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Russia Nizhni Novgorod
Year
2017
Volume
27
Issue
1
Pages
26-41
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Section Mathematics
Title The regularized iterative Pontryagin maximum principle in optimal control. II. Optimization of a distributed system
Author(-s) Kuterin F.A.a, Sumin M.I.a
Affiliations Nizhni Novgorod State Universitya
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
UDC 517.95, 517.977
MSC 47A52, 93C20
DOI 10.20537/vm170103
Received 5 November 2016
Language Russian
Citation Kuterin F.A., Sumin M.I. The regularized iterative Pontryagin maximum principle in optimal control. II. Optimization of a distributed system, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 1, pp. 26-41.
References
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