Optimal Control through Leadership of the Cucker and Smale Flocking Model with Time Delays
The Cucker and Smale model is a well-known flocking model that describes the emergence of flocks based on alignment. The first part focuses on investigating this model, including the effect of time delay and the presence of a leader. Furthermore, the control function is inserted into the dynamics of...
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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/10.1155/2021/5545551 |
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| _version_ | 1832561442461581312 |
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| author | Adsadang Himakalasa Suttida Wongkaew |
| author_facet | Adsadang Himakalasa Suttida Wongkaew |
| author_sort | Adsadang Himakalasa |
| collection | DOAJ |
| description | The Cucker and Smale model is a well-known flocking model that describes the emergence of flocks based on alignment. The first part focuses on investigating this model, including the effect of time delay and the presence of a leader. Furthermore, the control function is inserted into the dynamics of a leader to drive a group of agents to target. In the second part of this work, leadership-based optimal control is investigated. Moreover, the existence of the first-order optimality conditions for a delayed optimal control problem is discussed. Furthermore, the Runge–Kutta discretization method and the nonlinear conjugate gradient method are employed to solve the discrete optimality system. Finally, the capacity of the proposed control approach to drive a group of agents to reach the desired places or track the trajectory is demonstrated by numerical experiment results. |
| format | Article |
| id | doaj-art-93e17d6a459f4661adb361d0dd0da006 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-93e17d6a459f4661adb361d0dd0da0062025-02-03T01:25:01ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/55455515545551Optimal Control through Leadership of the Cucker and Smale Flocking Model with Time DelaysAdsadang Himakalasa0Suttida Wongkaew1PhD Degree Program in Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandResearch Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandThe Cucker and Smale model is a well-known flocking model that describes the emergence of flocks based on alignment. The first part focuses on investigating this model, including the effect of time delay and the presence of a leader. Furthermore, the control function is inserted into the dynamics of a leader to drive a group of agents to target. In the second part of this work, leadership-based optimal control is investigated. Moreover, the existence of the first-order optimality conditions for a delayed optimal control problem is discussed. Furthermore, the Runge–Kutta discretization method and the nonlinear conjugate gradient method are employed to solve the discrete optimality system. Finally, the capacity of the proposed control approach to drive a group of agents to reach the desired places or track the trajectory is demonstrated by numerical experiment results.http://dx.doi.org/10.1155/2021/5545551 |
| spellingShingle | Adsadang Himakalasa Suttida Wongkaew Optimal Control through Leadership of the Cucker and Smale Flocking Model with Time Delays Complexity |
| title | Optimal Control through Leadership of the Cucker and Smale Flocking Model with Time Delays |
| title_full | Optimal Control through Leadership of the Cucker and Smale Flocking Model with Time Delays |
| title_fullStr | Optimal Control through Leadership of the Cucker and Smale Flocking Model with Time Delays |
| title_full_unstemmed | Optimal Control through Leadership of the Cucker and Smale Flocking Model with Time Delays |
| title_short | Optimal Control through Leadership of the Cucker and Smale Flocking Model with Time Delays |
| title_sort | optimal control through leadership of the cucker and smale flocking model with time delays |
| url | http://dx.doi.org/10.1155/2021/5545551 |
| work_keys_str_mv | AT adsadanghimakalasa optimalcontrolthroughleadershipofthecuckerandsmaleflockingmodelwithtimedelays AT suttidawongkaew optimalcontrolthroughleadershipofthecuckerandsmaleflockingmodelwithtimedelays |