Partial Controllability Analysis Of Discrete-Time Multi-Agent System

Generally speaking,controllability of multi-agent systems(MAS)refer to changing the other agents from any arbitrary initial state to any arbitrary final state by controlling dynamics of a small amount of agents under exchanged information between each other,which makes the system reflect the effect of a whole,that is the complete controllability.Based on the controllability of the whole system,we research the controllability of the part in the system,which is more close to the actual life.In this paper,partial controllability of multi-agent systems is studied by using the graph theory,modern control theory and matrix theory.This paper deeply addresses partial controllability problems in discrete multi-agent system with a Leader,discrete multi-agent system with a Leader and time delay.The main contents and contributions of this article are as follows:1.We propose the concept of controllable node group and the definition of partial controllability in discrete multi-agent systems.Based on this,the partial controllability of discrete multi-agent systems with Leader is discussed.We find that the local controllability of discrete multi-agent system with Leader is related to the information transmission between the leader and the followers,and is independent of the moving track of the agents.Some necessary and sufficient conditions are given for partial controllability of the discrete-time multi-agent system with a single Leader.Moreover,the partial controllability criteria of some special cases are given.Finally,a numerical example and simulations are given to illustrate the correctness of the theoretical results.2.We concentrates on the partial controllability problems of discrete-time multi-agent systems with a Leader and time-delay,establishes partial controllability criteria.It is concluded that the partial controllability of the discrete-time multi-agent system with a Leader and time-delay can be determined by judging whether the corresponding principal minor in the Gramm matrix is reversible or not,and the partial controllability is related to the linear relationship of the corresponding rows in the controllable matrix.The corresponding examples and Matlab simulations are supplied to illustrate the results.