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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 54

One Remark on the Existence Theorems for Generalized Impulsive Control Problems

Author(s)

Dmitry Y. Karamzin1

1 Federal Research Center “Computer Science and Control” RAS, Moscow, Russian Federation

Abstract
In this work, generalized solutions to optimal control problems are discussed. A notion of generalized impulsive control is introduced. Some extension is proposed for a constrained control problem governed by the dynamics of a general type. A corresponding existence theorem is formulated within the class of discontinuous arcs. The presented extension is smaller than those previously derived in literature for this type of problems, as it contains less generalized impulsive controls, and, correspondingly, less trajectories. This is achieved by rejecting the problem convexification. As the main tool for investigation, the generally known Lebesgue discontinuous time variable change is employed. It is important noting that the obtained existence theorem is not always applicable. Therefore, a task of finding more subtle conditions for the existence of a solution arises. In this regard, a number of classical variational calculus problems are discussed in the context of presented nonlinear impulsive extension. This article is dedicated to the memory of Vladimir Alexandrovich Dykhta.
About the Authors
Dmitry Y. Karamzin, Dr. Sci. (Phys.-Math.), Leading Research Scientist, Federal Research Center “Computer Science and Control” RAS, Moscow, 119991, Russian Federation, dmitry karamzin@mail.ru
For citation
Karamzin D. Y. One Remark on the Existence Theorems for Generalized Impulsive Control Problems. The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 54, pp. 18–32. https://doi.org/10.26516/1997-7670.2025.54.18
Keywords
optimal impulsive control, generalized solutions, existence theorems
UDC
517.977.57
MSC
49J21
DOI
https://doi.org/10.26516/1997-7670.2025.54.18
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