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Necessary Extremum Conditions and the Neustadt–Eaton Method in the Time-Optimal Control Problem for a Group of Nonsynchronous Oscillators

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Abstract

The time-optimal control problem for an arbitrary number of nonsynchronous oscillators with a limited scalar control is considered. An analytical investigation of the problem is performed. The property of strong accessibility and global controllability is proved, and a program control is found that brings the system from the origin to a fixed point in the shortest time. Trajectories satisfying both the motion equations of the system and the additional conditions based on the matrix nondegeneracy conditions of the relay control have been found for bringing a group of oscillators to the origin. Two classification methods of trajectories according to the number of control switchings are compared: the one based on the necessary extremum conditions and the Neustadt–Eaton numerical algorithm.

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Funding

This research was funded by a grant to support youth scientific schools of Trapeznikov Institute of Control Sciences, Russian Academy of Sciences.

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    L. M. Berlin, A. A. Galyaev & P. V. Lysenko

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  1. L. M. Berlin
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  2. A. A. Galyaev
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  3. P. V. Lysenko
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Correspondence to L. M. Berlin, A. A. Galyaev or P. V. Lysenko.

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This paper was recommended for publication by P.S. Shcherbakov, a member of the Editorial Board

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Berlin, L.M., Galyaev, A.A. & Lysenko, P.V. Necessary Extremum Conditions and the Neustadt–Eaton Method in the Time-Optimal Control Problem for a Group of Nonsynchronous Oscillators. Autom Remote Control 85, 543–556 (2024). https://doi.org/10.1134/S0005117924060043

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