Stackelberg strategy on a degenerate parabolic equation with missing data

This paper deals with the hierarchic control of a degenerate parabolic\nequation with missing initial condition. We present a Stackelberg strategy\ncombining the concept of null controllability with low-regret control. We\nassume that we can act on the system through a set of hierarchic controls. The\nmain control called the leader is in charge of the null controllability while\nthe second control named the follower solves an optimal control problem\ninvolving a missing data. The main novelty of this work is the derivation of a\nnew Carleman inequality for a degenerate system, which is used in a standard\nway to show observability inequality of the adjoint degenerate systems.\n