On determination of gradient in optimal control problems for frictionless mechanical oscillatory systems

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Abstract

This paper investigates the problem of gradient computation for an optimal control algorithm applied to a distributed system. The mathematical model of the system is described by an initial-boundary value problem for a linear high-order hyperbolic partial differential equation. The study considers an oscillatory process without energy dissipation. The proposed model covers a wide class of applied problems, including vibrations of strings, beams, rods, and other one-dimensional elastic mechanical systems, as well as systems reducible to these cases. By using the method of integral estimates, we prove a uniqueness theorem for the solution and derive an explicit expression for the gradient of the minimized quadratic functional.

About the authors

Alexander S. Zinchenko

Moscow Aviation Institute (National Research University)

Author for correspondence.
Email: zinchenkoas@mai.ru
ORCID iD: 0000-0001-7971-4572
SPIN-code: 7948-5040
Scopus Author ID: 59124941500
ResearcherId: AAJ-2633-2020
https://www.mathnet.ru/rus/person229294

Cand. Econom. Sci.; Associate Professor; Dept. of Mathematics

Russian Federation, 125993, Moscow, Volokolamskoe Shosse, 4

Aleksander A. Nekhaev

Federal Research Center “Computer Science and Control” of Russian Academy of Sciences

Email: ganzol177@gmail.com
ORCID iD: 0009-0004-2062-7967
ResearcherId: JMR-4736-2023
https://www.mathnet.ru/rus/person230881

Research Engineer; Dept. of Mathematical Modeling of Heterogeneous Systems

Russian Federation, 119333, Moscow, Vavilova str., 44/2

Alexander M. Romanenkov

Moscow Aviation Institute (National Research University); Federal Research Center “Computer Science and Control” of Russian Academy of Sciences

Email: romanaleks@gmail.com
ORCID iD: 0000-0002-0700-8465
SPIN-code: 7586-0934
Scopus Author ID: 57196480014
ResearcherId: AAH-9530-2020
https://www.mathnet.ru/rus/person29785

Cand. Techn. Sci., Associate Professor; Associate Professor; Dept. of Mathematics; Senior Researcher; Dept. of Mathematical Modeling of Heterogeneous Systems

Russian Federation, 125993, Moscow, Volokolamskoe Shosse, 4; 119333, Moscow, Vavilova str., 44/2

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