We study the controllability of a coupled system of linear parabolic equations, with nonnegativity constraint on the state. We establish two results of controllability to trajectories in large time: one for diagonal diffusion matrices with an “approximate” nonnegativity constraint, and a another stronger one, with “exact” nonnegativity constraint, when all the diffusion coefficients are equal and the eigenvalues of the coupling matrix have nonnegative real part. The proofs are based on a “staircase” method. Finally, we show that state-constrained controllability admits a positive minimal time, even with weaker unilateral constraint on the state.
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Keywords: Control theory, controllability, state-constrained controllability, parabolic equations
@article{COCV_2021__27_1_A72_0,
author = {Lissy, Pierre and Moreau, Cl\'ement},
editor = {Buttazzo, G. and Casas, E. and de Teresa, L. and Glowinski, R. and Leugering, G. and Tr\'elat, E. and Zhang, X.},
title = {State-constrained controllability of linear reaction-diffusion systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021057},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021057/}
}
TY - JOUR AU - Lissy, Pierre AU - Moreau, Clément ED - Buttazzo, G. ED - Casas, E. ED - de Teresa, L. ED - Glowinski, R. ED - Leugering, G. ED - Trélat, E. ED - Zhang, X. TI - State-constrained controllability of linear reaction-diffusion systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021057/ DO - 10.1051/cocv/2021057 LA - en ID - COCV_2021__27_1_A72_0 ER -
%0 Journal Article %A Lissy, Pierre %A Moreau, Clément %E Buttazzo, G. %E Casas, E. %E de Teresa, L. %E Glowinski, R. %E Leugering, G. %E Trélat, E. %E Zhang, X. %T State-constrained controllability of linear reaction-diffusion systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021057/ %R 10.1051/cocv/2021057 %G en %F COCV_2021__27_1_A72_0
Lissy, Pierre; Moreau, Clément. State-constrained controllability of linear reaction-diffusion systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 70. doi: 10.1051/cocv/2021057
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