MENU

You are here

On conjugate times of LQ optimal control problems

TitleOn conjugate times of LQ optimal control problems
Publication TypeJournal Article
Year of Publication2014
AuthorsAgrachev, AA, Rizzi, L, Silveira, P
KeywordsOptimal control, Lagrange Grassmannian, Conjugate point
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 $\vec{H}$.

URLhttp://hdl.handle.net/1963/7227
DOI10.1007/s10883-014-9251-6

Sign in