The time-optimal problem is considered for the controllable heat conduction process in a rod. Using the Fourier method, the problem is usually reduced to an infinite system of one-dimensional control equations whose control parameters are connected by complex relationships that make it difficult to solve. This article presents a method for regrouping the terms of the Fourier series of the control function, enabling the reduction of the problem to a finite-dimensional framework. The resulting reduced problem facilitates the more effective construction of a suboptimal control.
| Mualliflar | Azamov, Abdulla, Bakhramov , Jasurbek |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2025-11-03 |
| Jild | 69 |
| Son | 4 |
| Betlar | 35-39 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2025-4-4 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2025-4-4 · Maqolaning asl sahifasi
heat equation, control problem, time optimality, Fourier expansion, regrouping, finite dimensional reduction, suboptimal control.
| APA | Azamov, Abdulla, & Bakhramov , Jasurbek (2025). On Finite-Dimensional Approximations of the Time-Optimal Control Problem for the Heat Equation in a Rod. O‘zbekiston matematika jurnali, 69(4), 35-39. https://doi.org/10.29229/uzmj.2025-4-4 |
|---|---|
| GOST (OAK) | Azamov, Abdulla, Bakhramov , Jasurbek On Finite-Dimensional Approximations of the Time-Optimal Control Problem for the Heat Equation in a Rod // O‘zbekiston matematika jurnali. – 2025. – T. 69, № 4. – P. 35-39. – DOI: 10.29229/uzmj.2025-4-4. |
| MLA | Azamov, Abdulla, and Bakhramov , Jasurbek. “On Finite-Dimensional Approximations of the Time-Optimal Control Problem for the Heat Equation in a Rod.” O‘zbekiston matematika jurnali, 69(4), 35-39, 2025. https://doi.org/10.29229/uzmj.2025-4-4 |
| Chicago | Azamov, Abdulla, and Bakhramov , Jasurbek. “On Finite-Dimensional Approximations of the Time-Optimal Control Problem for the Heat Equation in a Rod.” O‘zbekiston matematika jurnali, 69(4), 35-39 (2025). https://doi.org/10.29229/uzmj.2025-4-4 |
| Harvard | Azamov, Abdulla, and Bakhramov , Jasurbek (2025) ‘On Finite-Dimensional Approximations of the Time-Optimal Control Problem for the Heat Equation in a Rod’, O‘zbekiston matematika jurnali, 69(4), 35-39. https://doi.org/10.29229/uzmj.2025-4-4 |
| BibTeX | @article{azamovabdulla2025,
title = {On Finite-Dimensional Approximations of the Time-Optimal Control Problem for the Heat Equation in a Rod},
author = {Azamov, Abdulla and Bakhramov , Jasurbek},
journal = {O‘zbekiston matematika jurnali},
year = {2025},
volume = {69},
number = {4},
pages = {35-39},
doi = {10.29229/uzmj.2025-4-4},
url = {https://doi.org/10.29229/uzmj.2025-4-4}
} |
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