Fixed-Time Consensus For Multi-Agent Systems Via Pinning Control

For multi-agent systems,the collaborative control is a main research topic,which has extensive practical applications in transportation,military,computer,and many other aspects.The consensus problem is a fundamental one in collaborative control and a critical condition for multi-agent systems to complete collaborative control tasks.Different from previous situations that the systems control each agent,based on pinning control method,this paper studies the fixed-time consensus problem of multi-agent systems with a single leader and multiple leaders as follows:For nonlinear multi-agent systems,the first part of these paper mainly studies the fixed-time tracking consensus problem with a single leader.Firstly,the distributed control laws are designed by pinning control principle based on the state feedback control protocol.Then,the theory of Lyapunov stability and fixed-time consensus are used to prove tracking consensus problem under the designed protocols.Finally,numerical simulations are used to illustrate the conclusions and verify the effectiveness of the designed control protocols.Considering that only a group of agents is difficult to complete complex tasks in practical application,in the second part all of the agents in the system are divided into many subgroups firstly.And state feedback control protocols different from the first part are designed to enable each group of agents to track the state of their leaders within a fixed time,thereby achieving group consensus.At the same time,in the study of group consensus problem,information interaction not only exists between agents in the same subgroup,but also between agents in different subgroups.The conclusion is general and more conducive to practical applications.Then the theory of Lyapunov stability and fixed-time consensus are used to prove the proposed conclusion.Finally,numerical simulations are used to illustrate the effectiveness of the designed control protocols.