TY - JOUR
T1 - On conjugate times of LQ optimal control problems
Y1 - 2014
A1 - Andrei A. Agrachev
A1 - Luca Rizzi
A1 - Pavel Silveira
KW - Optimal control, Lagrange Grassmannian, Conjugate point
AB - 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 $\vec{H}$.
PB - Springer
UR - http://hdl.handle.net/1963/7227
N1 - 14 pages, 1 figure
U1 - 7261
U2 - Mathematics
U4 - 1
U5 - MAT/05 ANALISI MATEMATICA
ER -