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Russia Nizhni Novgorod
Year
2016
Volume
26
Issue
4
Pages
474-489
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Section Mathematics
Title The regularized iterative Pontryagin maximum principle in optimal control. I. Optimization of a lumped 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 system of ordinary differential equations with pointwise phase equality constraint and a finite number of functional equality and inequality constraints. 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 errors 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 methods of dual regularization and iterative dual regularization.
Keywords optimal control, instability, iterative dual regularization, regularized iterative Lagrange principle, regularized iterative Pontryagin's maximum principle
UDC 517.91, 517.977
MSC 47A52, 93C15
DOI 10.20537/vm160403
Received 15 September 2016
Language Russian
Citation Kuterin F.A., Sumin M.I. The regularized iterative Pontryagin maximum principle in optimal control. I. Optimization of a lumped system, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 4, pp. 474-489.
References
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