FAMILY OF LOGARITHMIC SPIRALS IN HAMILTONIAN SYSTEMS OF DIMENSION 8 WITH CONTROL IN A DISK

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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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