Control the Coefficient of a Differential Equation as an Inverse Problem in Time

Vladimir Ternovski and Victor Ilyutko ()
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Vladimir Ternovski: Department of Computational Mathematics and Cybernetics, Shenzhen MSU-BIT University, International University Park Road 1, Shenzhen 518172, China
Victor Ilyutko: Department of Computational Mathematics and Cybernetics, Shenzhen MSU-BIT University, International University Park Road 1, Shenzhen 518172, China

Mathematics, 2024, vol. 12, issue 2, 1-16

Abstract: There are many problems based on solving nonautonomous differential equations of the form x ¨ ( t ) + ω 2 ( 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 also unknown, but the initial and final values of the phase variables are given. The variation principle of the minimum time for the entire dynamic process allows for the determination of the optimal solution. Thus, the inverse problem is an optimal control problem. No simplifying assumptions were made.

Keywords: optimal control; reachability set; inverse problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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