Research On Consensus Algorithms Of Multi-agent Networks With A Time-varying Leader

With the rapid development of automation technology and wireless communicationnetwork technology, multi-agent network coordination control has been the research hotpot inthe field of control. The researchers pay more and more attention on the multi-agent networkaccount of the reason on what can complete that single agent is difficult to complete tasks. Asa typical problem of multi-agent network coordination control, formation control has a largenumber of potential applications in military and civilian. And in the practical application, dueto network coordination task is complex and changeable, The state information of leader istime-varying.Therefore, Research on methods of multi-agent network for a time-varyingleader has extremely important theory significance and practical value.Based on algebraicgraph theory,matrix theory,Lyapunov stability principle, it is focused on Methods ofmulti-agent network formation control for a time-varying leader in this paper.At first, the consensus problem is investigated for the multi-agent network with atime-varying leader where the dynamics of agents is modeled as single-integrator. Based onthe relative states between agents, the distributed control protocol is proposed when only aportion of the agents have access to the leader reference state. Furthermore, Necessary andsufficient condition are developed to achieve consensus of multi-agent network under thefixed topology applying graph theory, matrix theory and stability theory. Additionally, thealgorithm proposed is expanded to the condition of maintaining a constant reference statedeviation between agents, the distributed control protocol and the necessary and sufficientcondition of achieving consensus are also given. And simulation research validate the validityof the algorithm．And then the consensus problem is investigated for the multi-agent network with atime-varying leader where the dynamics of agents is modeled as second-integrator. Based onthe local velocity states information and relative states information of time-varying velocityand accelerated speed, the distributed control protocol is proposed. By model transformations,we turn the original system into an equivalent system whose system matrix has the propertythat all the row sums are zero.Therefore the consensus problem for the multi-agent networkwhere the dynamics of agents is modeled as second-integrator is transformed to the consensusproblem for the multi-agent network where the dynamics of agents is modeled as single–integrator.By constructing a new graph and using nonnegative matrix theory, the necessaryand sufficient condition of achieving consensus are also given,respectively,under thecondition on fixed and switching topology. Additionally, the algorithm proposed is expandedto the condition of maintaining a constant reference state deviation between agents, thedistributed control protocol and the necessary and sufficient condition of achieving consensusare also given. Simulation experiment validate the validity of the algorithm． At last, the consensus problem is investigated for the multiple nonholonomic mobilerobots network. A continuous distributed finite-time observer is proposed for each follower toestimate the leader’s states in a finite time under the condition that the states of leaders areavailable to only a subset of the followers. And based on the algebraic graph theory andmatrix theory, theoretical proof are also given. On this basis of the above state informationestimation, the standard error system is defined. By the introduced standard error system todesign consistency protocol to achive the average consistency and formation. As welltheoretical proof is given based on the graph and matrix theory. Simulation experimentvalidate the correctness and effectiveness of the algorithm．...