In this paper, we study second-order optimality conditions for some optimal control problems governed by some semi-linear parabolic equations with periodic state constraint in time. We obtain a necessary condition and a sufficient condition in terms of the second order derivative of the associated Lagrangian. These two conditions correspond to the positive definite and the nonnegativity of the second order derivative of the Lagrangian on the same cone, respectively.
Keywords: Semi-linear parabolic equations, periodic state constraint, second order optimality conditions
@article{COCV_2021__27_1_A26_0,
author = {Liu, Hanbing and Wang, Gengsheng},
title = {Second order optimality conditions for periodic optimal control problems governed by semilinear parabolic differential equations},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021028},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021028/}
}
TY - JOUR AU - Liu, Hanbing AU - Wang, Gengsheng TI - Second order optimality conditions for periodic optimal control problems governed by semilinear parabolic differential equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021028/ DO - 10.1051/cocv/2021028 LA - en ID - COCV_2021__27_1_A26_0 ER -
%0 Journal Article %A Liu, Hanbing %A Wang, Gengsheng %T Second order optimality conditions for periodic optimal control problems governed by semilinear parabolic differential equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021028/ %R 10.1051/cocv/2021028 %G en %F COCV_2021__27_1_A26_0
Liu, Hanbing; Wang, Gengsheng. Second order optimality conditions for periodic optimal control problems governed by semilinear parabolic differential equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 24. doi: 10.1051/cocv/2021028
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Cité par Sources :
This work was Supported by the National Natural Science Foundation of China under grant No. 11971022 and No. 11926337, and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) under grant CUGSX01.
