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 condition.To keep the act...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 condition.To keep the actions of all players in their action sets all the time,one has to resort to the projected gradient-based method.Under 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 equilibrium.Further,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 sets.Two examples are used to illustrate the proposed approach.展开更多
This paper focuses on the impulsive orbital pursuit–evasion game(OPEG)with limited action sets for the pursuer and evader.Initially,a mathematical model is developed by combining game theory and orbital dynamics,form...This paper focuses on the impulsive orbital pursuit–evasion game(OPEG)with limited action sets for the pursuer and evader.Initially,a mathematical model is developed by combining game theory and orbital dynamics,forming a finite-round impulsive OPEG problem.The problem is then formulated as a bilateral optimization problem,employing a minimum-maximum optimization index based on terminal distance.To tackle this problem,an algorithm based on game tree search is designed,enabling the determination of the optimal pursuit–evasion strategy with limited action sets.Additionally,we explore the influence of the initial pursuing orientation on OPEG.The optimal initial pursuit orientation is analytically derived using relative motion dynamics under uncontrolled conditions.Furthermore,considering factors such as the initial status of the pursuit spacecraft,initial relative distance,transfer time,and maneuverability,the impulsive OPEG problem with limited action sets is numerically solved using game tree search.The findings of this study showcase the efficacy of game tree search in addressing impulsive OPEG problems with limited action sets.The study also demonstrates that the initial pursuing orientation selection at the start of the game plays a crucial role in increasing the success rate of pursuit.The research findings of this study have important implications for future practical engineering applications.展开更多
基金supported in part by the Research Grants Council of the Hong Kong Special Administration Region under Grant No.14202619in part by the National Natural Science Foundation of China under Grant No.61973260。
文摘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 condition.To keep the actions of all players in their action sets all the time,one has to resort to the projected gradient-based method.Under 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 equilibrium.Further,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 sets.Two examples are used to illustrate the proposed approach.
基金supported by the National Natural Science Foundation of China(No.12172288)the National Key Basic Research Program of China:Gravitational Wave Detection Project(Nos.2021YFC2202601 and 2021YFC2202603).
文摘This paper focuses on the impulsive orbital pursuit–evasion game(OPEG)with limited action sets for the pursuer and evader.Initially,a mathematical model is developed by combining game theory and orbital dynamics,forming a finite-round impulsive OPEG problem.The problem is then formulated as a bilateral optimization problem,employing a minimum-maximum optimization index based on terminal distance.To tackle this problem,an algorithm based on game tree search is designed,enabling the determination of the optimal pursuit–evasion strategy with limited action sets.Additionally,we explore the influence of the initial pursuing orientation on OPEG.The optimal initial pursuit orientation is analytically derived using relative motion dynamics under uncontrolled conditions.Furthermore,considering factors such as the initial status of the pursuit spacecraft,initial relative distance,transfer time,and maneuverability,the impulsive OPEG problem with limited action sets is numerically solved using game tree search.The findings of this study showcase the efficacy of game tree search in addressing impulsive OPEG problems with limited action sets.The study also demonstrates that the initial pursuing orientation selection at the start of the game plays a crucial role in increasing the success rate of pursuit.The research findings of this study have important implications for future practical engineering applications.
