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

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Abstract

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.

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Authors and Affiliations

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

    Aziz Belmiloudi

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  1. Aziz Belmiloudi
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Belmiloudi, A. Nonlinear Robust Control Problems of Parabolic Type Equations with Time-Varying Delays Given in the Integral Form. Journal of Dynamical and Control Systems 9, 469–512 (2003). https://doi.org/10.1023/A:1025872901378

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  • DOI: https://doi.org/10.1023/A:1025872901378

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