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nash equilibrium seeking with prescribed performance

Control Theory and Technology 2023年第3期21卷 437-447页

作者： Chao Sun Guoqiang Hu Continental-NTU Corporate Lab Nanyang Technological University639798 NanyangSingapore School of Electrical and Electronic Engineering Nanyang Technological University639798 NanyangSingapore

In this work,we study a nash equilibrium(NE)seeking problem for strongly monotone non-cooperative games with prescribed *** general NE seeking algorithms,the proposed prescribed-performance NE seeking laws ensure that the convergence error evolves within a predefined ***,the settling time,convergence rate,and maximum overshoot of the algorithm can be ***,we develop a second-order Newton-like algorithm that can guarantee prescribed performance and asymptotically converge to the NE of the ***,we develop a first-order gradient-based *** remove some restrictions on this first-order algorithm,we propose two discontinuous dynamical system-based algorithms using tools from non-smooth analysis and adaptive *** study the special case in optimization ***,we investigate the robustness of the *** can be proven that the proposed algorithms can guarantee asymptotic convergence to the nash equilibrium with prescribed performance in the presence of bounded ***,we consider a second-order dynamical system *** simulation results verify the effectiveness and efficiency of the algorithms,in terms of their convergence rate and disturbance rejection ability.

关键词： nash equilibrium seeking Non-cooperative games Prescribed performance Disturbance rejection

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Distributed nash equilibrium seeking on Compact Action Sets over Jointly Strongly Connected Switching Networks

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Journal of Systems Science & Complexity 2024年第1期37卷 63-81页

作者： HE Xiongnan HUANG Jie Department of Mechanical and Automation Engineering The Chinese University of Hong KongHong Kong 999077China.

This paper studies the distributed nash equilibrium seeking(DNES)problem for games whose action sets are compact and whose network graph is switching satisfying the jointly strongly connected *** keep the actions of all players in their action sets all the time,one has to resort to the projected gradient-based *** the assumption that the unique nash equilibrium is the unique equilibrium of the pseudogradient system,an algorithm is proposed that is able to exponentially find the nash ***,the authors also consider the distributed nash equilibrium seeking problem for games whose actions are governed by high-order integrator dynamics and belong to some compact *** examples are used to illustrate the proposed approach.

关键词： Compact action sets jointly strongly connected switching graphs nash equilibrium seeking projected gradient-based algorithm.

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

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Control Theory and Technology 2023年第3期21卷 363-373页

作者： Shu Liang Shuyu Liu Yiguang Hong Jie Chen The Department of Control Science and Engineering Tongji UniversityShanghai 201804China Shanghai Research Institute for Intelligent Autonomous Systems Shanghai 201210China

In this paper,we consider a networked game with coupled constraints and focus on variational nash equilibrium *** 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 ***,these conditions are only based on strategy and multiplier variables,without auxiliary ***,we present a distributed order-reduced dynamics that updates the strategy and multiplier variables with guaranteed *** with many other distributed algorithms,our algorithm contains no auxiliary variable,and therefore,it can save computation and communication.

关键词： Game theory nash equilibrium seeking Distributed algorithm Coupled constraints Order-reduced dynamics

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Distributed best response dynamics for nash equilibrium seeking in potential games

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Control Theory and Technology 2020年第3期18卷 324-332页

作者： Shijie HUANG Peng YI Key Lab of Systems and Control Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100190China Department of Control Science&Engineering Tongji UniversityShanghai 201804China Shanghai Institute of Intelligent Science and Technology Tongji UniversityShanghai 201804China

In this paper,we consider distributed nash equilibrium(NE)seeking in potential games over a multi-agent network,where each agent can not observe the actions of all its *** on the best response dynamics,we design a distributed NE seeking algorithm by incorporating the non-smooth finite-time average tracking dynamics,where each agent only needs to know its own action and exchange information with its neighbours through a communication *** give a sufficient condition for the Lipschitz continuity of the best response mapping for potential games,and then prove the convergence of the proposed algorithm based on the Lyapunov *** simulations are given to verify the resultandillustrate the effectiveness of the algorithm.

关键词： Distributed algorithms nash equilibrium seeking best response dynamics non-smooth finite-time tracking dynamics potential games

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Simultaneous Social Cost Minimization and nash equilibrium seeking in Non-cooperative Games 36

Simultaneous Social Cost Minimization and Nash Equilibrium S...

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第36届中国控制会议

作者： Maojiao Ye Guoqiang Hu School of Electrical and Electronic Engineering Nanyang Technological University

ISBN: (纸本)9781538629185

An N-coalition non-cooperative game is formulated in this paper. In the considered game, there are N interacting coalitions and each of them includes a set of agents. Each coalition acts as a virtual player（VP） in the game that aims to minimize its own objective function, which is defined as the sum of the agents’ local objective functions in the coalition. However, the actual decision-makers are not the coalitions but the agents therein. That is, the agents within each coalition collaboratively minimize the coalition’s objective function while constituting an entity that serves as a self-interested player（i.e., the coalition）in the game among the interacting coalitions. A seeking strategy is designed for the agents to find the nash equilibrium of the N-coalition non-cooperative games. The equilibrium seeking strategy is based on an adaptation of a dynamic average consensus protocol and the gradient play. The dynamic average consensus protocol is leveraged to estimate the averaged gradients of the coalitions’ objective functions. The gradient play is then implemented by utilizing the estimated information to achieve the nash equilibrium seeking. Convergence results are established by utilizing Lyapunov stability analysis. A numerical example is given in supportive of the theoretical results.

关键词： nash equilibrium seeking social cost minimization interacting coalitions non-cooperative game

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Distributed Heavy-Ball nash equilibrium seeking Algorithm in Aggregative Games

Distributed Heavy-Ball Nash Equilibrium Seeking Algorithm in...

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第三十九届中国控制会议

作者： Chenhui Song Chenpeng Wu Zhongtao Lv Fangshuo Zhang Jingyu Li Shaofu Yang Chien-Shiung Wu College Southeast University School of Economics and Management Southeast University School of Computer Science and Engineering Southeast University

In this paper, we address the distributed nash equilibrium seeking problem in an aggregative game, in which each agent is required to optimize a self-interested objective function that depends on both its own decision and the aggregate of all agents’ decisions. By integrating the heavy-ball method with consensus-based gradient method, a novel distributed algorithm is proposed for seeking the nash equilibrium with an improved convergence rate. Rigorous theoretical analysis is provided to prove the convergence of the algorithm. Finally, detailed numerical simulation results are provided to show the effectiveness and the acceleration performance of our algorithm.

关键词： Aggregative Game nash equilibrium seeking Distributed Algorithm Heavy-Ball Method

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