Group Consensus For Delayed Heterogeneous Multiagent Systems In Cooperative-Competitive Networks

Group consensus is the basic problem of cooperative control of multi-agent systems.Recently,with the rapid development of artificial intelligence technology,group consensus has been widely applied in smart cities,power systems,formation control and so on.Studying the group consensus of multi-agent systems has important research significance and application value for exploring theories and methods of collaborative control of complex systems.At present,the research on group consensus is mostly based on homogeneous MAS.However,due to the influence of environment and other factors,the agents in the systems usually have different states dynamics characteristics,the homogeneous systems gradually unable to meet this special situation.In addition,most researchers on group consensus of heterogeneous MASs are based on stationary group consensus.The stationary consensus means that the speed state of second-order agent is zero after the system reaches consensus,this is a special situation.In addition,most related researchers only consider the single relationship of cooperation or competition among agents,at the same time,with the gradual complexity of the system structure and the increase in the number of agents in the systems,the relationship between agents may be the coexistence of cooperation and competition.In addition,time delays always will be generated under various conditions,which will eventually affect the stability of the MASs.Therefore,inspired by the above work,in this paper,the group stationary consensus and group dynamic consensus issues for delayed heterogeneous MASs in cooperativecompetitive networks is studied,and the influence of cooperative and competitive strength among agents on system convergence is discussed.The research contents of this paper is summarized as follows:Firstly,this paper constructs a heterogeneous systems model composed of first-order and second-order agents under the influence of communication delay and input delay.Assume that there is a cooperative relationship between the agents in the same subgroup and a competitive relationship in different subgroups,on this basis,a reasonable and effective stationary group consensus protocol is designed.Based on algebraic graph theory and stability theorems,the obtained results reveal that the implementation of heterogeneous systems' stationary group consensus lies on the control parameters of systems,in-degree and input delays of the agents,and communication delay only affects the convergence rate of the system.some numerical simulation experiments verify the correctness of the theoretical results.Secondly,the dynamic group consensus problems of heterogeneous systems under the influence of input delay in cooperative-competitive networks is studied.According to the stability theory,frequency domain control and graph theory,in the network composed of all second-order agent,the zero in-degree of second-order agent need to pinned.In addition,a novel pinning control strategy is proposed: if the second-order agent does not receive information from other second-order agents,then,the agent will pinned.The final simulations results verify the correctness of the theoretical results.Finally,this paper further studied dynamic multi-group consensus issues for the heterogeneous MASs with input delays.On the basis of comprehensive consideration of the competitive and cooperative interaction between agents,the impact of the strength of cooperative-competitive on the systems convergence rate is further considered.The theoretical results reveal that the implementation of heterogeneous systems' dynamic multi-group consensus is not only related to the in-degree of the agent,control parameters of the system and input delay,but also lies on strength of cooperative-competitive among agents.The simulations results show that reducing the strength of cooperative or competitive among agents will reduce the convergence rate of the complex systems.