Research On Bipartite Consensus Of Heterogeneous Multi-agent System With Time Delay

Multi-agent system(MAS)is one of the widely used systems in distributed control systems,and its cooperative control has attracted the attention of many researchers.Consensus control,as the fundamental problem of cooperative control of agent system and the basis of other distributed control researches.It is main purpose is to achieve information exchange without relying on global communication,and to build cooperative or competitive networks with neighbor agents to coordinate their goals and behaviors.Achieving the same state of all agents in the system without central control.The time delay problem is an important research direction in consensus control problem.In this paper,a heterogeneous multi-agent system composed of first-order and second-order agents is adopted as the research object.Compared with homogeneous system,the consensus control of heterogeneous systems is more complex.Combined with the cooperation-competition network,this paper studies the bipartite consensus of multi-agent system affected by time delay.The main work is as follows:(1)In undirected topology,information communication between agents is bidirectional.Based on the neighborhood estimation rule,the estimation velocity of the first order agent is given by the position change of neighbor agents.Due to the difference of individuals in nature,the same and different time delay of agents are considered.New control protocols are designed to achieve bipartite consensus in heterogeneous systems when the agent is affected by time delay.By using algebraic graph theory matrix theory and frequency domain analysis the corresponding stability analysis and the calculation formula of the maximum allowable time delay of the system are obtained respectively.It is proved that the system can achieve bipartite consensus when the time delay of the agent is less than the maximum allowable time delay of the system.Numerical examples are given to verify the theoretical analysis.(2)Information between agents in a directed topology can be transmitted in one direction.Research on cooperative control of multi-agent system under directed topology has many advantages,such as avoiding repeated transmission of information and reducing communication consumption.Based on the neighborhood estimation rule,an estimation speed is given to the first-order agent,and a new bipartite consensus control protocol is designed by considering the one-way information exchange between agents and the effects of agents' time delays(both simultaneous and different time delays).Based on the matrix theory of algebraic graph theory and the frequency domain analysis,the system stability analysis and the formula for calculating the maximum allowable time delay are given respectively under the same and different effects of agent time delay.The theory proves that the system achieves bipartite consensus when the agents in the system are affected by the time delay less than the maximum allowable time delay.Finally,the effectiveness of the proposed control protocol is proved by a simulation example.