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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/7685460 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849691113077604352 |
|---|---|
| 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. |
| format | Article |
| id | doaj-art-e95719f852eb4db28ee7407308666aea |
| institution | DOAJ |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| 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 |
| work_keys_str_mv | AT shuailiu jordanformbasedalgebraicconditionsforcontrollabilityofmultiagentsystemsunderdirectedgraphs AT zhijianji jordanformbasedalgebraicconditionsforcontrollabilityofmultiagentsystemsunderdirectedgraphs AT huizima jordanformbasedalgebraicconditionsforcontrollabilityofmultiagentsystemsunderdirectedgraphs |