Application of the parametrization method for solving optimal control problems with discontinuous phase trajectories
- Authors: Lutoshkin I.V.1, Rybina M.S.1
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Affiliations:
- Ulyanovsk State University
- Issue: Vol 241 (2025)
- Pages: 40-54
- Section: Articles
- URL: https://ogarev-online.ru/2782-4438/article/view/312561
- DOI: https://doi.org/10.36535/2782-4438-2025-241-40-54
- ID: 312561
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Abstract
In this paper, we consider an optimal control problem involving delays in phase variables and controlled discontinuities in the phase trajectory. To solve this type of problem, we propose the parametrization method based on representing control functions as generalized splines with movable nodes and subsequently reducing the original problem to a finite-dimensional nonlinear programming problem for control parameters. In this work, the moments of discontinuity of the phase trajectory are considered as variables of the resulting finite-dimensional problem. Also, we propose an algorithm for calculating the derivatives of the objective function based on the use of the adjoint variables of the original optimal control problem. The algorithm proposed for solving the considered problems was tested by examples presented in the work.
About the authors
Igor' Viktorovich Lutoshkin
Ulyanovsk State UniversityCandidate of physico-mathematical sciences, Associate professor
Maria Sergeevna Rybina
Ulyanovsk State University
References
- Будак Б. М., Беркович Е. М., Соловьева Е. П., “О сходимости разностных аппроксимаций для задач оптимального управления”, Ж. вычисл. мат. мат. физ., 9:3 (1969), 522–547
- Горбунов В. К., “О сведении задач оптимального управления к конечномерным”, Ж. вычисл. мат. мат. физ., 18:5 (1978), 1083–1095
- Горбунов В. К., “Метод параметризации задач оптимального управления”, Ж. вычисл. мат. мат. физ., 19:2 (1979), 292–303
- Дыхта В. А., Самсонюк О. Н., Оптимальное импульсное управление с приложениями, Физматлит, М., 2000
- Лутошкин И. В., Динамические модели экономических систем и методы их анализа, УлГУ, Ульяновск, 2024
- Лутошкин И. В., Рыбина М. С., “Оптимизация в модели управления социально-экономической системой в условиях массового заболевания”, Изв. Иркут. гос. ун-та. Сер. Мат., 2024, № 49, 16–-31
- Максимов В. П., “Достижимые значения целевых функционалов в задачах экономической динамики”, Прикл. мат. вопр. управл., 2019, № 4, 124–135
- Aubin J.-P., Time and Money. How Long and How Much Money is Needed to Regulate a Viable Economy, Springer, 2014
- Lutoshkin I. V., Rybina M. S., “Optimal solution in the model of control over an economic system in the condition of a mass disease”, Изв. Саратов. ун-та. Нов. сер. Мат. Мех. Информ., 23:2 (2023), 264–273
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