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Home - President's Award, 2025 - Asymptotic Behavior and Controllability of Dynamic Systems of Complex Nature

Asymptotic Behavior and Controllability of Dynamic Systems of Complex Nature

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Work number - M 7 FILED

Presented Taras Shevchenko National University of Kyiv

Authors:
1. Tetiana ZHUK – PhD student, Assistant at the Department of Integral and Differential Equations, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv;
2. Roksolana LAKHVA – PhD student, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv;
3. Andrii TYMOSHENKO – PhD, Assistant at the Department of Computational Mathematics, Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv;
4. Viktoriia TSAN – PhD student, Faculty of Mechanics and Mathematics, Mathematics teacher at the Ukrainian Physics and Mathematics Lyceum, Taras Shevchenko National University of Kyiv.

The research focuses on the asymptotic properties and controllability of mathematical models described by nonlinear differential equations of complex structure. Special attention is given to optimal control of differential inclusions, including problems with rapidly oscillating parameters and optimal control for integrodifferential equations. Conditions for the existence of optimal control are established, and an averaging method is justified to transform the problem into a system of ordinary differential equations. An approach is proposed for determining the optimal power of sources embedded in porous media for the Richards equation.

Asymptotic and oscillatory properties of dynamic systems on time scales are investigated, with estimates of the graininess function and conditions for dissipativity in terms of the Lyapunov function. The existence of a corresponding Lyapunov function with specified properties is proven for the first time. The relationship between periodic solutions on time scales and corresponding differential systems is also discussed.

The scientific novelty lies in the advancement of optimal control methods for integrodifferential equations and approaches for studying the asymptotic properties of dynamic systems on time scales. The practical significance of the results includes applications in energy, biomedicine, and environmental safety. In 2021, a certificate of copyright registration was obtained for a computer program for optimizing the power of point sources in porous media.

Number of publications: 32 publications. Among them, 17 publications indexed in the Scopus database: 3 book chapters and 14 articles in peer-reviewed journals (7 – Q2 and 7 – Q3 according to SCImago Journal Rank), 7 articles in journals included in category "B" of the Ukrainian scientific journals list, and 6 abstracts (solo presentations). The total number of citations of the authors' publications / h-index according to databases is: Web of Science 14/2, Scopus 45/3, Google Scholar 87/4. The authors have obtained 1 copyright registration certificate.

President's Award, 2025

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