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Home » Issues » Archive of Issues » 2017 - 2 issue » pp. 162-177

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Russia Nizhni Novgorod
Year
2017
Volume
27
Issue
2
Pages
162-177
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Section Mathematics
Title Regularization of the Pontryagin maximum principle in the problem of optimal boundary control for a parabolic equation with state constraints in Lebesgue spaces
Author(-s) Gorshkov A.A.a, Sumin M.I.a
Affiliations Nizhni Novgorod State Universitya
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
UDC 517.97
MSC 47A52
DOI 10.20537/vm170202
Received 10 November 2016
Language Russian
Citation Gorshkov A.A., Sumin M.I. Regularization of the Pontryagin maximum principle in the problem of optimal boundary control for a parabolic equation with state constraints in Lebesgue spaces, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 2, pp. 162-177.
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