Some optimal control problems with boundary conditions of Robin type and singular cost functionals

• Autorzy: Akkouchi M.
• Języki publikacji: EN

Abstrakty

EN

We are concerned with the study of a class of linear boundary optimal control systems associated to the Laplace operator on a regular bounded domain in the n dimensional Euclidean space obtained by perturbing a singular system. The sets of admissible controls, taken here, are closed convex subsets of the Hilbert space of all square integrable functions on the boundary, verifying some natural conditions. The cost functional, used here, is singular. For these systems, we prove the existence of the (perturbed) states and optimal controls, and study their convergence.

Słowa kluczowe

EN

perturbed states; linear boundary; Robin type

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 3
• Strony: 671--680
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Akkouchi M.

• Department de Mathematiques Faculte des Sciences-Semlalia Universite Cadi Ayyad B.P.:2390 Marrakech, Maroc (Marocco)

Bibliografia

• [1] M. Akkouchi, A. Bounabat and T. Benkiran, Study of a perturbed boundary optimal control system, Appl. Math. Lett. Vol. 9, No. 1 (1996), 95-99.
• [2] M. Akkouchi, A. Bounabat and T. Benkiran, Some results on convergence linked to a perturbed boundary optimal control system, Extracta Math. Vol. 9, No. 2 (1994), 105-110.
• [3] A. Bounabat, Etude d'un problème de contrôle optimal, Thèse de 3-ème cycle, Université des Sciences et Techniques de Lille I (June 1981).
• [4] H. Brezis, Analyse Fonctionnelle, Théorie et Applications, Masson, Paris, (1983).
• [5] J. L. Lions and E. Magenes, Problèmes aux limites non Homogènes et Applications, Vol. 1, Dunod, Paris, 1968.
• [6] J. L. Lions, Contrôle Optimal de Systèmes Gouvernés par des Equations aux Dérivées Partielles, Dunod-Guthier-Villars, Paris, 1968.
• [7] J. L. Lions, Perturbation Singulère dans les problèmes aux limites et en Contrôle Optimal, Springer-Verlag, Berlin, 1973.
• [8] V. Mikhailov, Equations aux dérivées partielles, Editions Mir, Moscou, 1980.