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Avtomatika i Telemekhanika, 2014, Issue 11, Pages 19–37 (Mi at14140)  

This article is cited in 16 scientific papers (total in 16 papers)

Nonlinear Systems

Nonstandard duality and nonlocal necessary optimality conditions in nonconvex optimal control problems

V. A. Dykhta

Institute of System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia
References:
Abstract: To partially implement the idea of considering nonlinear optimal control problems immediately on the set of Pontryagin extremals (or on quasiextremals if the optimal solution does not exist), we introduce auxiliary functions of canonical variables, which we call bipositional, and the corresponding modified Lagrangian for the problem. The Lagrangian is subject to minimization on the trajectories of the canonical system from the Maximum Principle. This general approach is further specialized for nonconvex problems that are linear in state, leading to a nonstandard dual optimal control problem on the trajectories of the adjoint system. Applying the feedback minimum principle to both original and dual problems, we have obtained a pair of necessary optimality conditions that significantly strengthen the Maximum Principle and admit a constructive realization in the form of an iterative problem solving procedure. The general approach, optimality features, and the iterative solution procedure are illustrated by a series of examples.
Presented by the member of Editorial Board: V. I. Gurman

Received: 23.08.2013
English version:
Automation and Remote Control, 2014, Volume 75, Issue 11, Pages 1906–1921
DOI: https://doi.org/10.1134/S0005117914110022
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. A. Dykhta, “Nonstandard duality and nonlocal necessary optimality conditions in nonconvex optimal control problems”, Avtomat. i Telemekh., 2014, no. 11, 19–37; Autom. Remote Control, 75:11 (2014), 1906–1921
Citation in format AMSBIB
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\by V.~A.~Dykhta
\paper Nonstandard duality and nonlocal necessary optimality conditions in nonconvex optimal control problems
\jour Avtomat. i Telemekh.
\yr 2014
\issue 11
\pages 19--37
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\transl
\jour Autom. Remote Control
\yr 2014
\vol 75
\issue 11
\pages 1906--1921
\crossref{https://doi.org/10.1134/S0005117914110022}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84920928567}
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  • https://www.mathnet.ru/eng/at/y2014/i11/p19
  • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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