70730

Автор(ов): 

3

Параметры публикации
Тип публикации: 
Статья в журнале/сборнике
Название: 
Time-optimal control problem of two non-synchronous oscillators
Электронная публикация: 
Да
ISBN/ISSN: 
2227-7390
DOI: 
10.3390/math10193552
Наименование источника: 
Mathematics
Обозначение и номер тома: 
Volume 10, Issue 19
Город: 
Basel
Издательство: 
MDPI
Год издания: 
2022
Страницы: 
https://www.mdpi.com/2227-7390/10/19/3552
Аннотация
The time-optimal control problem for a system consisting of two non-synchronous oscillators is considered. Each oscillator is controlled with a shared limited scalar control. The objective of the control is to accelerate the oscillatory system to a given specific position, where the first oscillator must have non-zero phase coordinates, but the second one must remain motionless at the terminal moment. For an arbitrary number of unknown switching moments that determine the optimal relay control, the necessary extremum conditions in the form of nonlinear matrix equalities are proposed. The study of the necessary/sufficient conditions of the extremum made it possible to describe the reachability set in the phase space of the first oscillator, to find an analytical form of the curve corresponding to the two-switching control class, which also separates the reachability set of the three switching-control class. The corresponding theorems are proved and the dependence of the criteria on control constraints is shown. Matrix conditions for different classes of control switchings are found. All of the obtained analytical results are numerically validated and illustrated with mathematical modeling.
Библиографическая ссылка: 
Берлин Л.М., Галяев А.А., Лысенко П.В. Time-optimal control problem of two non-synchronous oscillators // Mathematics. 2022. Volume 10, Issue 19. С. https://www.mdpi.com/2227-7390/10/19/3552.