Research On Group Consensus Of Multi-agent Systems Via Pinning Control

With the development of network theory,computer technology and communication technology,people's research on control theory extends from a single dynamic system to multiple interconnected systems.In practical applications,a group of agents must reach a consistent state when the external environment changes,but this consistent state is often inconsistent with changes in the environment or collaborative tasks.Research on group consensus of multi-agent systems can effectively improve this situation.Group consensus means that agents belonging to the same group will eventually converge to the same value,while agents belonging to different groups will converge to different values.Obviously,for the research of multi-agent systems,the number of research objects will not be a few.Therefore,it is almost impossible to exert control over every object,but it is essential for the study of large-scale multi-agent systems in practical applications.Therefore,this paper introduces pinning control,which only needs to exert control on some objects with special properties to realize the global control.The main research contents are as follows:Firstly,the problem of group consensus of nonlinear first-order multi-agent systems based on pinning control is studied.The control protocol,the condition of group consensus and the selection strategy of pinned nodes are given,and the minimum number of pinned nodes is obtained in the simulation of several examples.Then the group consensus problem of nonlinear second-order multi-agent systems based on pinning control is studied.The control protocol,adaptive pinning gain design scheme and pinned nodes selection scheme which can achieve group consensus are given.In addition,several examples are used to verify the correctness of the above design.Finally,the group consensus problem of nonlinear second-order multi-agent systems with interconnected delay is studied.Assuming that the leader and his immediate followers have communication delay,the group consensus can be achieved by controlling the size of the delay,that is,different groups follow the leader's state at different times to achieve different consistency,and a reasonable sufficient condition of LMI form is given.In addition,sufficient conditions of LMI form without pinning control are given when all nodes have connection delay.In the end,the correctness of the above theory is verified by several examples.