Spiral-Like Extremals near a Singular Surface in a Rocket Control Problem

Авторы: Ronzhina Mariya I., Manita Larisa A.
Журнал: Regular and Chaotic Dynamics
Том: 28
Номер: 2
Год издания: 2023
Издательство: Pleiades Publishing, Ltd
Местоположение издательства: Road Town, United Kingdom
Первая страница: 148
Последняя страница: 161
DOI: 10.1134/s1560354723020028
Аннотация: In this paper, we consider the minimum time problem for a space rocket whose dynamics is given by a control-affine system with drift. The admissible control set is a disc. We study extremals in the neighbourhood of singular points of the second order. Our approach is based on applying the method of a descending system of Poisson brackets and the Zelikin – Borisov method for resolution of singularities to the Hamiltonian system of Pontryagin’s maximum principle. We show that in the neighbourhood of any singular point there is a family of spiral-like solutions of the Hamiltonian system that enter the singular point in a finite time, while the control performs an infinite number of rotations around the circle.
Добавил в систему: Ронжина Мария Игоревна

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