Robust control of a non-isothermal solidification model

International audienceWe consider robust control problems which are related to a phase-field model. The goal of this study is to reach a given target set, by a phase trajectory, of a model describing the process of a non-isothermal solidification, under action of disturbances. In order to take account the influence of noises in data, we suppose that disturbances as well as controls act upon the system. Firstly the robust control problems are formulated. Afterwards the existence and the uniqueness of the solution of the perturbed problem is proved along with stability under mild assumptions. An optimal solution is proven to exist and, finally, we give necessary optimality conditions