ON SOME ROBUST CONTROL PROBLEMS FOR NONLINEAR PARABOLIC EQUATIONS

Aziz Belmiloudi (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper, we study a robust control problem for a class of systems governed by nonlinear parabolic equations. Firstly the control is the forcing. We formulate the robust control problem, we prove the existence and the uniqueness of the solution and we give the necessary conditions of optimality. Secondly an initial perturbation problem is considered. A robust control problem is reformulated and the existence and the conditions of the uniqueness of the optimal solution are derived. First order necessary conditions of optimality are obtained.

Mots clés: robust control; nonlinear parabolic equations; existence and uniqueness of optimal solution; necessary optimality conditions

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

Aziz Belmiloudi. ON SOME ROBUST CONTROL PROBLEMS FOR NONLINEAR PARABOLIC EQUATIONS. International Journal of Pure and Applied Mathematics, 2004, Volume 11 (Issue 2), pp.119-149. ⟨hal-00648883⟩