On the Variational Stability of a Class of Nonlinear Parabolic Optimal Control Problems | Zendy

Νικόλαος Παπαγεωργίου | Zendy

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On the Variational Stability of a Class of Nonlinear Parabolic Optimal Control Problems

Author(s) -

Νικόλαος Παπαγεωργίου

Publication year - 1996

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/697

Subject(s) - class (philosophy) , nonlinear system , stability (learning theory) , mathematics , optimal control , control (management) , control theory (sociology) , mathematical optimization , computer science , physics , artificial intelligence , quantum mechanics , machine learning

In this paper we study parametric optimal control problems governed by a nonlinear parabolic equation in divergence form. The parameter appears in all the data of the problem, including the partial differential operator. Using as tools the G-convergence of operators and the f-convergence of functionals, we show that the set-valued map of optimal pairs is upper semicontinuous with respect to the parameter and the optimal value function responds continuously to changes of the parameter. Finally in the case of semilinear systems we show that our framework can also incorporate systems with weakly convergent coefficients.

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