Consensus Of Fractional-order Multi-agent Systems

Recently,due to the development of control theory and computer technology,the coordination control of multi-agent systems has become a research topic.The consensus problem of multi-agent systems is a basic research problem.In fact,many physical systems in complex environment show fractional-order dynamic behavior because of their special composition materials and properties.It's better to reveal the nature of the study object and its dynamic behavior by using the fractional-order dynamic equations to study the physical objects with the fractional-order.This paper used the theories of modem control,matrix,graph and fractional-order to study the consensus of fractional-order discrete-time multi-agent systems and gave the consensus conditions.The influences of leaders,time delays,and the predictor were considered to the fractional-order systems.The followings are main research contents of this paper:1.The consensus of fractional-order discrete-time multi-agent systems with a leader was investigated.Firstly,we gave the definition of convergence.As external control or input,the leader controlled the systems.Then the solvable conditions for the consensus of fractional-order discrete multi-agent systems were derived.2.The consensus of fractional-order discrete-time multi-agent systems with a leader and time delay was discussed.We got the fractional-order multi-agent systems,consensus sufficient conditions by applying Hermit-Biehler theorem and bilinear transformation,then influences of fractional-order ?,sampling interval h,time delay ? and interconnection topology to the consensus systems were discussed.3.The consensus of fractional-order discrete-time multi-agent systems with state predictor was studied.Designed the predictor,the systems more fast reached consensus state than systems without predictor.At the same time,the convergence speeds of such system with predictor and without predictor were compared.