Distributed Nash Equilibrium Seeking Algorithm And Its Application Based On Event-Triggered Mechanism

In recent years,game theory has received much attention on account of its wide applications in the area of the power grid,resource allocation,and mobile ad-hoc networks.Among them,the seeking for Nash equilibrium in non-cooperative games has always been a hot topic for researchers.In addition,with the continuous development of communication technology and artificial intelligence,reducing the waste of communication resources and making full use of broadband resources has become a key issue.Since the event-triggered control adopts aperiodic sampling,it has become an important technology to solve this problem.Based on this,this paper studies the Nash equilibrium seeking problem of distributed non-cooperative games under an event-triggered mechanism.The main work includes:For the non-cooperative game problem under the topology of directed communication,because the player cannot obtain the action information of all the players,he can only update his actions by estimating the actions of other players by local neighbors.Firstly,a static eventtriggered mechanism is designed,so that only when the event-triggered condition is satisfied,the players can interact with their neighbors and estimate the actions of other players.Lyapunov stability theory is used to prove that the states and estimates of players in this mechanism converge exponentially to the unique Nash equilibrium point.Secondly,the dynamic event-triggered mechanism is designed by introducing auxiliary variables,and Zeno behavior is excluded by using the proof method.Finally,the proposed Nash equilibrium seeking strategy is applied to the user game problem in the electricity trading market,and the correctness and effectiveness of the method are demonstrated by simulation.To solve the problem that player dynamics may be subject to unmodeled and disturbing terms in engineering applications,a Nash equilibrium seeking method for non-cooperative games is studied.Firstly,the radial basis function neural network is used to fit the unmodeled items,and the symbol function is used to deal with the perturbation items.Based on this,a Nash equilibrium seeking strategy based on the event-triggered mechanism of the adaptive neural network is proposed to counteract the influence of the disturbance on the actions of the players.Secondly,through stability analysis,it is proved that under certain assumptions,the states and estimates of the players converge asymptotically to the unique Nash equilibrium.Finally,the validity of the seeking strategy is verified by numerical simulation,and the game problem of the communication trading market is solved by using the strategy.The paper has 20 pictures,3 tables,and 90 references.