Journal Article

Robust control problems associated with time‐varying delay nonlinear parabolic equations

Aziz Belmiloudi

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 20, issue 3, pages 305-334
Published in print September 2003 | ISSN: 0265-0754
Published online September 2003 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/20.3.305
Robust control problems associated with time‐varying delay nonlinear parabolic equations

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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

Journal Article.  0 words. 

Subjects: Mathematics

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