Constructing a controllable graph under edge constraints

This paper is concerned with the problem of constructing a controllable graph subject to some practical edge constraints. Specifically, suppose the total amount of vertices and the upper bounds on the graph diameter or on the vertex degree are given. We consider the problem of exploring a class of f...

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Bibliographic Details
Published inSystems & control letters Vol. 107; pp. 110 - 116
Main Author Hsu, Shun-Pin
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.09.2017
Subjects
Controllability
Multi-agent systems
Path graph
Threshold graph
Controllability
Threshold graph
Path graph
Multi-agent systems
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Summary:This paper is concerned with the problem of constructing a controllable graph subject to some practical edge constraints. Specifically, suppose the total amount of vertices and the upper bounds on the graph diameter or on the vertex degree are given. We consider the problem of exploring a class of feasible graphs that satisfy the constraints. Using the hybrid of a path graph and an antiregular graph we propose a simple and systematic method to generate a class of controllable graphs whose diameters or degrees cover the full possible ranges. The method to select the control vector to ensure the controllability of the combined graph is also proposed. Numerical examples are provided to demonstrate our results.
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2017.07.015