A nonlinear conflict-controlled process involving two players is considered, with a terminal set being the sum of a linear subspace and a convex compact set in its orthogonal complement. The process is viewed from the perspective of the first player. Their goal is to bring the controlled object to the terminal set. The first player is assumed to know the dynamic characteristics of the controlled object, the phase variables, and the control of the second player up to the current moment. Sufficient conditions are presented under which the first player can guarantee the bringing of the game’s phase vector to the terminal set. A form of positional countercontrols by the first player that guarantees the termination of the process is presented. Examples are given.
Keywords: differential games, positional control, counter-control, positional counter-control, object bringing problem, structural synthesis, guide control, analytical design of aggregated controllers
Received December 29, 2025
Revised February 10, 2026
Accepted February 16, 2026
Funding Agency: The paper was published with the financial support of the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics under the agreement no. 075-15-2022-284 and state-funded research topic № 5.4 of the Faculty of Computational Mathematics and Cybernetics of the Moscow State University.
Nikolay Leontievich Grigorenko, Dr. Phis.-Math Sci., Faculty of Computational Mathematics and Cybernetics of the Lomonosov Moscow State University, Moscow, 119991 Russia, e-mail: grigor@cs.msu.ru
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Cite this article as: N.L. Grirorenko. On linear differential games of convergence in the class of positional countercontrols. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2026, vol. 32, no. 2, pp. 77–86.
