A Research On Consensus Problem Of High-order Cooperative-Competitive Multi-agent Systems

Consensus of multi-agent systems has been an emerging research topic in the systems and control community in recent years.A common feature of most current research is that the interaction among agents is cooperative.However,in some practical scenarios,it is reasonable to assume that some agents cooperative,while others competitive.A signed graph is generally used to model the cooperative-competitive network.The behavior of the cooperative-competitive multi-agent systems can be bipartite consensus,which means all agents converge to a common value with same modulus but different sign.With the help of matrix theory,graph theory,Schur complement Lemma,Lyapunov Theorem,output regulation theory,linear matrix inequality,we consider bipartite consensus of high-order multi-agent systems with Brunovsky form and unknown disturbance,bipartite consensus and output regulation of general linear multi-agent systems,bipartite consensus of general linear multi-agent systems with communication noises.The sufficient conditions are provided to guarantee the stability of closed-loop systems and tracking error systems.Finally,simulation examples are given to validate the effectiveness and correctness of our results.1.A leader-following bipartite consensus problem is studied for a high-order multiagent system with unknown disturbance dynamics.The agents can cooperate or compete with other agents,and a signed graph is used to model the cooperative-competitive network.When the cooperative-competitive network is structurally balanced,all the agents can be split into two subgroups.An exosystem is introduced to intervene the two subgroups such that bipartite consensus can be achieved.If the unknown nonlinear disturbance ban be linearly parameterized,adaptive laws are proposed to estimate the unknown constant parameter vector.Fully distributed controllers are also designed for every agents.For the case that the cooperative-competitive network is time-varying switching topology,if the leader is the root of the spanning tree in the augmented graph,the Lyapunov function can be used to analyze the convergence of the bipartite consensus and parameter estimation errors.2.The bipartite consensus problem is considered for general linear multi-agent systems with unknown nonlinear disturbances.A signed graph is used to describe the cooperative-competitive communication network.The unknown nonlinear disturbance can be described by linearly parameterized models,then adaptive laws are designed to estimate the unknown constant parameter vector.For the leaderless bipartite consensus problem,fully distributed adaptive controllers are proposed to ensure the bipartite consensus.For the leader-following bipartite consensus problem,another fully distributed adaptive controllers are designed to guarantee the purpose.When the communication network is structurally balanced,the closed-loop system can be stable by designing distributed adaptive control laws.In addition,the persistent excitation condition can guarantee the convergence of the parameter estimation errors.3.A output regulation problem is considered for general linear cooperative-competitive multi-agent systems,where not all the agents can obtain the state,output,system matrix and output matrix of the exosystem.Under this assumption,only a part of agents can obtain the internal model,which is associated with the system matrix of the exosystem.Thus,distributed observers are designed for every agents to estimate the state,output,system matrix,output matrix and internal model of the exosystem.Then,distributed dynamic output feedback controller is designed,the exponential stability of the closed-loop system can be guaranteed by using the output regulation theory.4.Under the cooperative-competitive network,bipartite consensus problem is considered for general linear multi-agent systems with communication noises.A signed graph can be used to describe the cooperative-competitive network,and the dynamic model of each agent is described by high-order multi-agent systems.By only using the relative state information,a novel stochastic-approximation control strategy is designed for every agent.With the stochastic stability theory,the convergence analysis of the bipartite consensus error is provided.