Maryse MOUTAMAL (LAMIA) : No-regret control of parabolic space-time fractional Sturm-Liouville problems in a star graph.

We are concerned with a parabolic fractional initial-boundary value problems of Sturm-Liouville type in an interval and in a general star graph with mixed Dirichlet and Neumann boundary controls. We first give several existence, uniqueness and regularity results of weak and very-weak solutions. Using the notion of no-regret control introduced by Lions, we prove the existence and uniqueness of the low regret control of a quadratic boundary optimal control problem, then we prove that this low regret control converges to the no-regret control and we provide the optimality system which characterize that no-regret control.