Archive of Issues
Russia Nizhni Novgorod
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 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 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. 474489. 
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