Existence and Uniqueness of Optimal Control for a Distributed-Parameter Bilinear System

Authors:
A. Addou;A. Benbrik
Affiliations:
Université Mohamed I, Faculté des Sciences, Département de mathématiques et Informatique, Oujda, Maroc. E-mail: addou@sciences.univ-oujda.ac.ma;Université Mohamed I. Faculté des Sciences, Département de mathématiques et Informatique, Oujda, Maroc. E-mail: benbrik@sciences.univ-oujda.ac.ma
Venue:
Journal of Dynamical and Control Systems
Year:
2002

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Abstract

In this paper, we study an optimal control problem of bilinear type. The system is governed by a fourth-order parabolic operator. The performance index is of the form J(u) = \int_{0}^{T}L(z(t), u(t)) dt. Under suitable hypotheses, it is shown that there exists an optimal control ū and it satisfies an appropriate optimality system. Further, for a small initial state ū is unique.