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IMA Journal of Mathematical Control and Information 2003 20(3):305-334; doi:10.1093/imamci/20.3.305
© 2003 by Institute of Mathematics and its Applications
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Robust control problems associated with time-varying delay nonlinear parabolic equations

Aziz Belmiloudi1

1 IRMAR-Université Rennes1, centre de maths-INSA de Rennes, 20 avenue des Buttes de Coësmes, CS 14315, 35043 Rennes Cédex, France

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.

Keywords: robust control; nonlinear parabolic equations; existence and uniqueness of optimal solution; necessary optimality conditions; time-varying delays.


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