Target Controllability Of Multi-agent Systems And Related Researc

With the emergence and development of artificial intelligence,the research of multi-agent systems has attracted extensive attention in various fields.In this paper,we mainly study the target controllability and structural target controllability of multi-agent systems,and obtain some graph-theoretic and algebraic conditions.The main work of the paper is as follows:Firstly,the graph-theoretic conditions of target controllability for a special general linear multi-agent system under undirected weighted topology are studied.By using leader-follower connected topology,a sufficient condition for target controllability of multi-agent system is obtained.Through the analysis of specific examples,the essential reason why this condition is not a necessary and sufficient condition is found,and then a necessary and sufficient condition for target controllability of multi-agent system is obtained.The results show that under the leader-follower connected topology,the multi-agent system is target controllable if and only if the connected component containing the follower target nodes is target controllable.We also found that this necessary and sufficient condition applies equally to non-leader-follower connected topology.Secondly,the target controllability of multi-agent systems under directed weighted topology is considered.A graph partition is constructed,and a necessary and sufficient graph-theoretic condition for the target controllability of a first-order multi-agent system is obtained by using the graph partition.In this paper,the connection between the target nodes reachable from the leader set and the target controllability matrix is obtained.In the case that the topology,leaders,and target nodes are fixed,we obtain that the high-order multi-agent system is target controllable if and only if the first-order multi-agent system is target controllable.Through independent strongly connected component and leader-target follower connected topology,a necessary graph-theoretic condition for target controllability of general linear multi-agent system is obtained.Algebraic conditions for the target controllability of the system are also obtained.At the same time,the target node selection methods are also proposed to make the system target controllable.Finally,based on the weighted graph,the structural target controllability of multi-agent systems is studied.Under the fixed topology,a necessary and sufficient algebraic condition that the multi-agent system is not the structural target controllable is obtained.We also extend this necessary and sufficient condition from fixed topology to switching topology,and obtain the necessary and sufficient algebraic condition that the multi-agent system is not the structural target controllable under switching topology.At the same time,the switching sequence of structural target controllability of multi-agent system is studied and its length is estimated.