Output Sign-consensus And Controllability Of Multi-agent Systems Over Signed Graphs

In recent years,multi-agent systems have been widely applied in many fields including power system,military,unmanned aerial vehicles and so on.Cooperative control of multi-agent systems has attracted significant attention due to its broad applications.For the past two decades,researches on multi-agent systems mainly focus on some fundamental questions,such as consensus,swarm and controllability.This thesis investigates two problems of multi-agent systems,i.e.,output sign-consensus problem and controllability.The main results of this thesis are based on signed graphs which mean the weights of edges have both positive and negative values.Compared with the study over nonnegative graphs,the study over signed graphs is more challenging and practical.The contents of this thesis are as follows.Firstly,this thesis studies heterogeneous linear-time-invariant systems and investigates the output sign-consensus problem over signed graphs.The distributed controller for multi-agent systems has been designed to achieve output sign-consensus.In addition,the heterogeneous multi-agent systems will achieve output bipartite sign-consensus,when the graph topology satisfies structurally balanced condition.Detailed theoretical analysis and simulations are provided to demonstrate the effectiveness of the method.Secondly,this thesis studies the output sign-consensus problem of heterogeneous multi-agent systems over switching signed graphs and shows that the heterogeneous multi-agent systems controlled by certain controller will achieve output sign-consensus,when the switching signed graph satisfies jointly eventually positive condition.And the effectiveness of the conclusion is demonstrated by some simulations.In the last,the controllability of multi-agent system over weighted directed signed graph is investigated.In order to eliminate the influence of the agent itself,the dynamics of agents are modeled by integrators.And,the agents are divided into two groups,i.e.,the leader group and follower group.The controllability of the system is studied under this leader-follower framework.We show that the controllability of structurally balanced signed graph is identical to its corresponding nonnegative graph.For general signed graph,we propose a sign-weighted-balanced partition and find an upper bound of controllability subspace of leader-follower system under this partition.In the same time,the uncontrollable sufficient condition is provided.Finally,detailed theoretical analysis and simulation are provided.