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Zh. Vychisl. Mat. Mat. Fiz., 2007, Volume 47, Number 11, Pages 1865–1879 (Mi zvmmf221)  

This article is cited in 8 scientific papers (total in 8 papers)

Optimal control problems with terminal functionals represented as the difference of two convex functions

A. S. Strekalovskii

Institute of System Dynamics and Control Theory, Siberian Division, Russian Academy of Sciences, ul. Lermontova 134, Irkutsk, 664033, Russia

Abstract: Two control problems for a state-linear control system are considered: the minimization of a terminal functional representable as the difference of two convex functions (d.c. functions) and the minimization of a convex terminal functional with a d.c. terminal inequality contraint. Necessary and sufficient global optimality conditions are proved for problems in which the Pontryagin and Bellman maximum principles do not distinguish between locally and globally optimal processes. The efficiency of the approach is illustrated by examples.

Key words: optimal control, locally and globally optimal processes, optimality principles and conditions.

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English version:
Computational Mathematics and Mathematical Physics, 2007, 47:11, 1788–1801

Bibliographic databases:

UDC: 519.626.2+517.977.5
Received: 29.03.2007

Citation: A. S. Strekalovskii, “Optimal control problems with terminal functionals represented as the difference of two convex functions”, Zh. Vychisl. Mat. Mat. Fiz., 47:11 (2007), 1865–1879; Comput. Math. Math. Phys., 47:11 (2007), 1788–1801

Citation in format AMSBIB
\by A.~S.~Strekalovskii
\paper Optimal control problems with terminal functionals represented as the difference of two convex functions
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 11
\pages 1865--1879
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 11
\pages 1788--1801

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. S. Strekalovskii, M. V. Yanulevich, “Global search in the optimal control problem with a terminal objective functional represented as the difference of two convex functions”, Comput. Math. Math. Phys., 48:7 (2008), 1119–1132  mathnet  crossref  isi
    2. V. G. Antonik, V. A. Srochko, “Method for nonlocal improvement of extreme controls in the maximization of the terminal state norm”, Comput. Math. Math. Phys., 49:5 (2009), 762–775  mathnet  crossref  zmath  isi
    3. Gornov A.Yu., Zarodnyuk T.S., “Metod krivolineinogo poiska globalnogo ekstremuma v zadache optimalnogo upravleniya”, Sovremennye tekhnologii. Sistemnyi analiz. Modelirovanie, 2009, no. 3, 19–27  elib
    4. A. S. Strekalovsky, “Maximizing a state convex Lagrange functional in optimal control”, Autom. Remote Control, 73:6 (2012), 949–961  mathnet  crossref  isi
    5. Strekalovsky A.S., “Global Optimality Conditions for Optimal Control Problems with Functions of Ad Alexandrov”, J. Optim. Theory Appl., 159:2 (2013), 297–321  crossref  mathscinet  zmath  isi  elib  scopus
    6. Strekalovsky A.S. Yanulevich M.V., “Global Search in a Noncovex Optimal Control Problem”, J. Comput. Syst. Sci. Int., 52:6 (2013), 893–908  crossref  mathscinet  zmath  isi  elib  scopus
    7. A. S. Strekalovskii, “Sovremennye metody resheniya nevypuklykh zadach optimalnogo upravleniya”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 8 (2014), 141–163  mathnet
    8. Strekalovsky A.S. Yanulevich M.V., “on Global Search in Nonconvex Optimal Control Problems”, J. Glob. Optim., 65:1, SI (2016), 119–135  crossref  mathscinet  zmath  isi  elib  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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