of Petroleum—Beijing at Karamay, Karamay 834000, ChinaIn 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.https://www.mdpi.com/2227-7390/11/10/2295Nash equilibriuminput saturationfinite timesigmoid functionnon-cooperative gameLyapunov stability analysis |
| spellingShingle | Dong Wang Zhenzhen Gao Long Sheng Distributed Finite-Time and Fixed-Time Nash Equilibrium Seeking for Non-Cooperative Game with Input Saturation Mathematics Nash equilibrium input saturation finite time sigmoid function non-cooperative game Lyapunov stability analysis |
| title | Distributed Finite-Time and Fixed-Time Nash Equilibrium Seeking for Non-Cooperative Game with Input Saturation |
| title_full | Distributed Finite-Time and Fixed-Time Nash Equilibrium Seeking for Non-Cooperative Game with Input Saturation |
| title_fullStr | Distributed Finite-Time and Fixed-Time Nash Equilibrium Seeking for Non-Cooperative Game with Input Saturation |
| title_full_unstemmed | Distributed Finite-Time and Fixed-Time Nash Equilibrium Seeking for Non-Cooperative Game with Input Saturation |
| title_short | Distributed Finite-Time and Fixed-Time Nash Equilibrium Seeking for Non-Cooperative Game with Input Saturation |
| title_sort | distributed finite time and fixed time nash equilibrium seeking for non cooperative game with input saturation |
| topic | Nash equilibrium input saturation finite time sigmoid function non-cooperative game Lyapunov stability analysis |
| url | https://www.mdpi.com/2227-7390/11/10/2295 |
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