Dear Editor,This letter addresses the Nash equilibrium seeking problem for games with second-order players subject to unknown input deadzones and denial-of-service(DoS)attacks.By using ideas from the digital twin,a di...Dear Editor,This letter addresses the Nash equilibrium seeking problem for games with second-order players subject to unknown input deadzones and denial-of-service(DoS)attacks.By using ideas from the digital twin,a distributed Nash equilibrium seeking strategy is proposed.In the proposed strategy,the twin players are designed to be second-order integrators,based on which a distributed control law is provided so as to find the Nash equilibrium under DoS attacks.Moreover,adaptive control laws and sliding mode control laws are synthesized for the actual players such that they can track the twin players under unknown input dead-zones.Theoretical investigations show that the proposed strategy is effective to drive the actions of actual players to the Nash equilibrium under the given conditions.A numerical example is provided to verify the effectiveness of the proposed strategy.展开更多
Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate...Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate this impulse game problem with the modified objective function including interaction costs among the players in a discontinuous fashion,and subsequently,to derive a verification theorem for identifying the feedback Nash equilibrium strategy.展开更多
Dear Editor,This letter presents a solution to the problem of seeking Nash equilibrium(NE)in a class of non-cooperative games of multi-agent systems(MASs)subject to the input disturbance and the networked communicatio...Dear Editor,This letter presents a solution to the problem of seeking Nash equilibrium(NE)in a class of non-cooperative games of multi-agent systems(MASs)subject to the input disturbance and the networked communication.To this end,a novel distributed robust predefined-time algorithm is proposed,which ensures the precise convergence of agent states to the NE within a settling time that can be directly determined by adjusting one or more parameters.The proposed algorithm employs an integral sliding mode strategy to effectively reject disturbances.Additionally,a consensus-based estimator is designed to overcome the challenge of limited information availability,where each agent can only access information from its directly connected neighbors,which conflicts with the computation of the cost function that requires information from all agents.Finally,a numerical example is provided to demonstrate the algorithm's effectiveness and performance.展开更多
Dear Editor,This letter studies the distributed Nash equilibrium seeking problem of aggregative game,in which the decision of each player obeys second-order dynamics and is constrained by nonidentical convex sets.To s...Dear Editor,This letter studies the distributed Nash equilibrium seeking problem of aggregative game,in which the decision of each player obeys second-order dynamics and is constrained by nonidentical convex sets.To seek the generalized Nash equilibrium(GNE),a projectionbased distributed algorithm via constant step-sizes is developed with linear convergence.In particular,a variable tracking technique is incorporated to estimate the aggregative function,and an event-triggered mechanism is designed to reduce the communication cost.Finally,a numerical example demonstrates the theoretical results.展开更多
This paper presents a comprehensive overview of distributed Nash equilibrium(NE)seeking algorithms in non-cooperative games for multiagent systems(MASs),with a distinct emphasis on the dynamic control perspective.It s...This paper presents a comprehensive overview of distributed Nash equilibrium(NE)seeking algorithms in non-cooperative games for multiagent systems(MASs),with a distinct emphasis on the dynamic control perspective.It specifically focuses on the research addressing distributed NE seeking problems in which agents are governed by heterogeneous dynamics.The paper begins by introducing fundamental concepts of general non-cooperative games and the NE,along with definitions of specific game structures such as aggregative games and multi-cluster games.It then systematically reviews existing studies on distributed NE seeking for various classes of MASs from the viewpoint of agent dynamics,including first-order,second-order,high-order,linear,and Euler-Lagrange(EL)systems.Furthermore,the paper highlights practical applications of these theoretical advances in cooperative control scenarios involving autonomous systems with complex dynamics,such as autonomous surface vessels,autonomous aerial vehicles,and other autonomous vehicles.Finally,the paper outlines several promising directions for future research.展开更多
This paper designs distributed Nash equilibrium seeking strategies for heterogeneous dynamic cyber-physical systems.In particular, we are concerned with parametric uncertainties in the control channel of the players. ...This paper designs distributed Nash equilibrium seeking strategies for heterogeneous dynamic cyber-physical systems.In particular, we are concerned with parametric uncertainties in the control channel of the players. Moreover, the weights on communication links can be compromised by time-varying uncertainties, which can result from possibly malicious attacks,faults and disturbances. To deal with the unavailability of measurement of optimization errors, an output observer is constructed,based on which adaptive laws are designed to compensate for physical uncertainties. With adaptive laws, a new distributed Nash equilibrium seeking strategy is designed by further integrating consensus protocols and gradient search algorithms.Moreover, to further accommodate compromised communication weights resulting from cyber-uncertainties, the coupling strengths of the consensus module are designed to be adaptive. As a byproduct, the coupling strengths are independent of any global information. With theoretical investigations, it is proven that the proposed strategies are resilient to these uncertainties and players' actions are convergent to the Nash equilibrium. Simulation examples are given to numerically validate the effectiveness of the proposed strategies.展开更多
Dear Editor,This letter proposes a novel Nash bargaining solution-based multiobjective model predictive control(MPC)scheme to deal with the interaction force control and the path-following problem of the constrained i...Dear Editor,This letter proposes a novel Nash bargaining solution-based multiobjective model predictive control(MPC)scheme to deal with the interaction force control and the path-following problem of the constrained interactive robot.Considering the elastic interaction force model,a mechanical trade-off always exists between the interaction force and position,which means that neither force nor path following can satisfy their desired demands completely.Based on this consideration,two irreconcilable control specifications,the force object function and the position track object function,are proposed,and a new multi-objective MPC scheme is then designed.展开更多
基金supported by the National Natural Science Foundation of China(NSFC)(62222308,62173181,62221004)the Natural Science Foundation and Maojiao Ye of Jiangsu Province(BK20220139).
文摘Dear Editor,This letter addresses the Nash equilibrium seeking problem for games with second-order players subject to unknown input deadzones and denial-of-service(DoS)attacks.By using ideas from the digital twin,a distributed Nash equilibrium seeking strategy is proposed.In the proposed strategy,the twin players are designed to be second-order integrators,based on which a distributed control law is provided so as to find the Nash equilibrium under DoS attacks.Moreover,adaptive control laws and sliding mode control laws are synthesized for the actual players such that they can track the twin players under unknown input dead-zones.Theoretical investigations show that the proposed strategy is effective to drive the actions of actual players to the Nash equilibrium under the given conditions.A numerical example is provided to verify the effectiveness of the proposed strategy.
基金supported in part by the National Natural Science Foundation of China(62173051)the Fundamental Research Funds for the Central Universities(2024CDJCGJ012,2023CDJXY-010)+1 种基金the Chongqing Technology Innovation and Application Development Special Key Project(CSTB2022TIADCUX0015,CSTB2022TIAD-KPX0162)the China Postdoctoral Science Foundation(2024M763865)
文摘Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate this impulse game problem with the modified objective function including interaction costs among the players in a discontinuous fashion,and subsequently,to derive a verification theorem for identifying the feedback Nash equilibrium strategy.
基金supported by the National Natural Science Foundation of China(62373162,U24A20268,624B2055).
文摘Dear Editor,This letter presents a solution to the problem of seeking Nash equilibrium(NE)in a class of non-cooperative games of multi-agent systems(MASs)subject to the input disturbance and the networked communication.To this end,a novel distributed robust predefined-time algorithm is proposed,which ensures the precise convergence of agent states to the NE within a settling time that can be directly determined by adjusting one or more parameters.The proposed algorithm employs an integral sliding mode strategy to effectively reject disturbances.Additionally,a consensus-based estimator is designed to overcome the challenge of limited information availability,where each agent can only access information from its directly connected neighbors,which conflicts with the computation of the cost function that requires information from all agents.Finally,a numerical example is provided to demonstrate the algorithm's effectiveness and performance.
基金supported by the National Natural Science Foundation of China(62473048,61925303,62088101,62273195,U19B2029).
文摘Dear Editor,This letter studies the distributed Nash equilibrium seeking problem of aggregative game,in which the decision of each player obeys second-order dynamics and is constrained by nonidentical convex sets.To seek the generalized Nash equilibrium(GNE),a projectionbased distributed algorithm via constant step-sizes is developed with linear convergence.In particular,a variable tracking technique is incorporated to estimate the aggregative function,and an event-triggered mechanism is designed to reduce the communication cost.Finally,a numerical example demonstrates the theoretical results.
基金National Natural Science Foundation of China(62325304).
文摘This paper presents a comprehensive overview of distributed Nash equilibrium(NE)seeking algorithms in non-cooperative games for multiagent systems(MASs),with a distinct emphasis on the dynamic control perspective.It specifically focuses on the research addressing distributed NE seeking problems in which agents are governed by heterogeneous dynamics.The paper begins by introducing fundamental concepts of general non-cooperative games and the NE,along with definitions of specific game structures such as aggregative games and multi-cluster games.It then systematically reviews existing studies on distributed NE seeking for various classes of MASs from the viewpoint of agent dynamics,including first-order,second-order,high-order,linear,and Euler-Lagrange(EL)systems.Furthermore,the paper highlights practical applications of these theoretical advances in cooperative control scenarios involving autonomous systems with complex dynamics,such as autonomous surface vessels,autonomous aerial vehicles,and other autonomous vehicles.Finally,the paper outlines several promising directions for future research.
基金supported by the National Key R&D Program of China(2022ZD0119604)the National Natural Science Foundation of China(NSFC)(62173181,62222308,62221004)the Natural Science Foundation of Jiangsu Province(BK20220139)
文摘This paper designs distributed Nash equilibrium seeking strategies for heterogeneous dynamic cyber-physical systems.In particular, we are concerned with parametric uncertainties in the control channel of the players. Moreover, the weights on communication links can be compromised by time-varying uncertainties, which can result from possibly malicious attacks,faults and disturbances. To deal with the unavailability of measurement of optimization errors, an output observer is constructed,based on which adaptive laws are designed to compensate for physical uncertainties. With adaptive laws, a new distributed Nash equilibrium seeking strategy is designed by further integrating consensus protocols and gradient search algorithms.Moreover, to further accommodate compromised communication weights resulting from cyber-uncertainties, the coupling strengths of the consensus module are designed to be adaptive. As a byproduct, the coupling strengths are independent of any global information. With theoretical investigations, it is proven that the proposed strategies are resilient to these uncertainties and players' actions are convergent to the Nash equilibrium. Simulation examples are given to numerically validate the effectiveness of the proposed strategies.
基金supported by the National Natural Science Foundation of China(62303095)the Natural Science Foundation of Sichuan Province(2023NSFSC0872).
文摘Dear Editor,This letter proposes a novel Nash bargaining solution-based multiobjective model predictive control(MPC)scheme to deal with the interaction force control and the path-following problem of the constrained interactive robot.Considering the elastic interaction force model,a mechanical trade-off always exists between the interaction force and position,which means that neither force nor path following can satisfy their desired demands completely.Based on this consideration,two irreconcilable control specifications,the force object function and the position track object function,are proposed,and a new multi-objective MPC scheme is then designed.
