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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». 2025. Vol 51

Exact Formulas for the Increment of the Cost Functional in Optimal Control of Linear Balance Equation

Author(s)
Elena V. Goncharova1, Nikolay I. Pogodaev1, Maksim V. Staritsyn1

1Matrosov Institute for System Dynamics and Control Theory of SB RAS, Irkutsk, Russian Federation

Abstract
We study a state-linear optimal control problem for a transport equation with a source term in the space of finite signed Borel measures. For this problem, a version of the classical Pontryagin principle (in the form of the minimum principle) is obtained for the first time. In addition, we propose an approach to enhance the latter based on a certain unconventional procedure of variational analysis, namely, on exact increment formulas, representing the difference in values of the objective functional for any pair of admissible controls, without neglecting residual terms of any expansion. The approach relies on the standard duality and results in a series of necessary optimality conditions of a non-classical, “feedback” type. A constructive consequence of the feedback optimality conditions is a method of successive approximations, devoid of any parameters of “descent depth”.
About the Authors

Elena V. Goncharova, Cand. Sci. (Phys.-Math.), Leading Researcher, Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, 664033, Russian Federation, goncha@icc.ru

Nikolay N. Pogodaev, Cand. Sci. (Phys.-Math.), Leading Researcher, Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, 664033, Russian Federation, nickpogo@gmail.com

Maksim V. Staritsyn, Cand. Sci. (Phys.-Math.), Leading Researcher, Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, 664033, Russian Federation, starmax@icc.ru

For citation

Goncharova E. V., Pogodaev N. I., Staritsyn M. V. Exact Formulas for the Increment of the Cost Functional in Optimal Control of Linear Balance Equation. The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 51, pp. 3–20. (in Russian)

https://doi.org/10.26516/1997-7670.2025.51.3

Keywords
nonlocal balance law, optimal control, feedback control, necessary optimality conditions, numerical algorithms
UDC
517.977
MSC
49J20
DOI
https://doi.org/10.26516/1997-7670.2025.51.3
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