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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 45

Resolution of Linear-quadratic Problems in a Discrete-continuous Format with External Actions

Author(s)
Vladimir A. Srochko1, Vladimir G. Antonik1

1Irkutsk State University, Irkutsk, Russian Federation

Abstract
Two linear-quadratic problems are considered on the set of piecewise-constant controls. The first problem contains a discrete perturbation on the right side of the controlled system and uncertain parameters in a quadratic functional with sign-indefinite matrices. Its solution is obtained by the guaranteed result rule and is implemented in the form of a finite-dimensional minimax problem. There are obtained conditions for the parameters that convert the objective function to a convex-concave structure and give the possibility of an effective solving of the problem. These are linear inequalities containing extreme eigenvalues of symmetric matrices. The second problem is related to the functional in the discrete variant, which is defined as the deviation of the phase trajectory from consecutive time realizations of the external influence. It gives the opportunity of the step by step searching of the extremmum at each node point of the time interval. Local problems can be effectively solved in a finite number of iterations.
About the Authors

Vladimir A. Srochko, Dr. Sci. (Phys.–Math.), Prof., Irkutsk State University, Irkutsk, 664003, Russian Federation, srochko@math.isu.ru

Vladimir G. Antonik, Cand. Sci. (Phys.Math.), Assoc. Prof., Irkutsk State University, Irkutsk, 664003, Russian Federation, vga@math.isu.ru

For citation
Srochko V. A., Antonik V. G. Resolution of Linear-quadratic Problems in a Discrete-continuous Format with External Actions. The Bulletin of Irkutsk State University. Series Mathematics, 2023, vol. 45, pp. 24–36. (in Russian) https://doi.org/10.26516/1997-7670.2023.45.24
Keywords
linear-quadratic problems, discrete actions to system and functional, reduction to convex problems
UDC
517.977
MSC
49M25
DOI
https://doi.org/10.26516/1997-7670.2023.45.24
References
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