The integrability condition for the Lagrangian implicit differential systems of (TP,ω̇), introduced in [7], is applied for the specialized control theory systems. The Pontryagin maximum principle was reformulated in the framework of implicit differential systems and the corresponding necessary and sufficient conditions were proved. The beginning of the classification list of normal forms for Lagrangian implicit differential systems according to the symplectic equivalence is provided and the corresponding differential caustics are calculated.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc62-0-8,
author = {Stanis\l aw Janeczko and Fernand Pelletier},
title = {Singularities of implicit differential systems and maximum principle},
journal = {Banach Center Publications},
volume = {60},
year = {2003},
pages = {117-132},
zbl = {1067.57029},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc62-0-8}
}
Stanisław Janeczko; Fernand Pelletier. Singularities of implicit differential systems and maximum principle. Banach Center Publications, Tome 60 (2003) pp. 117-132. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc62-0-8/