JZUS - Journal of Zhejiang University SCIENCE

Frontiers of Information Technology & Electronic Engineering 2015 Vol.16 No.10 P.838-847

Controllability analysis of second-order multi-agent systems with directed and weighted interconnection

Author(s): Di Guo, Rong-hao Zheng, Zhi-yun Lin, Gang-feng Yan
Affiliation(s): State Key Laboratory of Industrial Control Technology, College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China
Corresponding email(s): emaiguo@gmail.com, rzheng@zju.edu.cn
Key Words: Multi-agent systems, Controllability, Directed tree

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Abstract: This article investigates the controllability problem of multi-agent systems. Each agent is assumed to be governed by a second-order consensus control law corresponding to a directed and weighted graph. Two types of topology are considered. The first is concerned with directed trees, which represent the class of topology with minimum information exchange among all controllable topologies. A very simple necessary and sufficient condition regarding the weighting scheme is obtained for the controllability of double integrator multi-agent systems in this scenario. The second is concerned with a more general graph that can be reduced to a directed tree by contracting a cluster of nodes to a component. A similar necessary and sufficient condition is derived. Finally, several illustrative examples are provided to demonstrate the theoretical analysis results.

This paper proposes a method to choose weights in a directed graph that models a leader-follower network of double integrators so that the network is controllable. The proposed condition which basically consists in choosing different weights for each link is proven to be necessary and sufficient. The authors also consider contracted-trees, which slightly generalize the result to graphs in which nodes can clustered so that a directed tree connects the clusters and inside the clusters there can be arbitrary feedback links among nodes of the same cluster. The paper is well written and clear. The results seem technically sound.

基于有向权重拓扑的二阶多智能体系统可控性分析

目的：面向有向拓扑的二阶多智能体系统，分析其可控性的充要条件。
创新点：使用有向树作为研究起点，在此基础上研究拓展拓扑的可控性条件，使有向拓扑的可控性研究前进了一步。
方法：用标准线性系统可控性分析方法，利用代数矩阵论工具，可得到有向树拓扑的可控性充要条件（定理1）。在此基础上，研究拓展拓扑的可控性条件，得到定理2。特别地，当子拓扑结构为前向环或者后向环时，分别得到定理3和定理4。
结论：针对有向树，得到一个重要结论：当且仅当不同分支上的智能体选取不同的权值，整个系统可控；在此基础上，得到拓展拓扑的相似结论。

关键词：多智能体系统；可控性；有向树

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