Archive of Issues
Russia Nizhni Novgorod
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 University^{a} 
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. 2641. 
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