Controllability Analysis Of Multi-agent Systems Under Different Input Signal

The controllability of multi-agent systems is an important component of distributed network control and plays a significant role in the development of artificial intelligence,thus it has become one of the hot research directions in current society.Based on the singlesignal input and multi-signal inputs system models,this thesis studies the controllability of multi-agent systems with different signal inputs by using matrix theory and graph theory.The main contents include the following parts:Firstly,the controllability of multi-agent system with single-signal input is studied.The influence of the multiplicity of the eigenvalues on the controllability of the system is analyzed from the perspective of whether Laplacian matrix has repeated eigenvalues or not.Then,the controllability of multi-agent system with cells of equal capacity is studied,mainly from two aspects,on the one hand,the controllability conditions of the system are presented,and different conclusions are obtained according to the selection of different leaders.On the other hand,the relationship between the rank of Laplacian matrix and topological structures is analyzed,and the calculation expression of the rank of Laplacian matrix is obtained,and the relationship between the rank of Laplacian matrix and the rank of the Laplacian matrix of quotient graph is further studied.Moreover,the special topologies with cells of equal capacity are analyzed.The twin graphs and double twin graphs are defined,the leader selection methods are provided,and the sufficient and necessary conditions are given.Through these methods,the system can reach the controllable state even when fewer leaders are selected,which can greatly improve the efficiency and reliability of the system,and reduce the number of leader nodes required.Secondly,the controllability of multi-agent system with multi-signal inputs is studied.The relationship between the eigenvalues of the Laplacian matrix and the controllability of the system is provided.It is found that when Laplacian matrix has repeated eigenvalues,its controllability can be judged by the number of leaders.Subsequently,the controllability of multi-agent system with cells of equal capacity is studied by selecting nodes from different cells as leaders.In addition,since the Laplacian matrix is constant regardless of whether the system with single-signal input or multi-signal inputs,the rank of the Laplacian matrix and the relationship between the rank of Laplacian matrix and the rank of the Laplacian matrix of quotient graph are the same.Moreover,the corresponding leader selection methods are also provided for the special topologies with cells of equal capacity,and the sufficient and necessary conditions are given.Finally,the differences of the controllability of multi-agent system with different signal inputs are studied.The controllable subspaces of multi-agent systems with singlesignal input and multi-signal inputs are provided.For the system with single-signal input,the lower bound of its controllable subspace is provided.For the system with multi-signal inputs,the upper and lower bounds of its controllable subspace are given.In particular,it is found that there are differences between the controllability of these two systems.And the differences of the controllable subspace of the multi-agent system with cells of equal capacity under different control signal inputs are further analyzed.Although the system with single-signal input can be considered as a special case of the system with multi-signal inputs,there are few relevant conclusions on the differences of controllability between the two system models.The conclusion of this thesis provides a reference for a deeper understanding of the characteristics of controllability under different system models.