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Article Dans Une Revue Journal of Dynamical and Control Systems Année : 2014

On conjugate times of LQ optimal control problems

Résumé

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 $\vec{H}$.

Dates et versions

hal-01096715 , version 1 (18-12-2014)

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Andrei Agrachev, Luca Rizzi, Pavel Silveira. On conjugate times of LQ optimal control problems. Journal of Dynamical and Control Systems, 2014, 21 (4), pp.625-641. ⟨10.1007/s10883-014-9251-6⟩. ⟨hal-01096715⟩
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