Impulse and Sampled-Data Optimal Control of Heat Equations, and Error Estimates Article Swipe
Emmanuel Trélat
,
Lijuan Wang
,
Yubiao Zhang
·
YOU?
·
· 2016
· Open Access
·
· DOI: https://doi.org/10.1137/15m1040670
YOU?
·
· 2016
· Open Access
·
· DOI: https://doi.org/10.1137/15m1040670
We consider the optimal control problem of minimizing some quadratic\nfunctional over all possible solutions of an internally controlled\nmulti-dimensional heat equation with a periodic terminal state constraint. This\nproblem has a unique optimal solution, which can be characterized by an\noptimality system derived from the Pontryagin maximum principle. We define two\napproximations of this optimal control problem. The first one is an impulse\napproximation, and consists of considering a system of linear heat equations\nwith impulse control. The second one is obtained by the sample-and-hold\nprocedure applied to the control, resulting into a sampled-data approximation\nof the controlled heat equation. We prove that both problems have a unique\noptimal solution, and we establish precise error estimates for the optimal\ncontrols and optimal states of the initial problem with respect to its impulse\nand sampled-data approximations.\n
Related Topics
Concepts
Optimal control
Mathematics
Impulse (physics)
Impulse control
Heat equation
Applied mathematics
Maximum principle
Pontryagin's minimum principle
Quadratic equation
Approximations of π
Mathematical optimization
Control theory (sociology)
Mathematical analysis
Control (management)
Computer science
Psychotherapist
Psychology
Artificial intelligence
Physics
Quantum mechanics
Geometry
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1137/15m1040670
- OA Status
- green
- Cited By
- 29
- References
- 37
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2127615550
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W2127615550Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1137/15m1040670Digital Object Identifier
- Title
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Impulse and Sampled-Data Optimal Control of Heat Equations, and Error EstimatesWork title
- Type
-
articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2016Year of publication
- Publication date
-
2016-01-01Full publication date if available
- Authors
-
Emmanuel Trélat, Lijuan Wang, Yubiao ZhangList of authors in order
- Landing page
-
https://doi.org/10.1137/15m1040670Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/1509.05932Direct OA link when available
- Concepts
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Optimal control, Mathematics, Impulse (physics), Impulse control, Heat equation, Applied mathematics, Maximum principle, Pontryagin's minimum principle, Quadratic equation, Approximations of π, Mathematical optimization, Control theory (sociology), Mathematical analysis, Control (management), Computer science, Psychotherapist, Psychology, Artificial intelligence, Physics, Quantum mechanics, GeometryTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
29Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 2, 2024: 6, 2022: 1, 2021: 6, 2020: 1Per-year citation counts (last 5 years)
- References (count)
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37Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| primary_location.raw_source_name | SIAM Journal on Control and Optimization |
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| publication_date | 2016-01-01 |
| publication_year | 2016 |
| referenced_works | https://openalex.org/W1995018531, https://openalex.org/W2094254426, https://openalex.org/W2053362105, https://openalex.org/W1745577466, https://openalex.org/W2118481011, https://openalex.org/W1984479582, https://openalex.org/W89839489, https://openalex.org/W126240089, https://openalex.org/W2024295674, https://openalex.org/W1968702788, https://openalex.org/W2081581211, https://openalex.org/W2012666906, https://openalex.org/W2023940093, https://openalex.org/W1968834064, https://openalex.org/W2012408233, https://openalex.org/W2000334666, https://openalex.org/W2045354979, https://openalex.org/W2006681194, https://openalex.org/W1970963843, https://openalex.org/W2171568556, https://openalex.org/W2053756579, https://openalex.org/W2121623735, https://openalex.org/W1985491254, https://openalex.org/W2033517841, https://openalex.org/W2103284380, https://openalex.org/W1589236075, https://openalex.org/W30907860, https://openalex.org/W1866311589, https://openalex.org/W1509930179, https://openalex.org/W185172081, https://openalex.org/W1593038947, https://openalex.org/W187630271, https://openalex.org/W1524099673, https://openalex.org/W2964225436, https://openalex.org/W2952284893, https://openalex.org/W1628576809, https://openalex.org/W1499788862 |
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