Controllability Analysis Of General Multi-agent System

Controllability is a fundamental problem of multi-agent systems and is also a very important research topic in the modeling,analysis and coordination control of multi-agent system.The controllability of multi-agent system can be analyzed from different perspective.In this paper,we use graph theory,matrix theory and control theory to study the controllability of general multi-agent system.In this paper,the partial controllability of multi-agent system is studied,and we use ?-matrix to solve the problem of multi-agent system.The main contents and contributions are as follows:1.We have proposed the concept of partial controllability,and have given the criterion of partial controllability,which are Gramm criterion and rank criterion respectively.A sufficient condition for judging partial controllability of undirected graphs with multiple leaders is also given by using this criterion,and the example and simulations are given to verify the correctness of the theory.2.The controllability of the system is analyzed by using the ?-matrix.We mainly use determinant factor and invariant factor to characterize the controllability of the system.The sufficient and necessary conditions for the controllability of the general linear system are given.By analyzing the solutions of linear equations,we discuss the existence and uniqueness of feedback matrix in different cases in which the equations have the solution or not.and in the cases in which the existence and uniqueness of the solution.Furthermore,the controllability of the complex system is transformed into the controllability of its topological structure.At the same time combined with specific topology structure,its controllability is judged by calculating determinant factor and invariant factor.