State-constrained controllability of linear reaction-diffusion systems

Pierre Lissy (1) , Clément Moreau (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 EDF - EDF

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.

Mots clés: Control theory; controllability; state-constrained controllability; parabolic equations

Domaines: Mathématiques [math]

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-03277290⟩