Research On Group Tracking Control Of Second Order Multi-agent Systems

Recently,group tracking control issue has drawn many researchers' attention from mathematics,biology,control science,etc.Different from traditional tracking control issue,all the agents in a network are divided into multiple subgroups according to their physical characteristics and differences in task allocation,each subgroup is assigned a leader and all the followers in this subgroup will asymptotically track its own leader.This paper will study the second-order group tracking control issue of multi-agent systems(MASs)under fixed topology and Markov switching topology,respectively.Our main results and contributions are given as follows:1.The group consensus tracking issue of continuous-time second-order multiagent systems(MASs)under directed fixed topology is studied.For MASs with two subgroups,we first establish the relationship between the positive stability of matrix H and the connectedness of the topology graph.Then,we prove that MASs can achieve group consensus tracking if parameters satisfy some inequalities and matrix H is positive stable.Moreover,our paper extends the results for MASs with two subgroups to multiple ?-group consensus tracking.Especially,for a special graph with acyclic partition,a necessary and sufficient condition of ?-group consensus tracking can be obtained.2.The group consensus tracking issue of discrete-time second-order multi-agent systems(MASs)under directed fixed and Markovian switching topologies is studied.For MASs with m leaders,we first introduce a method to divide the whole MASs into m subgroups.Based on the subgroup-divided method,the condensation directed graph G of the communication topology of the whole MASs becomes a directed acyclic graph(DAG).Then,for MASs with fixed/Markovian switching topology,some sufficient/necessary and sufficient group consensus tracking criteria are established.