Necessary conditions of optimality in the form of Unmaximized Inclusions (UI) are derived for optimal control problems with state constraints. The conditions presented here generalize earlier optimality conditions to problems that may be nonconvex. The derivation of UI-type conditions in the absence of the convexity assumption is of particular importance when deriving necessary conditions for constrained problems. We illustrate this feature by establishing, as an application, optimality conditions for problems that in addition to state constraints incorporate mixed state-control constraints.
Mots-clés : optimal control, state constraints, nonsmooth analysis, Euler-Lagrange inclusion
@article{COCV_2005__11_4_614_0,
author = {de Pinho, Maria do Ros\'ario and Ferreira, Maria Margarida and Fontes, Fernando},
title = {Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {614--632},
publisher = {EDP-Sciences},
volume = {11},
number = {4},
year = {2005},
doi = {10.1051/cocv:2005020},
mrnumber = {2167877},
zbl = {1081.49016},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2005020/}
}
TY - JOUR AU - de Pinho, Maria do Rosário AU - Ferreira, Maria Margarida AU - Fontes, Fernando TI - Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2005 SP - 614 EP - 632 VL - 11 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2005020/ DO - 10.1051/cocv:2005020 LA - en ID - COCV_2005__11_4_614_0 ER -
%0 Journal Article %A de Pinho, Maria do Rosário %A Ferreira, Maria Margarida %A Fontes, Fernando %T Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2005 %P 614-632 %V 11 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2005020/ %R 10.1051/cocv:2005020 %G en %F COCV_2005__11_4_614_0
de Pinho, Maria do Rosário; Ferreira, Maria Margarida; Fontes, Fernando. Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 4, pp. 614-632. doi : 10.1051/cocv:2005020. http://www.numdam.org/articles/10.1051/cocv:2005020/
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