The article is devoted to the problem of optimal control of an object performing a high-speed maneuver in a plane with bounded thrust under the influence of the external forces. The purpose is to maximize the velocity along a given line in a finite specified time. The linear tangent law is used as the optimal control law. As an analog, a relay suboptimal control with a simpler structure is developed, the choice of which is governed by theorems and hypotheses depending on the initial velocity and process time. Domains are constructed that cover the conditions of each theorem within the solvability conditions of the problem.
Keywords: optimal control, suboptimal control, linear tangent law, trajectory optimization, bounded thrust
Received February 16, 2026
Revised March 20, 2026
Accepted March 23, 2026
Funding Agency: The work was completed on the topic of the state assignment (state registration number 124012500443-0).
Sergey Aleksandrovich Reshmin, Dr. Phys.-Math. Sci., Corresponding Member of RAS, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, 119526 Russia, e-mail: reshmin@ipmnet.ru
Madina Timurovna Bektybaeva, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, 119526 Russia, e-mail: bektybaeva@ipmnet.ru
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Cite this article as: S.A. Reshmin, M.T. Bektybaeva. Effective control of the dynamics of a point object with a bounded thrust. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2026, vol. 32, no. 2, pp. 203–220.
