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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2023. Vol 46

Optimal Control by a Cascade System of Hyperbolic and Ordinary Delayed Differential Equation

Author(s)
Alexander V. Arguchintsev1, Vasilisa P. Poplevko1

1Irkutsk State University, Irkutsk, Russian Federation

Abstract
In the class of smooth control functions, an optimal control problem of firstorder semilinear hyperbolic equations is investigated. We consider the case when the functional parameter in the right side of the hyperbolic system is determined from the controlled system of ordinary differential equations with constant state delay. Control functions are restricted by pointwise (amplitude) constraints. Problems of this kind arise when modeling a number of processes of population dynamics, interaction of a fluid (liquid or gas) with solids, etc. Optimal control methods based on the use of the Pontryagin maximum principle, its consequences and modifications are not applicable for such problems. The proposed approach is based on a special control variation, which ensures the smoothness of variable controls and the fulfillment of restrictions. The necessary optimality condition is proved. A scheme of a method for improving permissible control based on this condition is proposed, the convergence of the method is justified. An illustrative example is given.
About the Authors

Alexander V. Arguchintsev, Dr. Sci. (Phys.–Math.), Prof., Irkutsk State University, Irkutsk, 664003, Russian Federation, arguch@math.isu.ru

Vasilisa P. Poplevko, Cand. Sci. (Phys.Math.), Assoc. Prof., Irkutsk State University, Irkutsk, 664003, Russian Federation, vasilisa@math.isu.ru

For citation
Arguchintsev A. V., Poplevko V. P. Optimal Control by a Cascade System of Hyperbolic and Ordinary Delayed Differential Equation. The Bulletin of Irkutsk State University. Series Mathematics, 2023, vol. 46, pp. 3–18. (in Russian) https://doi.org/10.26516/1997-7670.2023.46.3
Keywords
hyperbolic system, delay, smooth controls, necessary optimality condition, improvement method
UDC
517.977
MSC
49J20, 49M05
DOI
https://doi.org/10.26516/1997-7670.2023.46.3
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