Email this article 
OPTIMIZATION OF CONTROLLED MOTIONS OF LINEAR MECHANICAL SYSTEM
- Authors: Kostin G.V.1
-
Affiliations:
- Ishlinsky Institute for Problems in Mechanics RAS
- Issue: No 6 (2025)
- Pages: 38–51
- Section: OPTIMAL MANAGEMENT
- URL: https://journals.rcsi.science/0002-3388/article/view/360449
- DOI: https://doi.org/10.7868/S3034543X25060042
- ID: 360449
Cite item
Open Access
Access granted
Subscription Access
Abstract
Motions of linear mechanical systems of a certain type are studied. The problem of control design that brings such a system to a given state in a fixed time and minimizes a functional, which is quadratic in phase and control variables, is posed. The solution is sought within the framework of a generalized formulation of the problem with an integral representation of the system constitutive laws. A numerical optimization algorithm based on successive minimization of the constitutive and cost functionals is proposed. Approximation of the phase trajectory and input signals is constructed in the class of piecewise polynomial splines.
About the authors
G. V. Kostin
Ishlinsky Institute for Problems in Mechanics RAS
Email: kostin@ipnmet.ru
Moscow, Russia
References
- Gray C.G., Karl G., Novikov V.A. The Four Variational Principles of Mechanics // Annals Phys. 1996. V. 251. № 1. P. 1–25.
- Tabarrok B., Rimrott F.P.J. Variational Methods and Complementary Formulations in Dynamics. Berlin: Springer, 1994.
- Galley C.R. Classical Mechanics of Nonconservative Systems // Phys. Review Let. 2013. V. 110. №174301. P. 1–5.
- Gray C.G., Taylor E.F. When Action is Not Least // Am. J. Phys. 2007. V. 75. № 5. P. 434–458.
- Костин Г.В., Саурин В.В. Вариационные подходы к решению начально-краевых задач динамики линейных упругих систем // ПММ. 2009. Т. 73. Вып. 6. С. 934–953.
- Kostin G.V., Saurin V.V. Integrodifferential Relations in Linear Elasticity. Berlin: De Gruyter, 2012.
- Костин Г.В. Вариационные формулировки задачи об управляемых движениях системы с упругими элементами // ПММ. 2016. Т. 80. Вып. 5. С. 525–534.
- Гантмахер Ф.Р. Лекции по аналитической механике. М.: Наука, 1966.
- Лурье А.Н. Аналитическая механика. М.: ГИФМЛ, 1961.
- Иосида К. Функциональный анализ. М.: Мир, 1968.
- Понтрягин Л.С., Болтянский В.Г., Гамкрелидзе Р.В., Мищенко Е.Ф. Математическая теория оптимальных процессов. М.: Наука, 1976.
- Мысовских Н.П. Интерполяционные кубатурные формулы. М.: Наука, 1981.
- Schwab C. p- and hp- Finite Element Methods: Theory and Applications in Solid and Fluid Mechanics. Numerical Mathematics and Scientific Computation. N.Y.: Oxford University Press, 1998.
Supplementary files
