Algorithm of the successive approximation method for optimal control problems with phase restrictions for mechanics tasks
| dc.citation.epage | 749 | |
| dc.citation.issue | 3 | |
| dc.citation.journalTitle | Математичне моделювання та комп'ютинг | |
| dc.citation.spage | 734 | |
| dc.contributor.affiliation | Дніпровський національний університет імені Олеся Гончара | |
| dc.contributor.affiliation | Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України | |
| dc.contributor.affiliation | Національний університет “Львівська політехніка” | |
| dc.contributor.affiliation | Oles Honchar Dnipro National University | |
| dc.contributor.affiliation | Pidstryhach Institute for Applied Problems of Mechanics and Mathematics | |
| dc.contributor.affiliation | Lviv Polytechnic National University | |
| dc.contributor.author | Дзюба, А. | |
| dc.contributor.author | Торський, А. | |
| dc.contributor.author | Dzyuba, A. | |
| dc.contributor.author | Torskyy, A. | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2025-03-04T11:33:02Z | |
| dc.date.created | 2022-02-28 | |
| dc.date.issued | 2022-02-28 | |
| dc.description.abstract | Запропоновано алгоритм методу послідовних наближень для задач оптимального керування за наявності довільних обмежень на керуючі та фазові змінні. Підхід базується на процедурах послідовного задоволення необхідних умов оптимальності у вигляді принципу максимуму Понтрягіна. Продемонстровано застосування алгоритму для задач оптимізації ваги силових елементів конструкцій за наявності обмежень міцності, жорсткості та технологічних вимог. | |
| dc.description.abstract | The algorithm of the method of successive approximations for problems of optimal control in the presence of arbitrary restrictions on control and phase variables is proposed. The approach is based on the procedures of consistent satisfaction of the necessary conditions of optimality in the form of Pontryagin's maximum principle. The algorithm application for the problems of weight optimization of power elements of structures in the presence of constraints of strength, rigidity, and technological requirements is demonstrated. | |
| dc.format.extent | 734-749 | |
| dc.format.pages | 16 | |
| dc.identifier.citation | Dzyuba A. Algorithm of the successive approximation method for optimal control problems with phase restrictions for mechanics tasks / A. Dzyuba, A. Torskyy // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 3. — P. 734–749. | |
| dc.identifier.citationen | Dzyuba A. Algorithm of the successive approximation method for optimal control problems with phase restrictions for mechanics tasks / A. Dzyuba, A. Torskyy // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 3. — P. 734–749. | |
| dc.identifier.doi | doi.org/10.23939/mmc2022.03.734 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/63470 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Математичне моделювання та комп'ютинг, 3 (9), 2022 | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 3 (9), 2022 | |
| dc.relation.references | [1] Bryson A. E., Yu-Chi Ho. Applied Optimal Control. Toronto, London (1969). | |
| dc.relation.references | [2] Dzyuba A. P., Sirenko V. N., Dzyuba A. A., Safronova I. A. Models and Algorithms for Optimizing Elements of Heterogeneous Shell Structures. Actual problems of mechanics: Monograph ed. by N. V. Polyakova. Dnipro, Lira. 225–244 (2018). | |
| dc.relation.references | [3] Fedorenko R. P. Approximate Solution of Optimal Control Problems. Moscow, Nauka (1978), (in Russian). | |
| dc.relation.references | [4] Gornov A. Yu. Algorithms for Solving Optimal Control Problems with Phase Constraints. Computational technologies. 15 (2), 24–30 (2010), (in Russian). | |
| dc.relation.references | [5] Karamzin D., Pereira F. L. On a Few Questions Regarding the Study of State-Сonstrained Problems in Optimal Control. Journal of Optimization Theory and Applications. 180, 235–255 (2019). | |
| dc.relation.references | [6] Srochko V. A. Iterative Methods for Solving Optimal Control Problems. Moscow, Fizmatgiz (2000), (in Russian). | |
| dc.relation.references | [7] Aisagaliev S., Zhunussova Zh., Akca H. Construction of a Solution for Optimal Control Problem with Phase and Integral Constructs. International Journal of Mathematics and Physics. 10 (1), 11–22 (2019). | |
| dc.relation.references | [8] Buldaev A. S., Burlakov I. D. Nonlocal Descent Method on the Set of Admissible Controls in Optimal Control Problems with Phase Constraints. Vesnik BSU. Series: Mathematics, Informatics. 3, 42–59 (2019). | |
| dc.relation.references | [9] Diveev A., Sofronova E., Zelinka I. Optimal Control Problem Solution With Phase Constraints for Group of Robots by Pontreagin Maximum Principle and Evolutionary Algorithm. Mathematics. 8 (12), 2105 (2020). | |
| dc.relation.references | [10] Trunin D. O. On One Procedure of Non-local Improvement of Controls in Systems Quadratic in State with Terminal Constraints. Bulletin of BSU. Ser.: Mathematics, Informatics. 2, 42–49 (2018), (in Russian). | |
| dc.relation.references | [11] Anorov V. Ya. The Maximum Principle for Processes with General Constraints, Automation and remote control. Part 1 (3), 5–15, Part 2 (4), 5–17 (1967). | |
| dc.relation.references | [12] Pontryagin L. S., Bolteanskii V. G., Gamkrelidze R. V., Mishchenko E. F. The Mathematical Theory of Optimal Processes. Interscience, New York, NY, USA (1962). | |
| dc.relation.references | [13] Bertsekas D. P. Constrained Optimization and Lagrange Multipliers Methods. Athena Scientific, Belmot, Mass. (1996). | |
| dc.relation.references | [14] Himmelblau D. M. Applied Nonlsnear Programming. Austsn. Texas (1972). | |
| dc.relation.references | [15] Krylov A. I., Chernousko F. L. An algorithm for the method of successive approximations in optimal control problems. USSR Computational Mathematics and Mathematical Physics. 12 (1), 15–38 (1972). | |
| dc.relation.references | [16] Voloshin V. V. On the Method of Successive Approximations for Optimal Control Problems. Discrete control systems: col. of sci. art., Kyiv, 24–32 (1972). | |
| dc.relation.references | [17] Dzyuba A. P., Safronova I. A., Levitina L. D. Algorithm for Computational Costs Reducing in Problems of Calculation of Asymmetrically Loaded Shells of Rotation. Strength of Materials and Theory of Structures. 105, 99–113 (2020). | |
| dc.relation.references | [18] Godunov S. K. Numerical solution of boundary-value problems for systems of linear ordinary differential equations. Uspekhi Matematicheskikh Nauk. 16 (3), 171–174 (1961), (in Russian). | |
| dc.relation.references | [19] Bulakajev P. I., Dzjuba A. P. An Algorithm for the Prediction of Search Trajectory in Nonlinear Programming Problems Optimum Design. Structural Optimization. 13 (2,3), 199–202 (1997). | |
| dc.relation.references | [20] Malkov V. P., Ugodchikov A. G. Optimization of Elastic Systems. Moscow, Nauka (1981), (in Russian). | |
| dc.relation.references | [21] Shamansky V. E. Methods for the numerical solution of boundary value problems on the computer. Kyiv, Publishing house of the Academy of Sciences of the Ukrainian SSR. Kyiv, Naukova Dumka (1963) Part 1, (1966) Part 2, (in Russian). | |
| dc.relation.references | [22] Dzyuba A. P., Dzyuba A. А., Levitina L. D., Safronova I. А. Mathematical Simulation of Deformation for the Rotation Shells with Variable Wall Thickness. Journal of Optimization, Differential Equations and Their Applications. 29 (1), 79–95 (2021). | |
| dc.relation.referencesen | [1] Bryson A. E., Yu-Chi Ho. Applied Optimal Control. Toronto, London (1969). | |
| dc.relation.referencesen | [2] Dzyuba A. P., Sirenko V. N., Dzyuba A. A., Safronova I. A. Models and Algorithms for Optimizing Elements of Heterogeneous Shell Structures. Actual problems of mechanics: Monograph ed. by N. V. Polyakova. Dnipro, Lira. 225–244 (2018). | |
| dc.relation.referencesen | [3] Fedorenko R. P. Approximate Solution of Optimal Control Problems. Moscow, Nauka (1978), (in Russian). | |
| dc.relation.referencesen | [4] Gornov A. Yu. Algorithms for Solving Optimal Control Problems with Phase Constraints. Computational technologies. 15 (2), 24–30 (2010), (in Russian). | |
| dc.relation.referencesen | [5] Karamzin D., Pereira F. L. On a Few Questions Regarding the Study of State-Sonstrained Problems in Optimal Control. Journal of Optimization Theory and Applications. 180, 235–255 (2019). | |
| dc.relation.referencesen | [6] Srochko V. A. Iterative Methods for Solving Optimal Control Problems. Moscow, Fizmatgiz (2000), (in Russian). | |
| dc.relation.referencesen | [7] Aisagaliev S., Zhunussova Zh., Akca H. Construction of a Solution for Optimal Control Problem with Phase and Integral Constructs. International Journal of Mathematics and Physics. 10 (1), 11–22 (2019). | |
| dc.relation.referencesen | [8] Buldaev A. S., Burlakov I. D. Nonlocal Descent Method on the Set of Admissible Controls in Optimal Control Problems with Phase Constraints. Vesnik BSU. Series: Mathematics, Informatics. 3, 42–59 (2019). | |
| dc.relation.referencesen | [9] Diveev A., Sofronova E., Zelinka I. Optimal Control Problem Solution With Phase Constraints for Group of Robots by Pontreagin Maximum Principle and Evolutionary Algorithm. Mathematics. 8 (12), 2105 (2020). | |
| dc.relation.referencesen | [10] Trunin D. O. On One Procedure of Non-local Improvement of Controls in Systems Quadratic in State with Terminal Constraints. Bulletin of BSU. Ser., Mathematics, Informatics. 2, 42–49 (2018), (in Russian). | |
| dc.relation.referencesen | [11] Anorov V. Ya. The Maximum Principle for Processes with General Constraints, Automation and remote control. Part 1 (3), 5–15, Part 2 (4), 5–17 (1967). | |
| dc.relation.referencesen | [12] Pontryagin L. S., Bolteanskii V. G., Gamkrelidze R. V., Mishchenko E. F. The Mathematical Theory of Optimal Processes. Interscience, New York, NY, USA (1962). | |
| dc.relation.referencesen | [13] Bertsekas D. P. Constrained Optimization and Lagrange Multipliers Methods. Athena Scientific, Belmot, Mass. (1996). | |
| dc.relation.referencesen | [14] Himmelblau D. M. Applied Nonlsnear Programming. Austsn. Texas (1972). | |
| dc.relation.referencesen | [15] Krylov A. I., Chernousko F. L. An algorithm for the method of successive approximations in optimal control problems. USSR Computational Mathematics and Mathematical Physics. 12 (1), 15–38 (1972). | |
| dc.relation.referencesen | [16] Voloshin V. V. On the Method of Successive Approximations for Optimal Control Problems. Discrete control systems: col. of sci. art., Kyiv, 24–32 (1972). | |
| dc.relation.referencesen | [17] Dzyuba A. P., Safronova I. A., Levitina L. D. Algorithm for Computational Costs Reducing in Problems of Calculation of Asymmetrically Loaded Shells of Rotation. Strength of Materials and Theory of Structures. 105, 99–113 (2020). | |
| dc.relation.referencesen | [18] Godunov S. K. Numerical solution of boundary-value problems for systems of linear ordinary differential equations. Uspekhi Matematicheskikh Nauk. 16 (3), 171–174 (1961), (in Russian). | |
| dc.relation.referencesen | [19] Bulakajev P. I., Dzjuba A. P. An Algorithm for the Prediction of Search Trajectory in Nonlinear Programming Problems Optimum Design. Structural Optimization. 13 (2,3), 199–202 (1997). | |
| dc.relation.referencesen | [20] Malkov V. P., Ugodchikov A. G. Optimization of Elastic Systems. Moscow, Nauka (1981), (in Russian). | |
| dc.relation.referencesen | [21] Shamansky V. E. Methods for the numerical solution of boundary value problems on the computer. Kyiv, Publishing house of the Academy of Sciences of the Ukrainian SSR. Kyiv, Naukova Dumka (1963) Part 1, (1966) Part 2, (in Russian). | |
| dc.relation.referencesen | [22] Dzyuba A. P., Dzyuba A. A., Levitina L. D., Safronova I. A. Mathematical Simulation of Deformation for the Rotation Shells with Variable Wall Thickness. Journal of Optimization, Differential Equations and Their Applications. 29 (1), 79–95 (2021). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2022 | |
| dc.subject | метод послідовних наближень | |
| dc.subject | принцип максимуму Понтрягіна | |
| dc.subject | фазові та проміжні обмеження | |
| dc.subject | оптимальне проектування структур | |
| dc.subject | successive approximations method | |
| dc.subject | Pontryagin’s maximum principle | |
| dc.subject | phase and terminal constraints | |
| dc.subject | optimal design of structures | |
| dc.title | Algorithm of the successive approximation method for optimal control problems with phase restrictions for mechanics tasks | |
| dc.title.alternative | Алгоритм методу послідовних наближень для задач оптимального керування з фазовим обмеженням для задач механіки | |
| dc.type | Article |
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