Robust Distributed Nash Equilibrium Seeking Subject to Communication Constraints

In this article, we address the robust distributed Nash equilibrium seeking problem of <inline-formula><tex-math notation="LaTeX">N</tex-math></inline-formula>-player games under switching networks and communication delays. The salient feature of this work is that t...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 70; no. 3; pp. 1941 - 1948
Main Authors: Liu, Lupeng, Lu, Maobin, Wang, Shimin, Deng, Fang, Chen, Jie
Format: Journal Article
Language:English
Published: New York IEEE 01.03.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Closed loops
Communication
Communication networks
Communications networks
Cost function
Delays
Distributed algorithms
distributed Nash equilibrium (NE) seeking
Equilibrium
Feedback control
Game theory
Games
Information exchange
Motion control
multi-agent systems
Nash equilibrium
Non-cooperative game
Robot control
Robot dynamics
robust control
Robustness
Subsystems
Switches
unreliable communication networks
Vectors
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:In this article, we address the robust distributed Nash equilibrium seeking problem of <inline-formula><tex-math notation="LaTeX">N</tex-math></inline-formula>-player games under switching networks and communication delays. The salient feature of this work is that the switching communication networks can be uniformly strongly connected, and the communication delays are allowed to be arbitrarily unknown, time-varying and bounded. To solve the problem, we construct a distributed estimator for each player to estimate all players' strategies through unreliable communication networks. Based on the gradient play technique, we design a distributed Nash equilibrium seeking law. Then, we obtain the closed-loop system, which is an interconnected system of a nonlinear subsystem and a linear time-delay subsystem. By constructing the Lyapunov-Krasovskii functional, and designing the controller parameter in the sense of the small gain theorem, we achieve robust Nash equilibrium seeking asymptotically in spite of unreliable communication networks. Finally, we illustrate our proposed approach by its application to practical motion control of mobile robots with an experiment.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2024.3476195