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Distributed Nash equilibrium Seeking for General Networked Games With Bounded Disturbances

IEEE/CAA Journal of Automatica Sinica 2023年第2期10卷 376-387页

作者： Maojiao Ye Danhu Li Qing-Long Han Lei Ding IEEE the School of Automation Nanjing University of Science and TechnologyNanjing 210094China the School of Science Computing and Engineering TechnologiesSwinburne University of TechnologyMelbourneVIC 3122Australia the Institute of Advanced Technology Nanjing University of Posts and TelecommunicationsNanjing 210023China

This paper is concerned with anti-disturbance Nash equilibrium seeking for games with partial information.First,reduced-order disturbance observer-based algorithms are proposed to achieve Nash equilibrium seeking for games with firstorder and second-order players,respectively.In the developed algorithms,the observed disturbance values are included in control signals to eliminate the influence of disturbances,based on which a gradient-like optimization method is implemented for each player.Second,a signum function based distributed algorithm is proposed to attenuate disturbances for games with secondorder integrator-type players.To be more specific,a signum function is involved in the proposed seeking strategy to dominate disturbances,based on which the feedback of the velocity-like states and the gradients of the functions associated with players achieves stabilization of system dynamics and optimization of players'objective functions.Through Lyapunov stability analysis,it is proven that the players'actions can approach a small region around the Nash equilibrium by utilizing disturbance observerbased strategies with appropriate control gains.Moreover,exponential(asymptotic)convergence can be achieved when the signum function based control strategy(with an adaptive control gain)is employed.The performance of the proposed algorithms is tested by utilizing an integrated simulation platform of virtual robot experimentation platform(V-REP)and MATLAB.

关键词： Distributed networks disturbance rejection Nash equilibrium networked games

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Fully Distributed Nash equilibrium Seeking for High-Order Players With Actuator Limitations

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IEEE/CAA Journal of Automatica Sinica 2023年第6期10卷 1434-1444页

作者： Maojiao Ye Qing-Long Han Lei Ding Shengyuan Xu the School of Automation Nanjing University of Science and TechnologyNanjing 210094China the School of Science Computing and Engineering TechnologiesSwinburne University of TechnologyMelbourne VIC 3122Australia the Institute of Advanced Technology Nanjing University of Posts and TelecommunicationsNanjing 210023China

This paper explores the problem of distributed Nash equilibrium seeking in games, where players have limited knowledge on other players' actions. In particular, the involved players are considered to be high-order integrators with their control inputs constrained within a pre-specified region. A linear transformation for players' dynamics is firstly utilized to facilitate the design of bounded control inputs incorporating multiple saturation functions. By introducing consensus protocols with adaptive and time-varying gains, the unknown actions for players are distributively estimated. Then, a fully distributed Nash equilibrium seeking strategy is exploited, showcasing its remarkable properties: (1) ensuring the boundedness of control inputs;(2) avoiding any global information/parameters;and (3) allowing the graph to be directed. Based on Lyapunov stability analysis, it is theoretically proved that the proposed distributed control strategy can lead all the players' actions to the Nash equilibrium. Finally, an illustrative example is given to validate effectiveness of the proposed method.

关键词： Actuator limitation directed networks games Nash equilibrium

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A Bayesian Approach with Prior Mixed Strategy Nash equilibrium for Vehicle Intention Prediction

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Automotive Innovation 2023年第3期6卷 425-437页

作者： Giovanni Lucente Reza Dariani Julian Schindler Michael Ortgiese Institute of Transporation Systems German Aerospace Center(DLR)Lilienthalplatz 738108 BraunschweigGermany Fakultat Verkehrs‑und Maschinensysteme TU BerlinStrabe des 17.Juni 13510623 BerlinGermany

The state-of-the-art technology in the field of vehicle automation will lead to a mixed traffic environment in the coming years,where connected and automated vehicles have to interact with human-driven vehicles.In this context,it is necessary to have intention prediction models with the capability of forecasting how the traffic scenario is going to evolve with respect to the physical state of vehicles,the possible maneuvers and the interactions between traffic participants within the seconds to come.This article presents a Bayesian approach for vehicle intention forecasting,utilizing a game-theoretic framework in the form of a Mixed Strategy Nash equilibrium(MSNE)as a prior estimate to model the reciprocal influence between traffic participants.The likelihood is then computed based on the Kullback-Leibler divergence.The game is modeled as a static nonzero-sum polymatrix game with individual preferences,a well known strategic game.Finding the MSNE for these games is in the PPAD∩PLS complexity class,with polynomial-time tractability.The approach shows good results in simulations in the long term horizon(10s),with its computational complexity allowing for online applications.

关键词： Vehicle intention prediction Trajectory prediction Bayesian approach Mixed strategy Nash equilibrium

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Distributed heavy-ball algorithm of Nash equilibrium seeking for aggregative games

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Journal of Control and Decision 2022年第4期9卷 489-501页

作者： Xu Yang Wei Ni School of Information Engineering Nanchang UniversityNanchangPeople’s Republic of China School of Science Nanchang UniversityNanchangPeople’s Republic of China

In this paper,we consider the Nash equilibrium(NE)seeking problem for aggregative games and design a distributed heavy-ball algorithm to solve it.This algorithm has faster convergence rate than the well-known distributed first-order algorithms for aggregative games.In order to seek the NE,each player needs to exchange information with its neighbours as well as a cen-tral aggregation.For aggregative games,the aggregative term can be either linear or nonlinear in this paper.Furthermore,we consider the generalised Nash equilibrium seeking problem for aggregative games by taking into account the linear coupled constraints among players,and modify our initial algorithm to include game constraints.

关键词： Aggregative games distributed heavy-ball algorithm Nash equilibrium coupled constraint generalised Nash equilibrium

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Nash equilibrium computation of two-network zero-sum games with event-triggered communication

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Journal of Control and Decision 2022年第3期9卷 334-346页

作者： Hongyun Xiong Jiangxiong Han Xiaohong Nian Shiling Li School of Automation Central South UniversityChangshaPeople’s Republic of China

In this paper,a zero-sum game Nash equilibrium computation problem with event-triggered communication is investigated under an undirected weight-balanced multi-agent network.A novel distributed event-triggered projection subgradient algorithm is developed to reduce the communication burden within the subnetworks.In the proposed algorithm,when the difference between the current state of the agent and the state of the last trigger time exceeds a given threshold,the agent will be triggered to communicate with its neighbours.Moreover,we prove that all agents converge to Nash equilibrium by the proposed algorithm.Finally,two simulation examples verify that our algorithm not only reduces the communication burden but also ensures that the convergence speed and accuracy are close to that of the time-triggered method under the appropriate threshold.

关键词： Zero-sum game Nash equilibrium multi-agent network event-triggered communication projection subgradient algorithm

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Nash equilibrium seeking over directed graphs

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Autonomous Intelligent Systems 2022年第1期2卷 79-86页

作者： Yutao Tang Peng Yi Yanqiong Zhang Dawei Liu School of Artificial Intelligence Beijing University of Posts and TelecommunicationsBeijing100876China Department of Control Science and Engineering Tongji UniversityShanghai200092China Shanghai Institute of Intelligent Science and Technology Tongji UniversityShanghai200092China School of Automation Hangzhou Dianzi UniversityHangzhou310018China China Research and Development Academy of Machinery Equipment Beijing100086China.

In this paper,we aim to develop distributed continuous-time algorithms over directed graphs to seek the Nash equilibrium in a noncooperative game.Motivated by the recent consensus-based designs,we present a distributed algorithm with a proportional gain for weight-balanced directed graphs.By further embedding a distributed estimator of the left eigenvector associated with zero eigenvalue of the graph Laplacian,we extend it to the case with arbitrary strongly connected directed graphs having possible unbalanced weights.In both cases,the Nash equilibrium is proven to be exactly reached with an exponential convergence rate.An example is given to illustrate the validity of the theoretical results.

关键词： Nash equilibrium Directed graph Exponential convergence Proportional control Distributed computation

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On the finite horizon Nash equilibrium solution in the differential game approach to formation control

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Journal of Systems Engineering and Electronics 2019年第6期30卷 1233-1242页

作者： JOND Hossein Barghi NABIYEV Vasif Department of Computer Engineering Karadeniz Technical University

The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if solvable)can be solved numerically by using the terminal value and the backward iteration.To investigate the solvability and solution of these equations the formation control problem as the differential game is replaced by a discrete-time dynamic game.The main contributions of this paper are as follows.First,the existence of Nash equilibrium controls for the discretetime formation control problem is shown.Second,a backward iteration approximate solution to the coupled Riccati differential equations in the continuous-time differential game is developed.An illustrative example is given to justify the models and solution.

关键词： formation control differential game dynamic game Nash equilibrium coupled Riccati equations.

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Comparing Competition equilibrium with Nash equilibrium in Electric Power Market

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CSEE Journal of Power and Energy Systems 2018年第3期4卷 299-304页

作者： Haibing Wang Jian Deng Chengmin Wang Weiqing Sun Ning Xie Department of Electrical Engineering Shanghai Jiaotong UniversityShanghai 200240China Department of Business Administration Jilin University of Finance&EconomicsChangchun 130117China Department of Electrical Engineering University of Shanghai for Science&TechnologyShanghai 200093China

The Nash equilibrium and competition equilibrium have been widely studied in the electric power market up to now.In this paper,it is explained that the Nash equilibrium can be achieved by using marginal cost pricing and the com-petition equilibrium can be performed by using accounting cost pricing based on the model of the power market system.The comparison between the Nash equilibrium and competition equilibrium indicates that surplus and unfair allocation of market benefits may be obtained by the Nash equilibrium,and the competition equilibrium realizes the optimization in economics with maximum market efficiency and fairness for market benefit allocations while the optimization in mathematics is achieved by the Nash equilibrium.There is sameness between the Nash equilibrium and competition equilibrium at the point when the power network characteristics are disregarded.The case study is made on a IEEE 30-bus system,and the calculation results indicate that it is the key issue to perform the competition equilibrium by using accounting cost pricing.

关键词： Accounting cost pricing competition equilibrium marginal cost pricing market failure market surplus Nash equilibrium power market

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A Rational Secret Sharing Scheme Against Coalition Based on Nash equilibrium and Neighbor's Strategy

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Chinese Journal of Electronics 2014年第3期23卷 564-568页

作者： CAI Cheng WANG Bojun Ditta Allah YANG Yi School of Electronic and Computer Engineering Shenzhen Graduate SchoolPeking University College of Computer Science and Technology Beijing University of Technology

In order to prevent any arbitrary subsets of coalition in rational secret sharing, we propose a new oneway information transmission mechanism, every player in a rational secret sharing protocol only interacts with his around two players, which means his decision is strictly based on previous neighboring player’s strategy. Combined with the punishment strategy of Maleka’s scheme and payoff distribution principle in Game Theory, our scheme is capable of achieving Nash equilibrium and has the feature of anti-coalition. For the conspirators, getting the secret at the same time or in less than necessary iteration rounds is almost impossible. Without repeated involvement of the dealer, our scheme has the features of verifiability, anticoalition, and more meaningfully, superiority of approaching reality model by taking rational behavior into consideration.

关键词： Secret sharing Game theory Anti-coalition Nash equilibrium One-way transmission

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Concurrent Learning-based Approximate Feedback-Nash equilibrium Solution of N-player Nonzero-sum Differential Games

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IEEE/CAA Journal of Automatica Sinica 2014年第3期1卷 239-247页

作者： Rushikesh Kamalapurkar Justin R.Klotz Warren E.Dixon the Department of Mechanical and Aerospace Engineering University of Florida

This paper presents a concurrent learning-based actor-critic-identifier architecture to obtain an approximate feedback-Nash equilibrium solution to an infinite horizon Nplayer nonzero-sum differential game.The solution is obtained online for a nonlinear control-affine system with uncertain linearly parameterized drift dynamics.It is shown that under a condition milder than persistence of excitation(PE),uniformly ultimately bounded convergence of the developed control policies to the feedback-Nash equilibrium policies can be established.Simulation results are presented to demonstrate the performance of the developed technique without an added excitation signal.

关键词： Convergence Function approximation Games Learning (artificial intelligence) Stability analysis Trajectory Nonlinear system data driven control dynamic programming optimal adaptive control Converge excitation signal Approximate function approximation Stability analysis differential games Nonlinear systems trajectory Game theory Nash equilibrium dynamic programming adaptive control

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