In optimal control, sensitivity relations are usually understood as inclusions that identify the pair formed by the dual arc and the Hamiltonian as a suitable generalized gradient of the value function, evaluated along a given minimizing trajectory. In this paper, sensitivity relations are obtained for the Mayer problem associated with the differential inclusion and applied to express optimality conditions. The first application of our results concerns the maximum principle and consists in showing that a dual arc can be constructed for every element of the superdifferential of the final cost as a solution of an adjoint system. The second and last application we discuss in this paper concerns optimal design. We show that one can associate a family of optimal trajectories, starting at some point , with every nonzero reachable gradient of the value function at , in such a way that families corresponding to distinct reachable gradients have empty intersection.
DOI : 10.1051/cocv/2014050
Mots-clés : Mayer problem, differential inclusions, optimality conditions, sensitivity relations
@article{COCV_2015__21_3_789_0,
author = {Cannarsa, Piermarco and Frankowska, H\'el\`ene and Scarinci, Teresa},
title = {Sensitivity relations for the {Mayer} problem with differential inclusions},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {789--814},
publisher = {EDP-Sciences},
volume = {21},
number = {3},
year = {2015},
doi = {10.1051/cocv/2014050},
mrnumber = {3358630},
zbl = {1319.49036},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2014050/}
}
TY - JOUR AU - Cannarsa, Piermarco AU - Frankowska, Hélène AU - Scarinci, Teresa TI - Sensitivity relations for the Mayer problem with differential inclusions JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 789 EP - 814 VL - 21 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2014050/ DO - 10.1051/cocv/2014050 LA - en ID - COCV_2015__21_3_789_0 ER -
%0 Journal Article %A Cannarsa, Piermarco %A Frankowska, Hélène %A Scarinci, Teresa %T Sensitivity relations for the Mayer problem with differential inclusions %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 789-814 %V 21 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2014050/ %R 10.1051/cocv/2014050 %G en %F COCV_2015__21_3_789_0
Cannarsa, Piermarco; Frankowska, Hélène; Scarinci, Teresa. Sensitivity relations for the Mayer problem with differential inclusions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 3, pp. 789-814. doi : 10.1051/cocv/2014050. http://archive.numdam.org/articles/10.1051/cocv/2014050/
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