Аннотация:
Предлагается применить метод Бубнова–Галеркина к решению задач управления билинейными системами. Решение задачи управления удается свести к конечномерной системе линейных проблем моментов. Рассмотрен конкретный пример применения указанной процедуры и приведено его численное решение.
Статья представлена к публикации членом редколлегии:О. А. Степанов
\RBibitem{Khu15}
\by Ас.~Ж.~Хуршудян
\paper Метод Бубнова--Галеркина в~задачах управления билинейными системами
\jour Автомат. и телемех.
\yr 2015
\issue 8
\pages 46--55
\mathnet{http://mi.mathnet.ru/at14265}
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\transl
\jour Autom. Remote Control
\yr 2015
\vol 76
\issue 8
\pages 1361--1368
\crossref{https://doi.org/10.1134/S0005117915080032}
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Эта публикация цитируется в следующих 12 статьяx:
Xuan Tung Nguyen, Tri N. M. Nguyen, Kha Loc Nguyen, Ki-Yong Yoon, Sun-Hee Park, Jung J. Kim, “Elastic Critical Lateral Buckling of Beams Subjected to Simultaneous Negative End Moments and Transverse Loads”, Applied Sciences, 13:2 (2023), 778
Ido Halperin, “Solution of the Continuous Time Bilinear Quadratic Regulator Problem by Krotov's Method”, IEEE Trans. Automat. Contr., 68:4 (2023), 2415
Halperin I., Agranovich G., Ribakov Yu., “Multi-Input Control Design For a Constrained Bilinear Biquadratic Regulator With External Excitation”, Optim. Control Appl. Methods, 40:6 (2019), 1045–1053
A. Zh. Khurshudyan, S. K. Ohanyan, “Vibration suspension of Euler-Bernoulli-von Karman beam subjected to oppositely moving loads by optimizing the placements of visco-elastic dampers”, ZAMM-Z. Angew. Math. Mech., 98:8 (2018), 1412–1419
A. Khurshudyan, S. Ohanyan, “Vibrations of geometrically nonlinear beam subjected to two oppositely moving loads and supported by three equidistant visco-elastic dampers”, 5th International Conference on Topical Problems of Continuum Mechanics With a Special Session in Honor of Alexander Manzhirov'S 60th Birthday, Journal of Physics Conference Series, 991, IOP Publishing Ltd, 2018, 012046
A. Khurshudyan, “Controllability of semi-infinite rod heating by a point source”, 5th International Conference on Topical Problems of Continuum Mechanics With a Special Session in Honor of Alexander Manzhirov'S 60th Birthday, Journal of Physics Conference Series, 991, IOP Publishing Ltd, 2018, 012045
I. Halperin, G. Agranovich, Yu. Ribakov, “Optimal control synthesis for the constrained bilinear biquadratic regulator problem”, Optim. Lett., 12:8 (2018), 1855–1870
A. Zh. Khurshudyan, “Min(max)imization of horizontal and vertical displacements of a fibre-reinforced magneto-elastic cantilever rod”, ZAMM-Z. Angew. Math. Mech., 98:11 (2018), 1924–1929
I. Halperin, G. Agranovich, Y. Ribakov, “Using constrained bilinear quadratic regulator for the optimal semi-active control problem”, J. Dyn. Syst. Meas. Control-Trans. ASME, 139:11 (2017), 111011
A. S. Avetisyan, A. Zh. Khurshudyan, “Green's function approach in approximate controllability for nonlinear physical processes”, Mod. Phys. Lett. A, 32:21 (2017), 1730015
I. Halperin, G. Agranovich, Yu. Ribakov, “Optimal control of a constrained bilinear dynamic system”, J. Optim. Theory Appl., 174:3 (2017), 803–817
S. H. Jilavyan, A. Zh. Khurshudyan, “Topology optimization for elastic base under rectangular plate subjected to moving load”, Arch. Control Sci., 25:3 (2015), 289–305