A New Perspective to Algebraic Characterization on Controllability of Multiagent Systems

Bo Liu,Licheng Wu,Housheng Su,Shengchao He

doi:10.1155/2020/9703972

Abstract

Recently, algebraic characterization of multiagent controllability through its topology has been widely concerned by the systems and control community. The controllability of leader-follower networked multiagent systems under the framework of generic linear dynamics is firstly discussed via λ-matrix. Some new algebra-theoretic necessary and/or sufficient conditions of the controllability for generic linear multiagent systems are established. Moreover, the controllable conditions for multiagent networks with special topological graphs through λ-matrix are presented.

Highlights

Cooperative and coordinated control of networked multiagent systems has become a surge of research activities. e controllability is a basic and important problem in modern control theory, which plays a key role in the analysis and synthesis of networked multiagent systems and has wide applications and advantages in formation control, pinning control, containment control and tracking control, etc [1,2,3,4,5,6,7,8,9,10]
Liu et al [12] first proposed the concept of the controllability for a leader-follower dynamic network with discrete-time state and established some algebraic criteria on the controllability under different topologies, respectively
Wang et al [17] studied the controllability of multiagent systems with the consensus protocols under directed topologies for high-order-integrator dynamic agents and general linear dynamic intelligent agents, respectively, in which the authors illustrated that the controllability congruously depended on the interconnection topology among agents and dynamics

Summary

Introduction

Cooperative and coordinated control of networked multiagent systems has become a surge of research activities. e controllability is a basic and important problem in modern control theory, which plays a key role in the analysis and synthesis of networked multiagent systems and has wide applications and advantages in formation control, pinning control, containment control and tracking control, etc [1,2,3,4,5,6,7,8,9,10]. Controllability problem for a group of systems was first put forward by Tanner [11] in 2004 from the viewpoint of algebra, in which singleintegrator continuous-time model with a leader in terms of nearest neighbor rules was formulated, and an algebraic controllable criterion in view of eigenvalues and right eigenvectors of submatrices of Laplacian matrix was obtained under a fixed topology. Studies in this algebraic point of view have provided a theoretical basis for understanding internal relationships and interactions among graph structures, evolutionary protocol, and controllability.

Problem Formulation and Preliminaries

Controllability Analysis Using λ-Matrix

Simulation Examples