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Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2021

State-constrained controllability of linear reaction-diffusion systems

Clément Moreau
EDF

Résumé

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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Dates et versions

hal-03277290 , version 1 (09-11-2020)
hal-03277290 , version 2 (18-12-2020)
hal-03277290 , version 3 (10-02-2021)
hal-03277290 , version 4 (17-05-2021)
hal-03277290 , version 5 (02-07-2021)

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Pierre Lissy, Clément Moreau. State-constrained controllability of linear reaction-diffusion systems. ESAIM: Control, Optimisation and Calculus of Variations, 2021, 27, pp.70. ⟨10.1051/cocv/2021057⟩. ⟨hal-03277290v5⟩
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