Open AccessOptimal spiral-like solutions near a singular extremal in a two-input control problem
Author(s) -
Лариса Анатольевна Манита,
Mariya Ronzhina
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021187
Subject(s) - mathematics , spiral (railway) , optimal control , affine transformation , bounded function , point (geometry) , singular point of a curve , singular control , inverted pendulum , singular solution , order (exchange) , combinatorics , pure mathematics , mathematical analysis , geometry , mathematical optimization , physics , finance , nonlinear system , quantum mechanics , economics
We study an optimal control problem affine in two-dimensional bounded control, in which there is a singular point of the second order. In the neighborhood of the singular point we find optimal spiral-like solutions that attain the singular point in finite time, wherein the corresponding optimal controls perform an infinite number of rotations along the circle \begin{document}$ S^{1} $\end{document} . The problem is related to the control of an inverted spherical pendulum in the neighborhood of the upper unstable equilibrium.