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 Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017, Volume 27, Issue 2, Pages 162–177 (Mi vuu578)

MATHEMATICS

Regularization of the Pontryagin maximum principle in the problem of optimal boundary control for a parabolic equation with state constraints in Lebesgue spaces

A. A. Gorshkov, M. I. Sumin

Lobachevsky State University of Nizhni Novgorod, pr. Gagarina, 23, Nizhni Novgorod, 603950, Russia

Abstract: A convex optimal control problem is considered for a parabolic equation with a strictly uniformly convex cost functional, with boundary control and distributed pointwise state constraints of equality and inequality type. The images of the operators that define pointwise state constraints are embedded into the Lebesgue space of integrable with $s$-th degree functions for $s\in(1,2)$. In turn, the boundary control belongs to Lebesgue space with summability index $r\in (2,+\infty)$. The main results of this work in the considered optimal control problem with pointwise state constraints are the two stable, with respect to perturbation of input data, sequential or, in other words, regularized principles: Lagrange principle in nondifferential form and Pontryagin maximum principle.

Keywords: optimal boundary control, parabolic equation, sequential optimization, dual regularization, stability, pointwise state constraint in the Lebesgue space, Lagrange principle, Pontryagin's maximum principle.

 Funding Agency Grant Number Russian Foundation for Basic Research 15-47-02294-ð_ïîâîëæüå_à Ministry of Education and Science of the Russian Federation 1727

DOI: https://doi.org/10.20537/vm170202

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Document Type: Article
UDC: 517.97
MSC: 47A52

Citation: A. A. Gorshkov, M. I. Sumin, “Regularization of the Pontryagin maximum principle in the problem of optimal boundary control for a parabolic equation with state constraints in Lebesgue spaces”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:2 (2017), 162–177

Citation in format AMSBIB
\Bibitem{GorSum17} \by A.~A.~Gorshkov, M.~I.~Sumin \paper Regularization of the Pontryagin maximum principle in the problem of optimal boundary control for a parabolic equation with state constraints in Lebesgue spaces \jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki \yr 2017 \vol 27 \issue 2 \pages 162--177 \mathnet{http://mi.mathnet.ru/vuu578} \crossref{https://doi.org/10.20537/vm170202} \elib{http://elibrary.ru/item.asp?id=29410189}