The control problem for a dynamic system is studied, specifically, the problem of approaching to a given target set over a finite time interval when the right-hand side of differential equations system isn’t precisely known and it’s replaced by a simpler one. It’s shown that replacement of the right-hand side of differential equations system with a simpler one doesn’t significantly degrade the result in the process of reaching the original system’s motion to a given target set. The resulting theoretical estimates are illustrated with a specific example.
Keywords: control system, reachable set, Euler’s polyline, Hausdorff distance
Received February 10, 2026
Revised March 12, 2026
Accepted March 16, 2026
Funding Agency: The work was performed as part of research conducted in the Ural Mathematical Center with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Agreement number 075-02-2026-737).
Aleksandr Vladimirovich Alekseev, Leading Design Engineer, Experimental Machine-Design Bureau “Novator”, Yekaterinburg, 620077 Russia, e-mail: sztern987@gmail.com
Aleksandr Anatol’evich Ershov, Cand. Sci. (Phys.-Math.), Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620077 Russia, e-mail: ale10919@yandex.ru
Vladimir Nikolaevich Ushakov, Corresponding Member of the Russian Academy of Sciences, Dr. Phys.-Math. Sci., Prof., Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620077 Russia, e-mail: ushak@imm.uran.ru
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Cite this article as: A.V. Alekseev, A.A. Ershov, V.N. Ushakov. On influence of control system right-hand side replacement on the accuracy in approaching problem. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2026, vol. 32, no. 2, pp. 9–28.
