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In this paper we analyze several concepts of solution to discontinuous ODEs in relation to feedbacks generated by optimal syntheses. Optimal trajectories are called Stratified Solutions in case of regular synthesis in the sense of Boltyanskii-Brunovsky. We introduce a concept of solution called Krasowskii Cone Robust that characterizes optimal trajectories for minimum time on the plane and for general problems under suitable assumptions.
@article{COCV_2002__7__291_0,
author = {Marigo, Alessia and Piccoli, Benedetto},
title = {Regular syntheses and solutions to discontinuous {ODEs}},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {291--307},
publisher = {EDP-Sciences},
volume = {7},
year = {2002},
doi = {10.1051/cocv:2002013},
mrnumber = {1925031},
zbl = {1053.49027},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002013/}
}
TY - JOUR AU - Marigo, Alessia AU - Piccoli, Benedetto TI - Regular syntheses and solutions to discontinuous ODEs JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2002 SP - 291 EP - 307 VL - 7 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002013/ DO - 10.1051/cocv:2002013 LA - en ID - COCV_2002__7__291_0 ER -
%0 Journal Article %A Marigo, Alessia %A Piccoli, Benedetto %T Regular syntheses and solutions to discontinuous ODEs %J ESAIM: Control, Optimisation and Calculus of Variations %D 2002 %P 291-307 %V 7 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002013/ %R 10.1051/cocv:2002013 %G en %F COCV_2002__7__291_0
Marigo, Alessia; Piccoli, Benedetto. Regular syntheses and solutions to discontinuous ODEs. ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 291-307. doi: 10.1051/cocv:2002013
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