This paper is devoted to describing second order conditions in the framework of extremal problems, that is, conditions obtained by reducing the optimal control problem to an abstract one in a suitable Banach (or Hilbert) space. The studied problem includes equality constraints both on the end-points and on the state-control trajectory. The second goal is to give a complete description of necessary and sufficient second order conditions for weak local optimality by describing first the associated linear-quadratic problem and then by giving a conjugate point theory for this linear quadratic problem with constraints.
@article{bwmeta1.element.bwnjournal-article-bcpv32z1p361bwm,
author = {Stefani, Gianna and Zezza, PierLuigi},
title = {Minima in control problems with constraints},
journal = {Banach Center Publications},
volume = {31},
year = {1995},
pages = {361-378},
zbl = {1055.49510},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv32z1p361bwm}
}
Stefani, Gianna; Zezza, PierLuigi. Minima in control problems with constraints. Banach Center Publications, Tome 31 (1995) pp. 361-378. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv32z1p361bwm/
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