Consensus Research Of Fractional-Order Multi-agent Systems

In recent years,the cooperative control of multi-agent systems(MASs)has received much attention from various scientific communities.Consensus is an important and fundamental problem for cooperative control of MASs,which has broad applications in many fields.This thesis focuses on the consensus of fractional-order multi-agent systems(FMASs).The main contributions are as follows:Firstly,the consensus of FMASs with double-integrator under fixed topologies is investigated,where the fractional-order ? satisfies 0(27)?(27)2.Based on the fractional-order stability theory,Mittag-Leffler function,and Laplace transform method,an appropriate consensus control protocol with control parameters is designed.A necessary and sufficient condition is obtained under the assumption that the directed graph for the communication network contains a directed spanning tree.Finally,some numerical simulations are presented to show the effectiveness and superiority of the theoretical results.Secondly,the consensus of FMASs with double-integrator under switching topologies is investigated,where the fractional-order ? satisfies 0(27)?(27)1.A new consensus protocol is designed.Based on Mittag-Leffler function,dwell time method and Laplace transform,a sufficient condition is derived to guarantee the consensus.In addition,the domain of the dwell time of switching signal is given.Finally,the numerical simulation is given to show the validity of the theoretical results.Finally,the consensus of FMASs with linear models is discussed,where the fractional-order ? satisfies 0(27)? ?n and n is a any given natural number.A distributed observer-type protocol based on output feedback is proposed.Based on the stability theory of fractional-order systems,properties of the Kronecker product,Mittag-Leffler function and Laplace transform,a sufficient condition is obtained,which ensures that the linear FMASs can achieve a consensus asymptotically.Numerial imulation results show that the theoretical results obtained in this part extend and improve some result in literature.