Two feedback control problems for a linear system of ordinary differential equations are considered. The first problem consists in constructing an algorithm for forming a control providing the guidance of a nonlinear system with unknown right-hand part. Namely, the closeness in uniform metric of a solution of the linear controlled system and a solution of the nonlinear system is required. In the second problem, the nonlinear system is replaced by a linear one being a copy of the original controlled system. The latter system includes an unknown disturbance instead of a control. In the case, the guidance problem is to construct an algorithm for forming a control providing the guidance of a solution of the system with disturbance by a solution of the controlled system. In this process, the expended resources of the guiding side can only slightly exceed the expended resources of the guided side. An algorithm oriented to computer realization is designed. This algorithm is applicable for solving both problems but under different informational conditions. Estimates of algorithm’s convergence rate are specified.
Keywords: linear differential equations, feedback control
Received February 10, 2026
Revised March 16, 2026
Accepted March 23, 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).
Vyacheslav Ivanovich Maksimov, 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: maksimov@imm.uran.ru
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Cite this article as: Maksimov V.I. An algorithm for solving a linear guidance problem. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2026, vol. 32, no. 2, pp. 148–164.
