Pontryagin’s Principle-Based Algorithms for Optimal Control Problems of Parabolic Equations
This paper applies the Method of Successive Approximations (MSA) based on Pontryagin’s principle to solve optimal control problems with state constraints for semilinear parabolic equations. Error estimates for the first and second derivatives of the function are derived under <inline-formula>&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/7/1143 |
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| author | Weilong You Fu Zhang |
| author_facet | Weilong You Fu Zhang |
| author_sort | Weilong You |
| collection | DOAJ |
| description | This paper applies the Method of Successive Approximations (MSA) based on Pontryagin’s principle to solve optimal control problems with state constraints for semilinear parabolic equations. Error estimates for the first and second derivatives of the function are derived under <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mo>∞</mo></msup></semantics></math></inline-formula>-bounded conditions. An augmented MSA is developed using the augmented Lagrangian method, and its convergence is proven. The effectiveness of the proposed method is demonstrated through numerical experiments. |
| format | Article |
| id | doaj-art-e96c287528eb47c38c64496ababa9c35 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-e96c287528eb47c38c64496ababa9c352025-08-20T02:15:58ZengMDPI AGMathematics2227-73902025-03-01137114310.3390/math13071143Pontryagin’s Principle-Based Algorithms for Optimal Control Problems of Parabolic EquationsWeilong You0Fu Zhang1College of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaThis paper applies the Method of Successive Approximations (MSA) based on Pontryagin’s principle to solve optimal control problems with state constraints for semilinear parabolic equations. Error estimates for the first and second derivatives of the function are derived under <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mo>∞</mo></msup></semantics></math></inline-formula>-bounded conditions. An augmented MSA is developed using the augmented Lagrangian method, and its convergence is proven. The effectiveness of the proposed method is demonstrated through numerical experiments.https://www.mdpi.com/2227-7390/13/7/1143optimal controlparabolic equationPontryagin’s principleMSA |
| spellingShingle | Weilong You Fu Zhang Pontryagin’s Principle-Based Algorithms for Optimal Control Problems of Parabolic Equations Mathematics optimal control parabolic equation Pontryagin’s principle MSA |
| title | Pontryagin’s Principle-Based Algorithms for Optimal Control Problems of Parabolic Equations |
| title_full | Pontryagin’s Principle-Based Algorithms for Optimal Control Problems of Parabolic Equations |
| title_fullStr | Pontryagin’s Principle-Based Algorithms for Optimal Control Problems of Parabolic Equations |
| title_full_unstemmed | Pontryagin’s Principle-Based Algorithms for Optimal Control Problems of Parabolic Equations |
| title_short | Pontryagin’s Principle-Based Algorithms for Optimal Control Problems of Parabolic Equations |
| title_sort | pontryagin s principle based algorithms for optimal control problems of parabolic equations |
| topic | optimal control parabolic equation Pontryagin’s principle MSA |
| url | https://www.mdpi.com/2227-7390/13/7/1143 |
| work_keys_str_mv | AT weilongyou pontryaginsprinciplebasedalgorithmsforoptimalcontrolproblemsofparabolicequations AT fuzhang pontryaginsprinciplebasedalgorithmsforoptimalcontrolproblemsofparabolicequations |