Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

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)

A peer-reviewed article of this Preprint also exists.

Ternovski, V.; Ilyutko, V. Control the Coefficient of a Differential Equation as an Inverse Problem in Time. Mathematics 2024, 12, 329. Ternovski, V.; Ilyutko, V. Control the Coefficient of a Differential Equation as an Inverse Problem in Time. Mathematics 2024, 12, 329.

Abstract

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.

Keywords

optimal control; reachability set; inverse problem

Subject

Computer Science and Mathematics, Computational Mathematics

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