A note on the minimum‐norm in dual space approach to some classical linear optimal control problems
Abstract Some classical optimal control problems of linear systems can be characterized as finding minimum‐norm vectors from within linear varieties in appropriate dual spaces. Then, the solution to such an optimal control problem can be derived from the alignment between the optimal vector in the d...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-06-01
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| Series: | The Journal of Engineering |
| Subjects: | |
| Online Access: | https://doi.org/10.1049/tje2.12277 |
| _version_ | 1797794575856697344 |
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| author | Yue Zhou Pushkin Kachroo Kaan Ozbay |
| author_facet | Yue Zhou Pushkin Kachroo Kaan Ozbay |
| author_sort | Yue Zhou |
| collection | DOAJ |
| description | Abstract Some classical optimal control problems of linear systems can be characterized as finding minimum‐norm vectors from within linear varieties in appropriate dual spaces. Then, the solution to such an optimal control problem can be derived from the alignment between the optimal vector in the dual space and the optimal vector in the primal space, and the dual maximization problem of the minimum‐norm problem. This note presents a detailed introduction to this minimum‐norm in dual space approach by examples of minimum‐supremum‐norm, minimum‐energy, and minimum‐time optimal control problems of linear systems. Connections and differences between these problems in light of the introduced approach are discussed. |
| first_indexed | 2024-03-13T03:04:58Z |
| format | Article |
| id | doaj.art-9e8d89d4ba464f8fa4a15d63f2c7a1f8 |
| institution | Directory Open Access Journal |
| issn | 2051-3305 |
| language | English |
| last_indexed | 2024-03-13T03:04:58Z |
| publishDate | 2023-06-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Journal of Engineering |
| spelling | doaj.art-9e8d89d4ba464f8fa4a15d63f2c7a1f82023-06-27T07:44:34ZengWileyThe Journal of Engineering2051-33052023-06-0120236n/an/a10.1049/tje2.12277A note on the minimum‐norm in dual space approach to some classical linear optimal control problemsYue Zhou0Pushkin Kachroo1Kaan Ozbay2Department of Consultation and Research China Intelligent Transportation Systems Association (ITS China) Beijing ChinaDepartment of Electrical and Computer Engineering University of Nevada Las Vegas Nevada USADepartment of Civil and Urban Engineering and Connected Cities with Smart Transportation (C2SMART) Center Tandon School of Engineering New York University Brooklyn New York USAAbstract Some classical optimal control problems of linear systems can be characterized as finding minimum‐norm vectors from within linear varieties in appropriate dual spaces. Then, the solution to such an optimal control problem can be derived from the alignment between the optimal vector in the dual space and the optimal vector in the primal space, and the dual maximization problem of the minimum‐norm problem. This note presents a detailed introduction to this minimum‐norm in dual space approach by examples of minimum‐supremum‐norm, minimum‐energy, and minimum‐time optimal control problems of linear systems. Connections and differences between these problems in light of the introduced approach are discussed.https://doi.org/10.1049/tje2.12277linear systemsoptimal control |
| spellingShingle | Yue Zhou Pushkin Kachroo Kaan Ozbay A note on the minimum‐norm in dual space approach to some classical linear optimal control problems The Journal of Engineering linear systems optimal control |
| title | A note on the minimum‐norm in dual space approach to some classical linear optimal control problems |
| title_full | A note on the minimum‐norm in dual space approach to some classical linear optimal control problems |
| title_fullStr | A note on the minimum‐norm in dual space approach to some classical linear optimal control problems |
| title_full_unstemmed | A note on the minimum‐norm in dual space approach to some classical linear optimal control problems |
| title_short | A note on the minimum‐norm in dual space approach to some classical linear optimal control problems |
| title_sort | note on the minimum norm in dual space approach to some classical linear optimal control problems |
| topic | linear systems optimal control |
| url | https://doi.org/10.1049/tje2.12277 |
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