Structural Balance Preserving In Cooperation-competition Networks

As a significant carrier of distributed strategy,Multi-Agent Systems(MASs),has attracted various attention of researchers in different scientific fields,especially in the control engineering field.The core of studying collective behaviors among agents is to design a series of distributed coordination controllers to realize the targeted collective behavior of the whole system based on the interactive network topology,which has profound engineering significance and application prospects.In this paper,based on algebraic graph theory,matrix theory,and stability analysis method of the potential functions,the structural balance preserving problem for MASs in initially structurally balanced and connected Cooperation-Competition networks.With the structural balance maintenance satisfied during the movement of agents,the corresponding collective behavior,that is,the static bipartite rendezvous and the static bipartite consensus in two kinds of dynamic equations,is also discussed in this paper,respectively.Specific contents include four parts given below.The first chapter summarizes the research and the progress of distributed coordinated control of MASs in Cooperation-Competition network.Also,the significance and the application prospect of structural balance and bipartite consensus of Multi-Agent System have been analysed so that leads to the research ideas and the main work of this paper.The related theoretical knowledge of algebraic graph theory,matrix theory,and Lyapunov stability theory have been introduced into the second chapter,including the definition of Cooperation-Competition network,the spectral characteristic definition theorem of Laplacian matrix,and Lyapunov stability theorem.In Chapter 3,a structural balance maintenance and static bipartite rendezvous of second-order heterogeneous MASs in Cooperation-Competition networks has been studied,where the heterogeneous agents are represented by a second-order integrator with the intrinsic nonlinear dynamics and velocity damping terms.For the initially given structurally balanced and connected Cooperation-Competition network,the classification design strategy based on a class of potential functions is adopted to design different evolution rules for cooperative neighbors and competitive neighbors.Further,a distributed protocol came into being,which makes the heterogeneous MAS not only maintain the structural balance during the evolution process but also can achieve the bipartite static rendezvous asymptotically,that is,the absolute values of the consistent states are equal and their signs are opposite.Finally,a numerical simulation example is given to verify the effectiveness of the theoretical analysis.In Chapter 4,a structural balance maintenance and bipartite static consensus consensus problem of Euler-Lagrange heterogeneous MASs in Cooperation-Competition undirected networks has been extensively discussed.The dynamic behaviors of the heterogeneous agents is modeled by Euler-Lagrange equations.Firstly,different evolution rules are set for the cooperative neighbors and the competitive neighbors of each agent.Differred from the problem in Chapter 3,the mathematical models considered is rather complex.Secondly,based on a class of potential functions constructed in this paper,a class of distributed adaptive coordination controllers are designed to preserve the structural balance of the whole system,and make achieve the asymptotically bipartite static consensus.Finally,a numerical simulation example is given to prove the feasibility and effectiveness of the proposed distributed controllers.In Chapter 5,the detailed summary and outlook are given,where the methods to be optimized and different angles to be added are mentioned about this paper.Furthermore,the further research goals and the future research topics are also given.