Robust control problems associated with time‐varying delay 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 gouverned by nonlinear parabolic equations with multiple time‐varying delays, in order to take account the influence of noise in data. 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 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

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

Aziz Belmiloudi. Robust control problems associated with time‐varying delay nonlinear parabolic equations. IMA Journal of Mathematical Control and Information, 2003, Volume 20 (Issue 3), pp.305-334. ⟨10.1093/imamci/20.3.305⟩. ⟨hal-00648892⟩