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Singularity of Fuller type in a control problem of a rocket

P. 90–92.
Manita L., Ronzhina M.

we show that in a  control problem of a rocket  there are spiral like extremals that attain the singular point (on the singular surface of the second order) in finite time, wherein the corresponding controls perform an infinite number of rotations along the circle S1.

Language: English
Text on another site
Keywords: singular extremalcontrol problem of a rocketlogarithmic spirals

In book

Дифференциальные уравнения и оптимальное управление: Материалы Международной конференции, посвященной 100-летию со дня рождения академика Евгения Фроловича Мищенко, Москва, 7–9 июня 2022 г
M.: Steklov Mathematical Institute, 2022.
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SPIRAL-LIKE SOLUTIONS IN OPTIMAL CONTROL PROBLEMS WITH CONTROL IN A DISK
Ronzhina M., Manita L., , in: Systems Analysis: Modeling and Control: Materials of the International Conference in memory of Academician A.V. Kryazhimskiy, Moscow, January 23–24, 2024. Abstracts.: -, 2024. P. 25–26.
For some class of small-dimensional optimal control problems we found a family of extremals in the form of logarithmic spirals. These extremals reach the singular surface in a finite time, while the control performs an infinite number of rotations around the circle. ...
Added: October 8, 2025
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We study a neighbourhood of a singular second-order extremal in optimal control problems that are affine in control in a disk. We consider the case in which the Hamiltonian system has dimension 8 and is a small (in the sense of the action of the Fuller group) perturbation of the Hamiltonian system of the generalized ...
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Added: June 27, 2024
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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 ...
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