Controllability of Flow-Conservation Transportation Networks with Fractional-Order Dynamics
In this paper, we adapt the fractional derivative approach to formulate the flow-conservation transportation networks, which consider the propagation dynamics and the users’ behaviors in terms of route choices. We then investigate the controllability of the fractional-order transportation networks b...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/8524984 |
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| _version_ | 1850232330167255040 |
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| author | Wei Chen Bo Zhou |
| author_facet | Wei Chen Bo Zhou |
| author_sort | Wei Chen |
| collection | DOAJ |
| description | In this paper, we adapt the fractional derivative approach to formulate the flow-conservation transportation networks, which consider the propagation dynamics and the users’ behaviors in terms of route choices. We then investigate the controllability of the fractional-order transportation networks by employing the Popov-Belevitch-Hautus rank condition and the QR decomposition algorithm. Furthermore, we provide the exact solutions for the full controllability pricing controller location problem, which includes where to locate the controllers and how many controllers are required at the location positions. Finally, we illustrate two numerical examples to validate the theoretical analysis. |
| format | Article |
| id | doaj-art-006af851e7dc4d92abfcd5ecb15829d5 |
| institution | OA Journals |
| issn | 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-006af851e7dc4d92abfcd5ecb15829d52025-08-20T02:03:14ZengWileyComplexity1099-05262021-01-01202110.1155/2021/8524984Controllability of Flow-Conservation Transportation Networks with Fractional-Order DynamicsWei Chen0Bo Zhou1College of Mathematics and StatisticsCollege of Mathematics and StatisticsIn this paper, we adapt the fractional derivative approach to formulate the flow-conservation transportation networks, which consider the propagation dynamics and the users’ behaviors in terms of route choices. We then investigate the controllability of the fractional-order transportation networks by employing the Popov-Belevitch-Hautus rank condition and the QR decomposition algorithm. Furthermore, we provide the exact solutions for the full controllability pricing controller location problem, which includes where to locate the controllers and how many controllers are required at the location positions. Finally, we illustrate two numerical examples to validate the theoretical analysis.http://dx.doi.org/10.1155/2021/8524984 |
| spellingShingle | Wei Chen Bo Zhou Controllability of Flow-Conservation Transportation Networks with Fractional-Order Dynamics Complexity |
| title | Controllability of Flow-Conservation Transportation Networks with Fractional-Order Dynamics |
| title_full | Controllability of Flow-Conservation Transportation Networks with Fractional-Order Dynamics |
| title_fullStr | Controllability of Flow-Conservation Transportation Networks with Fractional-Order Dynamics |
| title_full_unstemmed | Controllability of Flow-Conservation Transportation Networks with Fractional-Order Dynamics |
| title_short | Controllability of Flow-Conservation Transportation Networks with Fractional-Order Dynamics |
| title_sort | controllability of flow conservation transportation networks with fractional order dynamics |
| url | http://dx.doi.org/10.1155/2021/8524984 |
| work_keys_str_mv | AT weichen controllabilityofflowconservationtransportationnetworkswithfractionalorderdynamics AT bozhou controllabilityofflowconservationtransportationnetworkswithfractionalorderdynamics |