Group Consensus Dynamics For Asynchronous Multi-agent Systems

In recent years,the consensus of multi-agent systems is widely used in many scientific and engineering problems such as cluster problem and formation control.The basic method to solve the problem of consensus of multi-agent system is to design appropriate protocols or algorithms according to the system,so that the key quantities of the agents in the multi-agent system are ultimately consistent.At present,the research on the first-order or second-order multi-agent systems has been mature.However the research on group consensus of second-order multi-agent systems,especially in the environment of continuous time and asynchronous sampling,is not complete.Therefore,this paper chooses the group consensus of asynchronous multi-agent system as the research direction.Consider continuous time and asynchronous sampling environment in the second-order multi-agent system and gossip algorithm with scale coefficient in the first-order discrete multi-agent system.With the help of the nonnegative matrix theory and graph theory,this paper gives the sufficient conditions and strict rules for the communication topology graph of group consensus of agents in the designed protocol.Finally,simulation examples are given to demonstrate the proposed result.The main research of this paper is as follows:1.Consider the continuous time and asynchronous sampling environment for the second-order multi-agent system,the corresponding second-order control protocol is designed.By means of the formula of uniform acceleration motion,the continuous system is converted into discrete system,and the problem studied is finally transformed into the convergence of the product of infinite time-varying matrices.With the help of graph theory and nonnegative matrix theory,a judgement theorem which makes the individual states in the group tend to be consistent is obtained.Finally,simulation is used to prove the correctness of the conclusion.2.Investigate the group consensus problem of first-order discrete-time multi-agent system based on the broadcast gossip algorithm,in which only one agent wakes up in the light of the asynchronous time model at each time and sends its information.On the basis of the existing gossip algorithm,the scale coefficient is introduced to group and the control algorithm is designed.The influence of scale coefficient is eliminated through appropriate model transformation,and the group consensus problem is finally transformed into the problem of matrix product.By using the theory of nonnegative matrix and algebraic graph theory,the necessary and sufficient condition for the group consensus of multi-agent system is obtained,and the accuracy of the conclusion is verified by numerical simulation.