Bipartite Consensus And Tracking Conrol Of Fractional-order Nonlinear Multi-agent Systems With Delays

Distributed coordinated control of multi-agent systems has long been a hot topic based on its wide applications in various fields.With the introduction of cooperative competitive networks,the bipartite consensus problem,as one of the most fundamental problems of ditributed coordinated control of multi-agent systems,receives extensive attention.Fractional-order systems are an extension of integer-order systems.As modeling problems related to physics,mechanics,and biology become progressively more complex,the traditional integer-order systems are no longer applicable,and the introduction of fractional-order models can better characterize the dynamics of real systems.Thus,this thesis aims to study the bipartite consensus problem and bipartite tracking consensus problem of fractional-order nonlinear multi-agent systems with distributed delays using techniques such as graph theory,matrix analysis,and Razumikhin stability theorem.The main contents are as follows:Chapter 1 introduces the background and significance of the research on the bipartite consensus problem of fractional-order delayed nonlinear multi-agent systems,and outlines the research results of domestic and foreign scholars in relevant fields.Chapter 2 presents theoretical knowledge related to this thesis,including graph theory and matrix theory for describing and analyzing the multi-agent systems,and the definition of fractional-order derivatives.The chapter also outlines the stability theorems for fractional-order systems.Chapter 3 studies the bipartite consensus problem for fractional-order delayed nonlinear multi-agent systems with distributed delay and input delay.A continuous distributed controller is proposed based on the nature of structural balanced graphs with a spanning tree.By using techniques such as graph theory,matrix transformation and linear matrix inequalities,it is proven that the system can achive biparite consensus when the controller parameters are appropriately set.Finally,the effectiveness of the proposed bipartite consensus control protocol is verified through a simulation example.Chapter 4 investigates the bipartite tracking consensus problem for a class of heterogeneous fractional-order delayed nonlinear multi-agent systems.The system in this chapter considers a unknown leader with non-zero input.Sufficient conditions for achieving bipartite tracking consensus are obtained by designing a discontinuous distributed controller.The chapter concludes with a numerical simulation example to verify the effectiveness of the proposed discontinuous distributed controller.In Chapter 5,based on the research in the previous chapter,a continuous distributed controller is considered to eliminate the undesirable chattering phenomenon caused by the discontinuous controller.The bipartite tracking error is obtained to converge to a uniformly bounded range by a rigorous theoretical derivation.Chapter 6 summarizes the full research results and analyzes the shortcomings of the thesis and the areas for improvement.Possible directions for future research are also discussed.