Jordan Form-Based Algebraic Conditions for Controllability of Multiagent Systems under Directed Graphs

Based on the Jordan form of system matrix, this paper discusses algebraic conditions for the controllability of the multiagent network system with directed graph from two aspects: leader-follower network attribute and coupling input disturbance. Leader-follower network attribute refers to the topolo...

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Main Authors: Shuai Liu, Zhijian Ji, Huizi Ma
Format: Article
Language:English
Published: Wiley 2020-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2020/7685460
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author Shuai Liu
Zhijian Ji
Huizi Ma
author_facet Shuai Liu
Zhijian Ji
Huizi Ma
author_sort Shuai Liu
collection DOAJ
description Based on the Jordan form of system matrix, this paper discusses algebraic conditions for the controllability of the multiagent network system with directed graph from two aspects: leader-follower network attribute and coupling input disturbance. Leader-follower network attribute refers to the topology structure and information communication among agents. Coupling input disturbance includes the number of external coupling inputs and the selection of leader nodes. When the leader-follower network attribute is fixed, the selection method of coupling input disturbance is studied for the controllability, and when the coupling input disturbance is known, we derive necessity and sufficiency conditions to determine the controllability. The reliability of theoretical results is verified by numerical examples and model simulation. Besides, the generally perfect controllability is introduced, that is, the system is always controllable regardless of the number and the locations of leaders. In practical engineering applications, the perfectly controllable topology can improve the system fault tolerance and accelerate the commercialization process, which has a profound significance for promoting the modernization process.
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spelling doaj-art-e95719f852eb4db28ee7407308666aea2025-08-20T03:21:08ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/76854607685460Jordan Form-Based Algebraic Conditions for Controllability of Multiagent Systems under Directed GraphsShuai Liu0Zhijian Ji1Huizi Ma2Institute of Complexity Science, College of Automation, Qingdao University, Qingdao 266071, ChinaInstitute of Complexity Science, College of Automation, Qingdao University, Qingdao 266071, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaBased on the Jordan form of system matrix, this paper discusses algebraic conditions for the controllability of the multiagent network system with directed graph from two aspects: leader-follower network attribute and coupling input disturbance. Leader-follower network attribute refers to the topology structure and information communication among agents. Coupling input disturbance includes the number of external coupling inputs and the selection of leader nodes. When the leader-follower network attribute is fixed, the selection method of coupling input disturbance is studied for the controllability, and when the coupling input disturbance is known, we derive necessity and sufficiency conditions to determine the controllability. The reliability of theoretical results is verified by numerical examples and model simulation. Besides, the generally perfect controllability is introduced, that is, the system is always controllable regardless of the number and the locations of leaders. In practical engineering applications, the perfectly controllable topology can improve the system fault tolerance and accelerate the commercialization process, which has a profound significance for promoting the modernization process.http://dx.doi.org/10.1155/2020/7685460
spellingShingle Shuai Liu
Zhijian Ji
Huizi Ma
Jordan Form-Based Algebraic Conditions for Controllability of Multiagent Systems under Directed Graphs
Complexity
title Jordan Form-Based Algebraic Conditions for Controllability of Multiagent Systems under Directed Graphs
title_full Jordan Form-Based Algebraic Conditions for Controllability of Multiagent Systems under Directed Graphs
title_fullStr Jordan Form-Based Algebraic Conditions for Controllability of Multiagent Systems under Directed Graphs
title_full_unstemmed Jordan Form-Based Algebraic Conditions for Controllability of Multiagent Systems under Directed Graphs
title_short Jordan Form-Based Algebraic Conditions for Controllability of Multiagent Systems under Directed Graphs
title_sort jordan form based algebraic conditions for controllability of multiagent systems under directed graphs
url http://dx.doi.org/10.1155/2020/7685460
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AT zhijianji jordanformbasedalgebraicconditionsforcontrollabilityofmultiagentsystemsunderdirectedgraphs
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