Research On Distributed Control For Cooperative And Competitive Multi-agent Systems Subject To Saturation Constraints

The distributed control of multi-agent systems has attracted a lot of attention due to its extensive application in chemistry,computer,biology and other fields.However,a large number of previous studies have often assumed that there exist only cooperative interactions between agents.In fact,multi-agent systems not only have cooperative interactions,but also have antagonistic interactions.Due to the simultaneous existence of cooperative and antagonistic interactions,cooperative and competitive multi-agent systems present plentiful behavioral dynamics.Theory is always applied to practice,but the actual physical system is often limited by various practical factors,such as saturated constraints,communication delay,disturbance,etc.Therefore,it is more realistic and meaningful to study multi-agent systems that are limited by practical factors.This thesis mainly studies the distributed control for cooperative-competitive multi-agent systems subject to saturation constraints,and its main work is divided into the following parts:(1)The bipartite consensus problem of single-integrator agents subject to saturation constraints is studied.Based on the signed undirected graph of structural balance,the control protocol under the leader-follow frame is designed for the continuous and the discrete multi-agent systems subject to saturation constraints.A model transformation is introduced by taking advantage of the right eigenvector of Laplacian matrix associated with zero eigenvalue,based on which the bipartite consensus problems can be converted into the asymptotic stability problems.Through convergence analysis,it is obtained that the multi-agent systems can achieve bipartite consensus by selecting appropriate control gain.In addition,for discrete multi-agent systems,the control gain is also related to the sampling period.(2)The bipartite consensus problem of neutral stable agents subject to saturation constraints is studied.Based on the signed digraph is detailed balanced,structurally balanced and strongly connected,the control protocol with and without leader is designed for neutral stable agents.In the process of convergence analysis,the bipartite consensus problem is transformed into a stability problem.The Lyapunov function is constructed by combining the detailed balanced and structurally balanced signed digraph.The stability of the converted system is proved by Lyapunov’s stability theorem,which shows that the bipartite consensus of multi-agent systems can be reach.(3)The average bipartite consensus problem of single-integrator agents subject to saturation constraints is studied.For the multi-agent systems under signed digraph is weight unbalanced,a mirror signed digraph with balanced weights is constructed by using the left eigenvector corresponding to the zero eigenvalue of the Laplace matrix,and the control protocol is designed according to the nature of the mirror signed digraph.For the saturation constraint problem of multi-agent system,the multi-agent system is not subject to saturation constraints when it changes with time by selecting the appropriate gain.From the convergence analysis,it is obtained that when the signed digraph satisfies structural balance,the multi-agent systems can reach average bipartite consensus.When the signed digraph satisfies structural unbalance,the multi-agent systems can reach state stability.