Time optimal sampled-data controls for heat equations Article Swipe
Gengsheng Wang
,
Donghui Yang
,
Yubiao Zhang
·
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1701.06116
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1701.06116
In this paper, we first design a time optimal control problem for the heat equation with sampled-data controls, and then use it to approximate a time optimal control problem for the heat equation with distributed controls. Our design is reasonable from perspective of sampled-data controls. And it might provide a right way for the numerical approach of a time optimal distributed control problem, via the corresponding semi-discretized (in time variable) time optimal control problem. The study of such a time optimal sampled-data control problem is not easy, because it may have infinitely many optimal controls. We find connections among this problem, a minimal norm sampled-data control problem and a minimization problem. And obtain some properties on these problems. Based on these, we not only build up error estimates for optimal time and optimal controls between the time optimal sampled-data control problem and the time optimal distributed control problem, in terms of the sampling period, but also prove that such estimates are optimal in some sense.
Related Topics
Concepts
Optimal control
Discretization
Mathematical optimization
Control variable
Minification
Control (management)
Mathematics
Heat equation
Optimization problem
Computer science
Sampling (signal processing)
Control theory (sociology)
Statistics
Filter (signal processing)
Artificial intelligence
Mathematical analysis
Computer vision
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1701.06116
- https://arxiv.org/pdf/1701.06116
- OA Status
- green
- References
- 33
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2951026378
All OpenAlex metadata
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https://openalex.org/W2951026378Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.1701.06116Digital Object Identifier
- Title
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Time optimal sampled-data controls for heat equationsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2017Year of publication
- Publication date
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2017-01-22Full publication date if available
- Authors
-
Gengsheng Wang, Donghui Yang, Yubiao ZhangList of authors in order
- Landing page
-
https://arxiv.org/abs/1701.06116Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/1701.06116Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
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https://arxiv.org/pdf/1701.06116Direct OA link when available
- Concepts
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Optimal control, Discretization, Mathematical optimization, Control variable, Minification, Control (management), Mathematics, Heat equation, Optimization problem, Computer science, Sampling (signal processing), Control theory (sociology), Statistics, Filter (signal processing), Artificial intelligence, Mathematical analysis, Computer visionTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- References (count)
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33Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.variable) | 69 |
| abstract_inverted_index.infinitely | 91 |
| abstract_inverted_index.properties | 114 |
| abstract_inverted_index.reasonable | 39 |
| abstract_inverted_index.approximate | 23 |
| abstract_inverted_index.connections | 97 |
| abstract_inverted_index.distributed | 34, 60, 145 |
| abstract_inverted_index.perspective | 41 |
| abstract_inverted_index.minimization | 109 |
| abstract_inverted_index.sampled-data | 16, 43, 81, 104, 138 |
| abstract_inverted_index.corresponding | 65 |
| abstract_inverted_index.semi-discretized | 66 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile |