亚洲免费av电影一区二区三区,日韩爱爱视频,51精品视频一区二区三区,91视频爱爱,日韩欧美在线播放视频,中文字幕少妇AV,亚洲电影中文字幕,久久久久亚洲av成人网址,久久综合视频网站,国产在线不卡免费播放

        ?

        Fixed-Time Consensus-Based Nash Equilibrium Seeking

        2024-01-27 07:00:14MengweiSunJianLiuLuRenandChangyinSunSenior
        IEEE/CAA Journal of Automatica Sinica 2024年1期

        Mengwei Sun , Jian Liu ,,, Lu Ren , and Changyin Sun , Senior,

        Dear Editor,

        This letter examines the fixed-time stability of the Nash equilibrium (NE) in non-cooperative games.We propose a consensus-based NE seeking algorithm for situations where players do not have perfect information and communicate via a topology graph.The proposed algorithm can achieve NE in a fixed time that does not depend on initial conditions and can be adjusted in advance.In this strategy,players use their estimates of other players’ actions to update their own actions.We present sufficient conditions that ensure the fixedtime stability of the NE through rigorous Lyapunov stability analysis.Finally, we provide an example to verify the feasibility of the theoretical result.

        Game theoretic methods have become prevalent in engineering applications, such as power allocation [1], cooperative control [2],[3], energy consumption control [4], and self-driving [5].Once a specific problem has been modeled as a game, the question becomes how to find the NE.In a game, each player aims to find a strategy that minimizes its own cost function.The NE of a game is a set of actions for which players can no longer decrease their cost functions by solely changing their own actions.In [1], the zero-sum game of two networks of agents was investigated.The potential game and aggregate game were considered in [2] and [4], respectively.For more generalized non-cooperative games, an extreme seeking based method was developed in [6], but it required global information,which may not be applicable to practical problems.To tackle this issue, researchers have paid attention to studying NE seeking strategies under imperfect information.In [7], a gossip-based algorithm was designed for discrete-time NE seeking.In [8], the authors proposed a continuous-time NE seeking algorithm that incorporates a consensus protocol [9]-[14].A passivity-based approach was developed in [15] for nonlinear and heterogeneous players.The papers[16]-[18] studied NE seeking under disturbance, control input saturation, and switching topologies, respectively.

        The convergence rate is an important index for evaluating system performance.While the aforementioned results all achieved NE with an asymptotic convergence rate, where the fastest rate is exponential,the infinite convergence time usually does not meet the requirement of practical systems.To acquire NE more quickly, Fanget al.[19]proposed two finite-time NE seeking algorithms that employ signum and saturation functions.However, the convergence time of the finite-time result is related to the initial conditions, which are not always available in practice.To overcome this disadvantage, the authors of [20] proposed a fixed-time NE seeking algorithm based on extreme seeking.The prescribed-time algorithms were developed based on the motion-planning method in [21] and the time base generator in [22].

        Inspired by the fixed-time leader-following consensus protocol in[13], a new algorithm for fixed-time NE seeking under a communication graph is proposed by integrating leader-following consensus and gradient play in this letter.It is not a trivial extension, and difficulties arise from two aspects.Firstly, in the fixed-time leader-following consensus problem, the leader’s input is commonly assumed to be bounded.In the consensus-based NE seeking algorithm, the action update law is considered the leader’s input.However, to achieve fixed-time NE seeking, the action update law cannot be bounded.Secondly, the traditional quadratic form of the Lyapunov function is not applicable.The nonlinearity of the gradient play exists in the action update law, making the stability analysis more difficult.

        The contributions of this letter are summarized as follows.First,the proposed method extends the asymptotic consensus-based NE seeking strategies [8], [16], [18] to achieve a fixed-time convergence result.A new Lyapunov function is designed to prove fixed-time convergence.Moreover, it is a distinct method from that presented in[20].The explicit form of the settling time is given, which is independent of the initial conditions and only relies on the design parameters, allowing it to be predetermined prior to system operation.Second, in contrast to the NE seeking strategy studied in [22], which steers actions to a neighborhood of the NE with size dependent on the initial conditions, the proposed algorithm in this letter attains the exact NE.

        Fig.1.Communication topology between the three players.

        Fig.2 displays the evolution of the players’ actions under the proposed fixed-time NE seeking algorithm, which obtains the NE in 7 s.Fig.3 illustrates the players’ estimates of the actions, with the estimated values rapidly converging to the actual actions.

        Fig.2.Plot of the actions of players.

        Fig.3.Plot of the players’ estimates on actions.

        Conclusion: This letter investigates the fixed-time stability of the NE in networked games and provides an upper bound for the settling time.Future work can extend the proposed NE seeking algorithm to achieve prescribed-time convergence, realize fully distributed control, incorporate an event-triggered mechanism, or tackle practical situations such as switching topologies, external disturbances, and players with higher-order dynamics.It can also be adapted to solve different types of games, such as aggregative games and multi-cluster games.

        Acknowledgments: This work was supported by the National Natural Science Foundation of China (62373107, 61921004, 62303009),the Natural Science Foundation of Jiangsu Province of China(BK20202006), and the “Zhishan” Scholars Programs of Southeast University.

        乌克兰粉嫩xxx极品hd| 国产精品国产三级国产an不卡| 噜噜中文字幕一区二区| 毛片免费视频在线观看| 99久久综合狠狠综合久久| 中国人妻沙发上喷白将av| 国产亚洲综合另类色专区| 日韩av无码一区二区三区不卡| 色噜噜狠狠色综合成人网| 欧美高h视频| 国产三级不卡视频在线观看| 亚洲女同一区二区| 亚洲男同志gay 片可播放| 久久久亚洲精品免费视频| 亚洲写真成人午夜亚洲美女| 久久精品国产免费观看| 亚洲va在线va天堂va手机| 成人偷拍自拍在线视频| av网站在线观看入口| 中文字幕精品一二三四五六七八| 久久中国国产Av秘 入口| 青青草视频在线播放观看| 亚洲av无码一区二区一二区| 永久免费不卡在线观看黄网站| 产精品无码久久_亚洲国产精| 日本久久精品视频免费| 亚洲精品乱码8久久久久久日本| 国产精品18禁久久久久久久久| 中文字幕丰满人妻有码专区| 最新露脸自拍视频在线观看| 内射无码专区久久亚洲| 国产成社区在线视频观看| 中文字幕一区二区av| 亚洲国产精品久久人人爱 | 国产成人夜色在线视频观看| 日韩精品久久中文字幕| 无码精品人妻一区二区三区影院| 日本一区二区三区中文字幕最新| 国产精品自拍午夜伦理福利| 亚洲乱亚洲乱妇50p| 亚洲国产精品久久艾草|