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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». 2024. Vol 49

Parametric Regularization of the Functional in a Linear-quadratic Optimal Control Problem

Author(s)
Vladimir A. Srochko1, Alexander V. Arguchintsev1

1Irkutsk State University, Irkutsk, Russian Federation

Abstract
A linear-quadratic optimal control problem with parameters and arbitrary matrices in the quadratic cost functional is considered on the set of stepwise control functions. As a quality criterion of the admissible set of parameters it is proposed to choose a condition number of the final matrix, which is expressed through the boundaries of its spectrum. As a result, parameter optimization problems are constructed which provide a strong convexity of the objective function on control variables together with relatively good conditionality of the corresponding quadratic programming problem. A similar approach is realized for the minimax problem. In this case, the objective function acquires a convex-concave structure and the choice of parameters is based on minimization of some convolution of two condition numbers.
About the Authors

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

Alexander V. Arguchintsev, Dr. Sci. (Phys.Math.), Prof., Irkutsk State University, Irkutsk, 664003, Russian Federation, arguch@math.isu.ru

For citation

Srochko V. A., Arguchintsev A. V. Parametric Regularization of the Functional in a Linear-quadratic Optimal Control Problem. The Bulletin of Irkutsk State University. Series Mathematics, 2024, vol. 49, pp. 32–44. (in Russian)

https://doi.org/10.26516/1997-7670.2024.49.32

Keywords
linear-quadratic optimal control problem, cost functional with parameters, parameter optimization, minimization of the condition number
UDC
517.977
MSC
49M25
DOI
https://doi.org/10.26516/1997-7670.2024.49.32
References
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