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 H . We prove the following dichotomy: the number of conjugate times is identically zero or grows to innity. The latter case occurs if and only if 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 H.

On conjugate times of LQ optimal control problems / Agrachev, Andrey; Rizzi, Luca; Silveira, P.. - In: JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS. - ISSN 1079-2724. - 21:4(2015), pp. 625-641. [10.1007/s10883-014-9251-6]

On conjugate times of LQ optimal control problems

Agrachev, Andrey;Rizzi, Luca;
2015-01-01

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 H . We prove the following dichotomy: the number of conjugate times is identically zero or grows to innity. The latter case occurs if and only if 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 H.
2015
21
4
625
641
https://arxiv.org/abs/1311.2009
http://link.springer.com/article/10.1007%2Fs10883-014-9251-6
Agrachev, Andrey; Rizzi, Luca; Silveira, P.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/11868
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