Here we derive a variant of the nonsmooth maximum principle for optimal control problems with both pure state and mixed state and control constraints. Our necessary conditions include a Weierstrass condition together with an Euler adjoint inclusion involving the joint subdifferentials with respect to both state and control, generalizing previous results in [M.d.R. de Pinho, M.M.A. Ferreira, F.A.C.C. Fontes, Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems. ESAIM: COCV 11 (2005) 614–632]. A notable feature is that our main results are derived combining old techniques with recent results. We use a well known penalization technique for state constrained problem together with an appeal to a recent nonsmooth maximum principle for problems with mixed constraints.
DOI : 10.1051/cocv/2014047
Mots clés : Optimal control, state and mixed constraints, maximum principle
@article{COCV_2015__21_4_939_0,
author = {Haider Ali Biswas, Md. and do Rosario de Pinho, Maria},
title = {A maximum principle for optimal control problems with state and mixed constraints},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {939--957},
publisher = {EDP-Sciences},
volume = {21},
number = {4},
year = {2015},
doi = {10.1051/cocv/2014047},
mrnumber = {3395750},
zbl = {1330.49018},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2014047/}
}
TY - JOUR AU - Haider Ali Biswas, Md. AU - do Rosario de Pinho, Maria TI - A maximum principle for optimal control problems with state and mixed constraints JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 939 EP - 957 VL - 21 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2014047/ DO - 10.1051/cocv/2014047 LA - en ID - COCV_2015__21_4_939_0 ER -
%0 Journal Article %A Haider Ali Biswas, Md. %A do Rosario de Pinho, Maria %T A maximum principle for optimal control problems with state and mixed constraints %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 939-957 %V 21 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2014047/ %R 10.1051/cocv/2014047 %G en %F COCV_2015__21_4_939_0
Haider Ali Biswas, Md.; do Rosario de Pinho, Maria. A maximum principle for optimal control problems with state and mixed constraints. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 4, pp. 939-957. doi : 10.1051/cocv/2014047. http://www.numdam.org/articles/10.1051/cocv/2014047/
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