Optimal Control Problem for a Hyperbolic System with Delay on the Boundary in the Class of Smooth Controls

In this paper, we examine the optimal control problem for a hyperbolic system with differential constraints on the boundary, taking into account the delay. Controls are selected from the class of smooth functions that satisfy pointwise constraints. Problems of this type arise, in particular, in mode...

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Published inJournal of mathematical sciences (New York, N.Y.) Vol. 279; no. 5; pp. 586 - 593
Main Authors Arguchintsev, A. V., Poplevko, V. P.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 23.03.2024
Springer
Springer Nature B.V
Subjects
Analysis
Control systems
Hyperbolic systems
Iterative methods
Mathematics
Mathematics and Statistics
Optimal control
Optimization
Population biology
Smoothness
49M05
49J20
hyperbolic system
necessary optimality condition
system with delay
smooth control
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ISSN1072-3374
1573-8795
DOI10.1007/s10958-024-07040-0

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Summary:In this paper, we examine the optimal control problem for a hyperbolic system with differential constraints on the boundary, taking into account the delay. Controls are selected from the class of smooth functions that satisfy pointwise constraints. Problems of this type arise, in particular, in modeling the processes of population dynamics. The approach proposed in this paper is based on the use of “internal variations” of the control, which preserves the smoothness of the control function and ensures the fulfillment of pointwise constraints. We obtain an estimate of the state increment, prove a necessary optimality condition, and develop a scheme of an iterative method.
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-07040-0