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

GUO Di; ZHENG Rong-hao; LIN Zhi-yun; YAN Gang-feng

doi:10.1631/FITEE.1500069

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

Computer & Automation | Updated：2022-06-06

- Controllability analysis of second-order multi-agent systems with directed and weighted interconnection
- 基于有向权重拓扑的二阶多智能体系统可控性分析
- Frontiers of Information Technology & Electronic Engineering Vol. 16, Issue 10, Pages: 838-847(2015)
- Affiliations：
  
  State Key Laboratory of Industrial Control Technology, College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China
- Author bio：
  
  [ "Di GUO, E-mail: emaiguo@gmail.com" ]
  Rong-hao ZHENG, E-mail:rzheng@zju.edu.cn
- Funds：
- DOI：10.1631/FITEE.1500069
  CLC： TP13
- Received：07 March 2015，
  
  Revised：2015-08-25，
  
  Published：2015-10
- Accepted：
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GUO Di, ZHENG Rong-hao, LIN Zhi-yun, et al. Controllability analysis of second-order multi-agent systems with directed and weighted interconnection[J]. Frontiers of Information Technology & Electronic Engineering, 2015, 16(10): 838-847.
DOI：

GUO Di, ZHENG Rong-hao, LIN Zhi-yun, et al. Controllability analysis of second-order multi-agent systems with directed and weighted interconnection[J]. Frontiers of Information Technology & Electronic Engineering, 2015, 16(10): 838-847. DOI： 10.1631/FITEE.1500069.

摘要

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。

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.

关键词

Keywords

references

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