Averaging method in optimal control problems for integro-differential equations
Lakhva R. Uteshova R. Stanzhytskyi O. Mogylova V.
1 January 2025Walter de Gruyter GmbH
Open Mathematics
2025#23Issue 1
The averaging method is applied to the study of optimal control problems for systems of integro-differential equations with rapidly oscillating coefficients and a small parameter. The original problem is associated with an averaged optimal control problem, formulated for a system of ordinary differential equations, which significantly simplifies the analysis. It is proven that as the small parameter tends to zero, the quality criterion, optimal control, and optimal trajectory of the original problem converge to those of the averaged problem.
averaging , optimal control , oscillation , quality criterion , weak convergence , weakly compact
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Taras Shevchenko National University of Kyiv, 64/13 Volodymyrska St, Kyiv, 01601, Ukraine
Institute of Mathematics and Mathematical Modeling, 125 Pushkin St, Almaty, 050010, Kazakhstan
National Technical University of Ukraine, Igor Sikorsky Kyiv Polytechnic Institute, 37 Peremohy Ave, Kyiv, 03056, Ukraine
Taras Shevchenko National University of Kyiv
Institute of Mathematics and Mathematical Modeling
National Technical University of Ukraine
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