Multi-agent System Controllability

This paper studies controllability problems of multi-agent systems.Controllability theory is an emerging and fundamental research topic in coordinated control of multi-agent systems.The main results and contributions of this paper are as follows:1.This paper studies controllability problems for continuous-time multi-agent systems which described by undirected interconnection graphs with a kind of regular protocol,where the communication between different agents are under fixed topology and with fixed single time-delay or fixed multiple time-dehys.We first transform the time-delay systems into their equivalent non-delayed systems,and then by nonnegative matrix theory and algebraic graph theory,we derive some algebraic conditions for the solvability of controllability problems under single-integrator dynamics and double-integrator dynamics.We obtain the conclusion that the final states of internal agents are independent of time-delays between them.Theoretical results are presented to support the results.We also study the multi-agent systems with unidirectional communication between some agents which described by directed interconnection graphs,then derive some conditions for the systems with unidirectional communication topology to be controllable.At last,we give numerical simulations to illustrate how to control the system to solve controllability problems.2.This paper studies a discrete-time model of a class of multi-agent systems with more leaders.We investigate the relations among final states,communication topology, and time-dehys by using the similar method for continuous-time network.3.This paper studies the controllability problem for multi-agent systems from the point of view of graph topology.By appling the definition of the same direct neighbor set of parent vertices and the same indirect neighbor set of parent vertices,we give a new and simple method to judge the uncontrolhbility of the multi-agent systems.4.For a class of multi-agent systems which is uncontrollable,by selecting appropriate weights for communication links between some agents,we solve the controllability problem for the uncontrollable systems.