Consensus Of Multi-agent Systems With Second-order Dynamics

The distributed control of multi-agent systems has been an active researchfield. It has extensive applications in many engineering fields, such as multiple ve-hicles/robots systems, communication networks, automated highway systems, etc.Consensus is an important and essential problem in distributed control of multi-agent systems. This thesis mainly discusses the consensus problem of second-ordermulti-agent systems, including second-order discrete-time systems, second-ordersampled control systems with time-varying sampled intervals and second-ordersampled control systems with delay. Our main results and contributions are asfollows:1. For second-order discrete-time multi-agent system, by applying algebraicgraph theory, matrix theory and stability theory, it is proved that the systemis consensus if and only if the fixed topology contains a directed spanning treeand the scaling parameters satisfy some conditions. The novelty of this thesis isthat we not only prove the existence of the scaling parameters, but also give theapproach of how to choose them. Hence, our paper sloves the consensus problemfrom the quantitative point of view. Finally, an example is given to illustrate theresults.2. For second-order multi-agent system with non-periodic sampled-data con-trol and undirected fixed topology, we establish its consensus criteria. By iterativemethod, the system is equivalently transformed into a discrete-time system. Then,by the convergence of the system matrix and Jury criterion, we prove that theconsensus of second-order system depends not only on topology conditions andscaling parameters but also on the sampled intervals. Furthermore, we give therange of scaling parameters and sampled intervals to guarantee that the multi-agent system is average-consensus.3. For second-order sampled control system with delay and undirected fixedtopology, average-consensus of multi-agent system is studied. By iterative methodand augmented system method, the multi-agent system is equivalently trans- formed into a discrete-time system without delay, which reduces the difcultyof our research in a sence. Then, by applying matrix theory and stability theory,two necessary and sufcient conditions are proposed to ensure that the multi-agentsystem is average-consensus.