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 in | Journal of mathematical sciences (New York, N.Y.) Vol. 279; no. 5; pp. 586 - 593 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
23.03.2024
Springer Springer Nature B.V |
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| ISSN | 1072-3374 1573-8795 |
| DOI | 10.1007/s10958-024-07040-0 |
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| Abstract | 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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| AbstractList | 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. 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. Keywords and phrases: hyperbolic system, system with delay, necessary optimality condition, smooth control. AMS Subject Classification: 49J20, 49M05 |
| Audience | Academic |
| Author | Arguchintsev, A. V. Poplevko, V. P. |
| Author_xml | – sequence: 1 givenname: A. V. surname: Arguchintsev fullname: Arguchintsev, A. V. email: arguch@math.isu.ru organization: Irkutsk State University – sequence: 2 givenname: V. P. surname: Poplevko fullname: Poplevko, V. P. organization: Irkutsk State University |
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| References | ZabelloLEOn optimality conditions in nonlinear inertial control systems with delayDiffer. Uravn.1990268130913151074258 ArguchintsevAVOptimal Control for Hyperbolic Systems2007MoscowFizmatlit[in Russian] ZabelloLEOn the theory of necessary optimality conditions for systems with delay and derivatives of the controlDiffer. Uravn.1989253371379 ArguchintsevAVPoplevkoVPAn optimal control problem by parabolic equation with boundary smooth control and an integral constraintNum. Alg. Control Optim.2018821932023811578 LE Zabello (7040_CR2) 1989; 25 AV Arguchintsev (7040_CR4) 2018; 8 AV Arguchintsev (7040_CR1) 2007 LE Zabello (7040_CR3) 1990; 26 |
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| SubjectTerms | Analysis Control systems Hyperbolic systems Iterative methods Mathematics Mathematics and Statistics Optimal control Optimization Population biology Smoothness |
| Title | Optimal Control Problem for a Hyperbolic System with Delay on the Boundary in the Class of Smooth Controls |
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