Group Controllability Analysis Of Multi-Agent System With Time-delay

Controllability is a fundamental problem concerning control of multi-agent systems and a very important research topic in the modeling,analysis and coordination control of multi-agent system.Group controllability problem is a further extention of the controllability problem of the general multi-agent systems,which mainly studies the cooperation and control of multi-agent systems with multiple subgroups or multiple intelligent clusters.Comparing with the controllability of the general multi-agent systems,the group controllability is not only to consider the information interaction among the groups,but also to consider the interaction between the diverse groups,which makes the system reflect the whole effect and the internal structure of subgroups.In this paper,group controllability of multi-agent system is studied by using graph theory,matrix theory and control theory.And this paper deeply addresses group controllability problems in discrete multi-agent system with time delay,discrete multi-agent system with time delay and leaders,and continuous multi-agent system.The main contents and contributions are as follows.1.The group controllability of discrete multi-agent systems with time-delay on fixed topology and switched topology is studied.Discrete multi-agent system with is divided into subgroups,which is different from the controllability study of general multi-agent system with leader-follower protocol and the whole system does not have leader or external input,and sufficient/necessary conditions of the multi-agent system on fixed and switched topologies are given,which makes the system attains group controllability.2.We consider group controllability of discrete-time multi-agent system with time-delay and leaders.By a series of transformations,the discrete-time multi-agent system with time-delay and leader transforms into the discrete-time multi-agent system without time-delay.Compared with the time-delay system,the dimension of the system without time-delay significantly increases.The rank criterion and PBH rank criterion are given.The influence of the system internal coupling relation on the controllability of the system is discussed.3.The group controllability of continuous-time multi-agent systems with leaders is researched.The group controllable conditions of multi-agent system on fixed and switched topologies are discussed respectively.The Kronecker product is used to extend the system to the high dimension space,which makes the group controllable conditions of the system more general.In addition,the sufficient/necessary conditions of the controllable or uncontrollable system on the particular topology are given.