Distributed Nash Equilibrium Seeking for Games in Second-Order Systems Without Velocity Measurement

The design of distributed Nash equilibrium-seeking strategies for games in which the involved players are of second-order integrator-type dynamics is investigated in this article. Noticing that velocity signals are usually noisy or not available for feedback control in practical engineering systems,...

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Vydáno v:	IEEE transactions on automatic control Ročník 67; číslo 11; s. 6195 - 6202
Hlavní autoři:	Ye, Maojiao, Yin, Jizhao, Yin, Le
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York IEEE 01.11.2022 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Algorithms Equilibrium Feedback control Filter Game theory Games High pass filters Marine vehicles Nash equilibrium Nash equilibrium seeking Observers Players Robot sensing systems second-order dynamics state observer Symmetric matrices Velocity Velocity measurement without velocity measurement
ISSN:	0018-9286, 1558-2523
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Abstract	The design of distributed Nash equilibrium-seeking strategies for games in which the involved players are of second-order integrator-type dynamics is investigated in this article. Noticing that velocity signals are usually noisy or not available for feedback control in practical engineering systems, this article supposes that the velocity signals are not accessible for the players. To deal with the absence of velocity measurements, two estimators are designed. The first estimator is established by employing an observer, which has the same order as the players' dynamics, to estimate the unavailable system states (e.g., the players' velocities). The second estimator is designed based on a high-pass filter and is motivated by the incentive to reduce the order of the estimator, which in turn saves the computation costs of the seeking algorithms. On the basis of the designed observers/filters, distributed Nash equilibrium-seeking strategies are then established through incorporating them with consensus and gradient algorithms. It is analytically proven that the players' actions can be regulated to the Nash equilibrium point and their velocities can be regulated to zero by utilizing the proposed velocity-free Nash equilibrium-seeking strategies. A numerical example is provided for the verification of the proposed algorithms.
AbstractList	The design of distributed Nash equilibrium-seeking strategies for games in which the involved players are of second-order integrator-type dynamics is investigated in this article. Noticing that velocity signals are usually noisy or not available for feedback control in practical engineering systems, this article supposes that the velocity signals are not accessible for the players. To deal with the absence of velocity measurements, two estimators are designed. The first estimator is established by employing an observer, which has the same order as the players’ dynamics, to estimate the unavailable system states (e.g., the players’ velocities). The second estimator is designed based on a high-pass filter and is motivated by the incentive to reduce the order of the estimator, which in turn saves the computation costs of the seeking algorithms. On the basis of the designed observers/filters, distributed Nash equilibrium-seeking strategies are then established through incorporating them with consensus and gradient algorithms. It is analytically proven that the players’ actions can be regulated to the Nash equilibrium point and their velocities can be regulated to zero by utilizing the proposed velocity-free Nash equilibrium-seeking strategies. A numerical example is provided for the verification of the proposed algorithms.
Author	Ye, Maojiao Yin, Le Yin, Jizhao
Author_xml	– sequence: 1 givenname: Maojiao orcidid: 0000-0001-5553-9124 surname: Ye fullname: Ye, Maojiao email: ye0003ao@e.ntu.edu.sg organization: School of Automation, Nanjing University of Science and Technology, Nanjing, China – sequence: 2 givenname: Jizhao orcidid: 0000-0002-4004-0168 surname: Yin fullname: Yin, Jizhao email: yinjizhao@njust.edu.cn organization: School of Automation, Nanjing University of Science and Technology, Nanjing, China – sequence: 3 givenname: Le orcidid: 0000-0001-5016-7237 surname: Yin fullname: Yin, Le email: yinle0002@swu.edu.cn organization: School of Computer, and Information Science, Southwest University, Chongqing, China
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SubjectTerms	Algorithms Equilibrium Feedback control Filter Game theory Games High pass filters Marine vehicles Nash equilibrium Nash equilibrium seeking Observers Players Robot sensing systems second-order dynamics state observer Symmetric matrices Velocity Velocity measurement without velocity measurement
Title	Distributed Nash Equilibrium Seeking for Games in Second-Order Systems Without Velocity Measurement
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