An Analysis Of The Mathematical Mechanism Of Self-Organizing Movement Strategy

coordination control In recent decades,the problems of multi-agent coordination control have been paid attention by many scientists.Flocking control is a new subject and research direction,which is derived from the abstract of group behavior.Flocking control is a good theoretical explanation and mathematical description of the group behavior in nature.Flocking control has the same properties as group behavior,which is coordinated and self-organized.It has a good application prospect in the field of multi robot system and multi UAV system.As the basic research of the coordination control,the consensus analysis is that all agents can show the global coordination.In reality,because of individual differences or the tasks of each agent,their system structure will be different so as to complete different tasks.Thus,in the same multi-agent system(MAS),the dynamic equation of the agent will be different.The heterogeneous multi-agent system is a system composed of several agents of different dynamic equations(order).In reality,due to the packet loss and other reasons,the multi-agent system has time delays.Therefore,it is of great practical value to study the consensus problems of heterogeneous multi-agent systems with time delays.In this paper,based on the mathematical theory of self-organization motion,the heterogeneous multi-agent system is studied as the research object,and the consensus problems of the self-organization motion of the heterogeneous multi-agent system with time delays is studied.First of all,the paper introduces the consensus definition of the static,dynamic,average and group consensus;then,the paper will be divided into continuous-time and discrete-time heterogeneous multi-agent system to carry on the consensus analysis.In the continuous-time and discrete-time heterogeneous multi-agent system,it is divided into heterogeneous multi-agent system composed of first-order and second-order agents,and high-order heterogeneous multi-agent system composed of firstorder,second-order and higher order agents.In the heterogeneous multi-agent system,which is composed of first-order and second-order agent,the paper uses the frequency domain method and nonnegative matrix method to prove that the system can achieve static consensus,respectively;in the high-order heterogeneous multi-agent system,the paper proposes control protocol with time delays.Then using method based on nonnegative matrix to prove the system can achieve static consensus.In the end,the paper presents the simulation to prove the correctness of our obtained results.The main contribution of this paper is to study the consensus problems of heterogeneous MAS with delays,especially to study the consensus problems of high-order heterogeneous MAS with nonnegative matrix method,which fills the vacancy of the academic.Studying continuous-time and discrete-time heterogeneous MAS,we mainly innovative literatures [1] and [2] and improve their results by changing second-order MAS to heterogeneous MAS composed of first-order and second-order agents,which increasing the difficulty of system analysis.And the Laplacian matrix are redefined so as to obtain more complex system matrix.Finally,the paper obtains the sufficient conditions to achieve the consensus of the system,i.e.,the maximum delay to achieve the consensus of the system.