The Consensus Problem Of Networked Multi-agent Systems

A networked multi-agent system (NMASs) consists of many agents, whereagents interchange and cooperate through communication network. It has wideapplications in sensor networks, mobile robot system, intelligent trafc controlsystem, etc. One basic problem in the field of NMASs is consensus problem, whichdevelops distributed control strategies based on local information that enables allagents to reach an agreement on certain quantities of interest. This paper studiesconsensus and mean-square consensus problems of NMASs with general lineardynamics. The main results include:1. For NMASs with continuous-time dynamics, introducing the observer-based sampled-data control strategies with communication delays, we first es-tablish the system models of NMASs over fixed topology and Bernoulli switch-ing topology, respectively. Then, based on matrix theory and graph theory, theconsensus/mean-square consensus problem of multi-agent systems can be trans-formed into the stability/mean-square stability problem of N1delay systems,which can be unified as one common delay system under the assumption that thetopology has a directed spanning tree. Furthermore, if the LMIs concerning thestabilizability of the common delay system have a feasible solution, we prove thatthere exist feedback gain matrices K, G and connection weights ωijsuch that themulti-agent systems achieve consensus/mean-square consensus if and only if thegraph/the union of graphs in the switching topology set has a directed spanningtree.2. For NMASs with random packet dropouts, we assume that the commu-nication link failures among all the agents are synchronous and the packet-lossprocess is driven by a Markov chain. Using the agreement strategy based on statefeedback, matrix theory, graph theory and discrete-time markovian jump linearsystem theory, some necessary and sufcient conditions for the mean-square con-sensus problem of NMASs are established. Then, we generalize our results toNMASs with both random packet dropouts and delay. Finally, numerical exam- ples are given to illustrate the accuracy of our results.