Time-Optimal Control Problem of Two Non-Synchronous Oscillators

Article Mathematics

Periodic Solutions and Stability Analysis for Two-Coupled-Oscillator Structure in Optics of Chiral Molecules

Jing Li et al.

Summary: This paper investigates the nonlinear dynamic behavior and periodic vibration characteristic of a two-coupled-oscillator model in the optics of chiral molecules. The stability and local dynamic behavior of the system with two pairs of identical conjugate complex eigenvalues are systematically discussed. The existence and number of periodic solutions are studied by establishing the curvilinear coordinate and constructing a Poincare map to improve the Melnikov function. The accuracy of the theoretical analysis is verified by numerical simulations, and the nonlinear response of multiple periodic motion under certain conditions is comprehensively examined.

MATHEMATICS (2022)

添加到收藏夹

Article Mathematics

Extremum Conditions for Constrained Scalar Control of Two Nonsynchronous Oscillators in the Time-Optimal Control Problem

L. M. Berlin et al.

Summary: This paper considers the time-optimal control problem for two nonsynchronous oscillators, where the phase coordinates of the second oscillator become zero again at the terminal time. Necessary extremum conditions are proposed by analyzing the optimal bang-bang control with a given number of unknown switching times. An analytical form of the curve corresponding to the two switchings in the phase space of the first oscillator is found.

DOKLADY MATHEMATICS (2022)

添加到收藏夹

Article Mechanics

Time-Optimal Movement of Platform with Oscillators

O. R. Kayumov

Summary: This study investigates a system consisting of a rigid body with linear oscillators moving along a horizontal straight line without friction, controlled by an external limited force. It proposes a control structure that meets the necessary conditions for optimality and presents results of numerical experiments on a platform with two oscillators.

MECHANICS OF SOLIDS (2021)

添加到收藏夹

Proceedings Paper Automation & Control Systems