Nonlinear Robust Control Problems of Parabolic Type Equations with Time-Varying Delays Given in the Integral Form

Two classes of robust control problems associated with a class of nonlinear parabolic type systems with multiple time-varying delays are considered, in order to take an account of the influence of noises in data. The time-varying delays are given in the integral form and appear in the state equations. The controls appear either in the forcing terms or in the initial condition. First, the robust control problems are formulated. Afterwards the existence of an optimal solution is proved and necessary conditions of optimality are obtained. Finally the conditions of the uniqueness of the optimal solution are derived.