Mapping of the linear systems of the second order with two-dimensional control
Abstract
This paper deals with linear control systems with two-dimensional control. The main goal of the paper is to find the exact analytic solution of the time-optimal control problem for an arbitrary linear control system with constant coefficients using the analytic solution of this problem for the simplest system. For this aim, we construct a certain nonsmooth mapping between the 0-controllability sets of the given systems. In other words, by means of this mapping, we investigate the equivalence of the systems with the same qualitative behavior in a neighborhood of the stationary point.
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References
Коробов В.И., Скляр Г.М. Оптимальное быстродействие и степенная проблема моментов // Матем. сборник. 1987. Т. 134(176), № 2(10). С. 186 206.
Sklyar G.M., Ignatovich S.Yu. A Classication of Linear Time-Optimal Control Problems in a Neighborhood of the Origin // Journal of Mathematical Analysis and Applications. - 1996. - Vol. 203. - P. 791-811.
Korobov V.I., Ivanova T.I. Nonsmooth Mapping of Linear Control Systems // Journal of Optimization Theory and Applications. - 2001. - Vol. 108, No. 2. - P. 389-405.
В. Г. Болтянский. Математические методы оптимального управления. М., Наука. 1969. 408 с.
Математическая теория оптимальних процессов. / Понтрягин Л.С., Болтянский В.Г. Гамкрелидзе Р.В., Мищенко Е.Ф. М.: Наука, 1961. 391 с.
Курант Р. Уравнения с частными производными: Пер. с англ. М.: Мир. 1964. 830 с.
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