@article {2013,
title = {On conjugate times of LQ optimal control problems},
number = {Journal of Dynamical and Control Systems},
year = {2014},
note = {14 pages, 1 figure},
publisher = {Springer},
abstract = {Motivated by the study of linear quadratic optimal control problems, we
consider a dynamical system with a constant, quadratic Hamiltonian, and we
characterize the number of conjugate times in terms of the spectrum of the
Hamiltonian vector field $\vec{H}$. We prove the following dichotomy: the
number of conjugate times is identically zero or grows to infinity. The latter
case occurs if and only if $\vec{H}$ has at least one Jordan block of odd
dimension corresponding to a purely imaginary eigenvalue. As a byproduct, we
obtain bounds from below on the number of conjugate times contained in an
interval in terms of the spectrum of $\vec{H}$.},
keywords = {Optimal control, Lagrange Grassmannian, Conjugate point},
doi = {10.1007/s10883-014-9251-6},
url = {http://hdl.handle.net/1963/7227},
author = {Andrei A. Agrachev and Luca Rizzi and Pavel Silveira}
}