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 Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017, Volume 27, Issue 1, Pages 26–41 (Mi vuu566)

MATHEMATICS

The regularized iterative Pontryagin maximum principle in optimal control. II. Optimization of a distributed system

F. A. Kuterin, M. I. Sumin

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

Abstract: The stable sequential Pontryagin maximum principle or, in other words, the regularized Pontryagin maximum principle in iterative form is formulated for the optimal control problem of a linear parabolic equation with distributed, initial and boundary controls and operator semiphase equality constraint. The main difference between it and the classical Pontryagin maximum principle is that, firstly, it is formulated in terms of minimizing sequences, secondly, the iterative process occurs in dual space, and thirdly, it is resistant to error of raw data and gives a minimizing approximate solution in the sense of J. Warga. So it is a regularizing algorithm. The proof of the regularized Pontryagin maximum principle in iterative form is based on the dual regularization methods and iterative dual regularization. The results of model calculations of the concrete optimal control problem illustrating the work of the algorithm based on the regularized iterative Pontryagin maximum principle are presented. The problem of finding a control triple with minimal norm under a given equality constraint at the final instant of time or, in other words, the inverse final observation problem of finding a normal solution is used as a concrete model optimal control problem.

Keywords: optimal control, instability, iterative dual regularization, regularized iterative Lagrange principle, regularized iterative 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 172702.Â.49.21.0003

DOI: https://doi.org/10.20537/vm170103

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Bibliographic databases:

UDC: 517.95, 517.977
MSC: 47A52, 93C20

Citation: F. A. Kuterin, M. I. Sumin, “The regularized iterative Pontryagin maximum principle in optimal control. II. Optimization of a distributed system”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:1 (2017), 26–41

Citation in format AMSBIB
\Bibitem{KutSum17} \by F.~A.~Kuterin, M.~I.~Sumin \paper The regularized iterative Pontryagin maximum principle in optimal control. II. Optimization of a distributed system \jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki \yr 2017 \vol 27 \issue 1 \pages 26--41 \mathnet{http://mi.mathnet.ru/vuu566} \crossref{https://doi.org/10.20537/vm170103} \elib{http://elibrary.ru/item.asp?id=28808553} 

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This publication is cited in the following articles:
1. M. I. Sumin, “Regularized Lagrange principle and Pontryagin maximum principle in optimal control and inverse problems”, IFAC-PapersOnLine, 51:32 (2018), 871–876
2. M. I. Sumin, “Regulyarizovannye printsip Lagranzha i printsip maksimuma Pontryagina v optimalnom upravlenii i obratnykh zadachakh”, Tr. IMM UrO RAN, 25, no. 1, 2019, 279–296
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