Email this article FAMILY OF LOGARITHMIC SPIRALS IN HAMILTONIAN SYSTEMS OF DIMENSION 8 WITH CONTROL IN A DISK
- Authors: Ronzhina M.I1, Manita L.A2
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Affiliations:
- National University of Oil and Gas “Gubkin University”
- National Research University Higher School of Economics
- Issue: Vol 60, No 11 (2024)
- Pages: 1531-1540
- Section: CONTROL THEORY
- URL: https://ogarev-online.ru/0374-0641/article/view/273228
- DOI: https://doi.org/10.31857/S0374064124110085
- EDN: https://elibrary.ru/JDYXQP
- ID: 273228
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Abstract
We study the neighbourhood of a singular second-order extremal in optimal control problems that are affine in control in a disk. We consider the case when 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 Fuller problem with control in a disk. For this class of problems we prove the existence of extremals in the form of logarithmic spirals, which reach the singular second-order extremal in a finite time, while the control performs an infinite number of rotations around the circle.
About the authors
M. I Ronzhina
National University of Oil and Gas “Gubkin University”
Email: ronzhina.m@gubkin.ru
Moscow, Russia
L. A Manita
National Research University Higher School of Economics
Email: lmanita@hse.ru
Moscow, Russia
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