A necessary and sufficient condition for the controllability of single-leader multi-chain systems

被引：23

作者：

Hsu, Shun-Pin ^{[1
]}

机构：

[1] Natl Chung Hsing Univ, Dept Elect Engn, Taichung 402, Taiwan

来源：

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL | 2017年 / 27卷 / 01期

关键词：

controllability; multi-agent systems; multi-chain systems; DISTRIBUTED CONTROL; OBSERVABILITY; COORDINATION; NETWORKS; GRAPHS;

D O I：

10.1002/rnc.3566

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this work, the controllability of single-leader multi-agent systems with chain structures is studied. It is shown that the necessary and sufficient condition for the multi-chain system to be controllable is that there exist no two chain lengths in the form l(1) = i + k(1)(2i + 1) and l(2) + k(2)(2i + 1), where i is some natural number and k(1) and k(2) some nonnegative integers. Using this condition, the author derives an upper bound based on the length of the longest chain and proves that if the number of chains exceeds this bound, the multi-chain system must be uncontrollable. In addition, the author investigates an augmented system constructed by connecting some follower nodes of the multi-chain system and obtains a sufficient condition for the augmented system to be uncontrollable. Finally, the author shows how to select a minimum number of additional leaders to make an uncontrollable multi-chain system controllable. Numerical examples are provided to illustrate the results. Copyright (C) 2016 John Wiley & Sons, Ltd.

引用

页码：156 / 168

页数：13

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