This work is concerned with the time optimal control problem for evolution equations in Hilbert spaces. The attention is focused on the maximum principle for the time optimal controllers having the dimension smaller that of the state system, in particular for minimal time sliding mode controllers, which is one of the novelties of this paper. We provide the characterization of the controllers by the optimality conditions determined for some general cases. The proofs rely on a set of hypotheses meant to cover a large class of applications. Examples of control problems governed by parabolic equations with potential and drift terms, porous media equation or reaction-diffusion systems with linear and nonlinear perturbations, describing real world processes, are presented at the end.
Mots-clés : Time optimal control, optimality conditions, sliding mode control, evolution equations, maximum principle, reaction-diffusion systems
@article{COCV_2020__26_1_A46_0,
author = {Marinoschi, Gabriela},
title = {Minimal time sliding mode control for evolution equations in {Hilbert} spaces},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {26},
year = {2020},
doi = {10.1051/cocv/2019065},
mrnumber = {4144114},
zbl = {1450.35090},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2019065/}
}
TY - JOUR AU - Marinoschi, Gabriela TI - Minimal time sliding mode control for evolution equations in Hilbert spaces JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2019065/ DO - 10.1051/cocv/2019065 LA - en ID - COCV_2020__26_1_A46_0 ER -
%0 Journal Article %A Marinoschi, Gabriela %T Minimal time sliding mode control for evolution equations in Hilbert spaces %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2019065/ %R 10.1051/cocv/2019065 %G en %F COCV_2020__26_1_A46_0
Marinoschi, Gabriela. Minimal time sliding mode control for evolution equations in Hilbert spaces. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 46. doi : 10.1051/cocv/2019065. http://www.numdam.org/articles/10.1051/cocv/2019065/
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