REGULARIZATION OF PONTRYAGIN MAXIMUM PRINCIPLE IN OPTIMAL CONTROL OF DISTRIBUTED SYSTEMS
This article is devoted to studying dual regularization method applied to parametric convex optimal control problem of controlled third boundary–value problem for parabolic equation with boundary control and with equality and inequality pointwise state constraints. This dual regularization method yi...
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Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2016-11-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/53 |
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| author | Mikhail I. Sumin |
| author_facet | Mikhail I. Sumin |
| author_sort | Mikhail I. Sumin |
| collection | DOAJ |
| description | This article is devoted to studying dual regularization method applied to parametric convex optimal control problem of controlled third boundary–value problem for parabolic equation with boundary control and with equality and inequality pointwise state constraints. This dual regularization method yields the corresponding necessary and sufficient conditions for minimizing sequences, namely, the stable, with respect to perturbation of input data, sequential or, in other words, regularized Lagrange principle in nondifferential form and Pontryagin maximum principle for the original problem. Regardless of the fact that the stability or instability of the original optimal control problem, they stably generate a minimizing approximate solutions in the sense of J. Warga for it. For this reason, we can interpret these regularized Lagrange principle and Pontryagin maximum principle as tools for direct solving unstable optimal control problems and reducing to them unstable inverse problems. |
| format | Article |
| id | doaj-art-3bae63c40e774b6d8499d434a3a13e8c |
| institution | Matheson Library |
| issn | 2414-3952 |
| language | English |
| publishDate | 2016-11-01 |
| publisher | Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj-art-3bae63c40e774b6d8499d434a3a13e8c2025-08-02T05:43:20ZengUral Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and MechanicsUral Mathematical Journal2414-39522016-11-012210.15826/umj.2016.2.00823REGULARIZATION OF PONTRYAGIN MAXIMUM PRINCIPLE IN OPTIMAL CONTROL OF DISTRIBUTED SYSTEMSMikhail I. Sumin0Nizhnii Novgorod State University, Nizhnii NovgorodThis article is devoted to studying dual regularization method applied to parametric convex optimal control problem of controlled third boundary–value problem for parabolic equation with boundary control and with equality and inequality pointwise state constraints. This dual regularization method yields the corresponding necessary and sufficient conditions for minimizing sequences, namely, the stable, with respect to perturbation of input data, sequential or, in other words, regularized Lagrange principle in nondifferential form and Pontryagin maximum principle for the original problem. Regardless of the fact that the stability or instability of the original optimal control problem, they stably generate a minimizing approximate solutions in the sense of J. Warga for it. For this reason, we can interpret these regularized Lagrange principle and Pontryagin maximum principle as tools for direct solving unstable optimal control problems and reducing to them unstable inverse problems.https://umjuran.ru/index.php/umj/article/view/53Optimal boundary control, Parabolic equation, Minimizing sequence, Dual regularization, Stability, Lagrange principle, Pontryagin maximum principle |
| spellingShingle | Mikhail I. Sumin REGULARIZATION OF PONTRYAGIN MAXIMUM PRINCIPLE IN OPTIMAL CONTROL OF DISTRIBUTED SYSTEMS Ural Mathematical Journal Optimal boundary control, Parabolic equation, Minimizing sequence, Dual regularization, Stability, Lagrange principle, Pontryagin maximum principle |
| title | REGULARIZATION OF PONTRYAGIN MAXIMUM PRINCIPLE IN OPTIMAL CONTROL OF DISTRIBUTED SYSTEMS |
| title_full | REGULARIZATION OF PONTRYAGIN MAXIMUM PRINCIPLE IN OPTIMAL CONTROL OF DISTRIBUTED SYSTEMS |
| title_fullStr | REGULARIZATION OF PONTRYAGIN MAXIMUM PRINCIPLE IN OPTIMAL CONTROL OF DISTRIBUTED SYSTEMS |
| title_full_unstemmed | REGULARIZATION OF PONTRYAGIN MAXIMUM PRINCIPLE IN OPTIMAL CONTROL OF DISTRIBUTED SYSTEMS |
| title_short | REGULARIZATION OF PONTRYAGIN MAXIMUM PRINCIPLE IN OPTIMAL CONTROL OF DISTRIBUTED SYSTEMS |
| title_sort | regularization of pontryagin maximum principle in optimal control of distributed systems |
| topic | Optimal boundary control, Parabolic equation, Minimizing sequence, Dual regularization, Stability, Lagrange principle, Pontryagin maximum principle |
| url | https://umjuran.ru/index.php/umj/article/view/53 |
| work_keys_str_mv | AT mikhailisumin regularizationofpontryaginmaximumprincipleinoptimalcontrolofdistributedsystems |