Bipartite Consensus Of The Multi-agent Systems With Antagonistic Interactions

Recently,the consensus problem of multi-agent systems has received widespread attention from many researchers.It is worth pointing out that most of the existing works focus on the networks with nonnegative edge weights,in simple terms,the relationship between agents is "positive".However,considering that in many practical network models,the antagonistic interactions of relationship are common.In this thesis,we study the bipartite consensus problem of the multi-agent systems with antagonistic interactions.The objective is to make all agents' states converge to a value which is the same for all in modulus but not in sign.We employ the knowledge of graph theory,matrix theory and Lyapunov stability theory to analysis bipartite consensus of multi-agent systems.The main research contents and contributions can be summarized as follows:First,for the time-varying multi-agent systems,we introduced the concepts of signed node dynamics and signed edge dynamics,and proposed new transformation rules for signed node digraph and signed edge digraph.A distributed control algorithm is proposed for signed edge dynamic to achieve bipartite consensus,then the corresponding theoretical analysis is provided.Second,we have studied consensus control for heterogeneous multi-agent systems with antagonistic interaction,the difference of system matrixes can be compensate by control input.By establishing connection in structure between homogeneous system and heterogenous systems to research characteristic of heterogenous multi-agent systems,we design different distributed state feedback protocols to ensure that all agents' bipartite consensus is achieved asymptotically.Third,we proposed and analyzed a new model for opinion dynamics over signed social networks,every agent has the right to express theirs opinion to a particular problem,and allow the attitude has different degrees.Alternately,we could take a more global view,the network can be divide into opposing two groups.We presented an optimization problem that minimizes the budget of social links under this signed network reaches the bipartite consensus,eventually.