The Study Of A Class Of Group Controllability Of Multi-Agent Systems

The study of multi-agent system has a long history, its controllability study widely by the researchers, and it has an abundant achievements. The multi-agent system is composed by a number of dynamic intelligent agents with autonomous capability, which can complete the large-scale complex task through local interaction. Its controllability is a basic and key problem,the controllability of the multi-agent system refers to transferring the remaining intelligent agents of such system from any arbitrary initial state to any final state by controlling dynamics of a small amount of intelligent agents. With the improvement of multi-agent systems’ complexity, the whole system can be divided into some subgroups.The group controllability of the multi-agent system containing multiple subgroups can be investigated, that is, the intelligent agents of each subgroup in the multi-agent system can be transferred from any arbitrary initial state to any final state by controlling dynamics of a small amount of intelligent agents. This paper using graph theory, control theory,matrix theory, and other theories and methods, to research the group controllability problem of different model of multi-agent system more concentration, specific and detailed. The main contents and contributions of this paper are stated as follows:1. The group controllability of continuous-time multi-agent systems is discussed.Based on existing research results, this paper puts forward group controllability problem of multi-agent systems.A new and complex protocol will throughout the beginning and end of this paper, researching a new controllability problem by network clustering.The weight factor of agreement in the paper is different from the existing research on controllability conclusions, the scope of this weight factor is more general, it can be positive, negative, or zero. Solving the problem of external input of multi-agent system in the special perspective, in other word, it is a leader selection problem.The general definition of group controllability first proposed in this paper, establishing group controllability conditions,also studies group controllability of special topological structure such as charts,complete graph.A class of uncontrollable system is proved.Getting a general and popularize results via extended two sub-groups to multiple sub-groups.Finally,discussing group controllability in case of external input condition.At last,using Matlab simulation to verify correctness of results, the whole system can reach the specified final state from any initial state, can form arbitrary configuration without the help of external conditions.2. The group controllability of discrete-time multi-agent systems is presented. Whether the model or the research content,this part first time study.Firstly,model description and the general definition of group controllability of discrete-time multi-agent systems first proposed in this paper.Based on the foundation of graph theory and matrix theory,we discuss group controllability conditions and a type of uncontrollable system,respectively, and group controllability under road topology is considered.Furthermore, the model is developed to high dimensions via Kronecker product that given its group controllability’s conditions.The numerical examples are proposed to illustrate the theoretical results.