|
ИСТИНА |
Войти в систему Регистрация |
ИСТИНА ЦЭМИ РАН |
||
The Optimal Frequency Control Problem of a Nonlinear Oscillatorстатья
Статья опубликована в высокорейтинговом журнале
Статья опубликована в журнале из списка Web of Science и/или Scopus- Авторы: Ilyutko Victor, Kamzolkin Dmitrii, Ternovski Vladimir
- Журнал: Mathematics
- Том: 14
- Номер: 37
- Год издания: 2025
- Издательство: MDPI
- Местоположение издательства: Basel, Switzerland
- Первая страница: 1
- Последняя страница: 19
- DOI: 10.3390/math14010037
- Аннотация: We study a minimum-time (time-optimal) control problem for a nonlinear pendulum-type oscillator, in which the control input is the system’s natural frequency constrained to a prescribed interval. The objective is to transfer the oscillator from a given initial state to a prescribed terminal state in the shortest possible time. Our approach combines Pontryagin’s maximum principle with Bellman’s principle of optimality. First, we decompose the original problem into a sequence of auxiliary problems, each corresponding to a single semi-oscillation. For every such subproblem, we obtain a complete analytical solution by applying Pontryagin’s maximum principle. These results allow us to reduce the global problem of minimizing the transfer time between the prescribed states to a finite-dimensional optimization problem over a sequence of intermediate amplitudes, which is then solved numerically by dynamic programming. Numerical experiments reveal characteristic features of optimal trajectories in the nonlinear regime, including a non-periodic switching structure, non-uniform semi-oscillation durations, and significant deviations from the behavior of the corresponding linearized system. The proposed framework provides a basis for the synthesis of fast oscillatory regimes in systems with controllable frequency, such as pendulum and crane systems and robotic manipulators.
- Добавил в систему: Терновский Владимир Владимирович