Consensus Of Fractional-order Multi-agent Systems With Nonlinear Dynamics

In recent years,the distributed coordination control of multi-agent systems(MASs)has been paid more and more attention from various disciplines,such as applied mathematics,physics,computer sciences and control theory.There is no doubt that it is partly due to its broad applications,for example,unmanned air vehicles,sensor networks,flocking and tracking,etc.Within these applications,one object is to such all agents reach an agree-ment on a common qualities(position,velocity,phases and attitudes)by communicating with their local neighbors,which is called as consensus problem.In this paper,we con-sider the consensus of fractional-order multi-agent systems with nonlinear dynamics.The main works are as follows:1.Firstly,we consider the group multiple lags consensus of fractional-order non-linear leader-following multi-agent systems via adaptive control,in which two kinds of lag consensus are defined.One is called as outergroup lag consensus,which means that different group leaders reach lag consensus.The other one is called as innergroup lag consensus,which means the followers reach lag consensus with their own group leaders.Only the two kinds of lag consensus are reached can the group multiple lag consensus be realised.To achieve group multiple lags consensus,a class of distributed control protocols is designed and the corresponding sufficient conditions are obtained.Furthermore,con-sidering parametric uncertainties that may exist in the dynamics of leaders or followers,a class of adaptive control protocols for the fractional-order MASs is employed.Then the corresponding sufficient conditions are also obtained.2.Secondly,we consider the leader-follower output consensus of fractional-order heterogeneous MASs with general linear dynamics,in which three aspects are analyzed:the output consensus of fractional-order heterogeneous MASs without a leader and non-linear dynamics,the output consensus of fractional-order heterogeneous MASs with a leader but nonlinear dynamics,and the output consensus of fractional-order heterogeneous MASs with a leader and nonlinear dynamics.With the aid of internal models principles,the distributed control protocols are respectively proposed according to the above three aspects.By employing matrix theory,algebraic graph theory and the stability theory of fractional system,the state consensus of internal model systems and the output consensus of heterogenous fractional linear MAS are achieved.