We consider an optimal control problem of Mayer type and prove that, under suitable conditions on the system, the value function is differentiable along optimal trajectories, except possibly at the endpoints. We provide counterexamples to show that this property may fail to hold if some of our conditions are violated. We then apply our regularity result to derive optimality conditions for the trajectories of the system.
Mots-clés : optimal control, value function, semiconcavity
@article{COCV_2004__10_4_666_0,
author = {Sinestrari, Carlo},
title = {Regularity along optimal trajectories of the value function of a {Mayer} problem},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {666--676},
publisher = {EDP-Sciences},
volume = {10},
number = {4},
year = {2004},
doi = {10.1051/cocv:2004026},
mrnumber = {2111087},
zbl = {1068.49028},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2004026/}
}
TY - JOUR AU - Sinestrari, Carlo TI - Regularity along optimal trajectories of the value function of a Mayer problem JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2004 SP - 666 EP - 676 VL - 10 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2004026/ DO - 10.1051/cocv:2004026 LA - en ID - COCV_2004__10_4_666_0 ER -
%0 Journal Article %A Sinestrari, Carlo %T Regularity along optimal trajectories of the value function of a Mayer problem %J ESAIM: Control, Optimisation and Calculus of Variations %D 2004 %P 666-676 %V 10 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2004026/ %R 10.1051/cocv:2004026 %G en %F COCV_2004__10_4_666_0
Sinestrari, Carlo. Regularity along optimal trajectories of the value function of a Mayer problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 4, pp. 666-676. doi : 10.1051/cocv:2004026. http://www.numdam.org/articles/10.1051/cocv:2004026/
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