Distributed Consensus Protocol For Heterogeneous Multi-Agent Systems

Multi-agent systems are typical examples of complex networks in the real world and are widely found in natural,industrial,and social networks.It is important to study the synchronization problem of multi-agent systems for both explaining the cluster phenomenon in nature,realizing the coordinated control of unmanned systems in production practice and analyzing the game evolution mechanism in social networks.This paper studies the distributed consensus problem for a class of multi-agent systems named as heterogeneous multi-agent systems,which are more closely related to reality.Heterogeneity means that the dynamics of the agents in the system are not completely consistent.Obviously,this feature exists in many multi-agent systems,but sometimes the differences between agents,dynamics are neglected.A typical example of a heterogeneous multi-agent system is a hybrid formation consisting of unmanned aerial vehicles and surface vessels.In this paper,the distributed synchronization problem of a class of heterogeneous multi-agent systems is studied.An effective synchronization strategy is proposed.The sufficient condition and necessary conditiion for synchronization are obtained,respectively,and the synchronization rate is quantified.The study found that whether synchronization can be achieved is depended on the maximum real part of the non-zero eigenvalue of the the final dynamic matrix and the Laplacian matrix corresponding to the system communication diagram.Out of the need to prove the necessary condition,this paper also develops a study on a class of disturbance systems.In this paper,we first study a special kind of perturbation system.Based on the basis of linear steady-state system,this kind of system adds exponential convergence perturbation to the dynamic matrix.We find that the solution matrix of the disturbance system has a high similarity with the solution matrix of the linear time-invariant system,mainly reflected in:1.they can be divided based on the dominant growth rate,and the factors are independent matrixs.2.Their norms are the same order exponential functions,so the perturbation sys-tem is stable if the original system is stable.3.They have the same dominant left modality,and the growth rate of these dominant modal modalities are exponential functions in the same order.Then this paper studies the heterogeneous multi-agent system with interactive dynamics information,and proposes a computational distributed synchronization strategy.By separating the synchronization term and the error term,the difference between the system and the general homogeneous system is a convergent coupling term superimposed on the dynamics.Through an unconventional Lyapunov analysis method combined with the comparison principle,this paper proposes a sufficient condition for consensus and obtains the slowest rate of consensus.Through the study of the disturbed system,this paper proposes a necessary condition for consensus.The cases that are not covered are also analyzed.It is worth to mention that the analytical methods in the sufficient condition and necessary condition are also applicable to other similar coupling systems.Finally,the results of the simulation experiments in this paper are consistent with the theory.