Inverse Problem to Control the Coefficient of a Differential Equation in Time

VLADIMIR TERNOVSKI; VICTOR ILYUTKO

doi:10.20944/preprints202312.2333.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 27 December 2023 / Approved: 29 December 2023 / Online: 30 December 2023 (02:29:36 CET)
Version 2 : Received: 14 January 2024 / Approved: 15 January 2024 / Online: 15 January 2024 (07:15:48 CET)
Version 3 : Received: 19 January 2024 / Approved: 19 January 2024 / Online: 22 January 2024 (05:43:41 CET)

There are many problems based on solving non-autonomous differential equations of the form x¨(t)+ω2(t)x(t)=0, where x(t) represents the coordinate of a material point and ω is the angular frequency. The inverse problem involves finding the bounded coefficient ω. Continuity of the function ω(t) is not required. The trajectory x(t) is unknown, but the initial and final values of the phase variables are given. The variation principle of minimum time for the entire dynamic process allows for the determination of the optimal solution {x(t),ω(t)}. Thus, the inverse problem is an optimal control problem. No simplifying assumptions were made.

optimal control; reachability set; inverse problem

Computer Science and Mathematics, Computational Mathematics

Comment 1

Received: 15 January 2024
Commenter: Victor ILYUTKO
Commenter's Conflict of Interests: Author

Comment: The changes were made according to reviewers

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Inverse Problem to Control the Coefficient of a Differential Equation in Time

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