Stackelberg control with constraints on the state for a linear backward heat equation

L L Djomegne Njoukoue (1, 2) , Gisèle Mophou (3) , G Deugoue (1)

1 Université de Dschang
2 African Institute for Mathematical Sciences (AIMS-Cameroon)
3 LAMIA - Laboratoire de Mathématiques Informatique et Applications [UR1_1]

We are interested in the hierarchic control problem for a linear backward heat equation. We assume that we can act on the system via two distributed controls. One control called follower solves an optimal control problem which consist in bringing the flux of the system to zero. The other control called leader solves a null controllability problem. The results are achieved by means of inequality of observability associated to a non-homogeneous Dirichlet boundary condition.

Mots clés: Controllability; Carleman inequality; optimal control; Euler-Lagrange formula; linear heat equation

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

L L Djomegne Njoukoue, Gisèle Mophou, G Deugoue. Stackelberg control with constraints on the state for a linear backward heat equation. Advance in Evolution Equations, Evolutionary Processes and Applications, 2019, : Advances in Evolution Equations, 978-1-53616-350-6. ⟨hal-02548103⟩