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Itogi Nauki i Tekhniki. Seriya "Matematicheskii Analiz", 1977, Volume 14, Pages 101–166 (Mi intm40)  

This article is cited in 27 scientific papers (total in 27 papers)

Numerical and approximate methods of optimal control

F. L. Chernous'ko, V. B. Kolmanovskii
Abstract: Approximate methods of solving problems of optimal control are classified and analyzed, and their domain of applicability is indicated. Among the special problems the problem of the choice of optimal trajectories for aircraft is considered.
English version:
Journal of Soviet Mathematics, 1979, Volume 12, Issue 3, Pages 310–353
DOI: https://doi.org/10.1007/BF01098370
Bibliographic databases:
Language: Russian
Citation: F. L. Chernous'ko, V. B. Kolmanovskii, “Numerical and approximate methods of optimal control”, Itogi Nauki i Tekhn. Ser. Mat. Anal., 14, VINITI, Moscow, 1977, 101–166; J. Soviet Math., 12:3 (1979), 310–353
Citation in format AMSBIB
\Bibitem{CheKol77}
\by F.~L.~Chernous'ko, V.~B.~Kolmanovskii
\paper Numerical and approximate methods of optimal control
\serial Itogi Nauki i Tekhn. Ser. Mat. Anal.
\yr 1977
\vol 14
\pages 101--166
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intm40}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=483433}
\zmath{https://zbmath.org/?q=an:0418.49002|0421.49001}
\transl
\jour J. Soviet Math.
\yr 1979
\vol 12
\issue 3
\pages 310--353
\crossref{https://doi.org/10.1007/BF01098370}
Linking options:
  • https://www.mathnet.ru/eng/intm40
  • https://www.mathnet.ru/eng/intm/v14/p101
  • This publication is cited in the following 27 articles:
    1. Valery Y. Glizer, Vladimir Turetsky, “One Class of Stackelberg Linear–Quadratic Differential Games with Cheap Control of a Leader: Asymptotic Analysis of an Open-Loop Solution”, Axioms, 13:11 (2024), 801  crossref
    2. A. Yu. Gornov, A. S. Anikin, T. S. Zarodnyuk, P. S. Sorokovikov, “Modification of the confidence bar algorithm based on approximations of the main diagonal of the Hessian matrix for solving optimal control problems”, Autom. Remote Control, 83:10 (2022), 1590–1599  mathnet  crossref  crossref
    3. Yulia Danik, Mikhail Dmitriev, 2022 International Russian Automation Conference (RusAutoCon), 2022, 587  crossref
    4. T. A. Zvonareva, O. I. Krivorot'ko, “Comparative analysis of gradient methods for source identification in a diffusion-logistic model”, Comput. Math. Math. Phys., 62:4 (2022), 674–684  mathnet  mathnet  crossref  crossref  scopus
    5. Yulia Danik, Mikhail Dmitriev, Dmitry Makarov, Tatiana Zarodnyuk, Springer Proceedings in Mathematics & Statistics, 248, Dynamical Systems in Theoretical Perspective, 2018, 113  crossref
    6. Danik Yu E., M.G. Dmitriev, D.A. Makarov, 2018 Eleventh International Conference “Management of large-scale system development” (MLSD, 2018, 1  crossref
    7. Yu.E. Danik, M.G. Dmitriev, “Construction of Parametric Regulators for Nonlinear Control Systems Based on the Pade Approximations of the Matrix Riccati Equation Solution”, IFAC-PapersOnLine, 51:32 (2018), 815  crossref
    8. Mikhail G. Dmitriev, Dmitry A. Makarov, AIP Conference Proceedings, 1997, 2018, 020001  crossref
    9. A. O. Blinov, M. G. Dmitriev, “Chuvstvitelnost resheniya nekotorykh vozmuschennykh zadach optimizatsii”, Programmnye sistemy: teoriya i prilozheniya, 7:1 (2016), 47–59  mathnet
    10. Oles Vladimirovich Fesko, Vladimir Iosifovich Gurman, Irina Viktorovna Rasina, “General Schemes of Iterative Optimization with Applications to Optimal Control Problems”, J. Oper. Res. Soc. China, 4:2 (2016), 223  crossref
    11. E. V. Grigorieva, N. V. Bondarenko, E. N. Khailov, “Time Optimal Control Problem for the Waste Water Biotreatment Model”, J Dyn Control Syst, 21:1 (2015), 3  crossref
    12. “Parametrization of the attainable set for a nonlinear control model of a biochemical process”, Mathematical Biosciences and Engineering, 10:4 (2013), 1067  crossref
    13. V. I. Gurman, I. V. Rasina, A. O. Blinov, “Evolyutsiya i perspektivy priblizhennykh metodov optimalnogo upravleniya”, Programmnye sistemy: teoriya i prilozheniya, 2:2 (2011), 11–29  mathnet  elib
    14. A. I. Tyatyushkin, O. V. Morzhin, “Numerical investigation of attainability sets of nonlinear controlled differential systems”, Autom. Remote Control, 72:6 (2011), 1291–1300  mathnet  crossref  mathscinet  zmath  isi
    15. V. M. Aleksandrov, “Optimalnoe i kvazioptimalnoe po raskhodu resursov upravleniya dinamicheskimi sistemami”, Sib. elektron. matem. izv., 7 (2010), 166–249  mathnet
    16. O. V. Baturina, “Bilineinye dinamicheskie sistemy: issledovanie iterativnykh metodov optimizatsii”, Probl. upravl., 5 (2010), 22–27  mathnet
    17. S. Ya. Serovaǐskiǐ, “Sequential differentiation in nonsmooth infinite-dimensional extremal problems”, Russian Math. (Iz. VUZ), 52:1 (2008), 45–58  mathnet  crossref  mathscinet
    18. V. I. Gurman, Ni Ming Kang, M. Yu. Ukhin, “Practical control optimization schemes based on the extension principle”, Autom. Remote Control, 67:4 (2006), 538–551  mathnet  crossref  mathscinet  zmath
    19. M. Yu. Ukhin, “An approximate optimal control for discrete models: Its design”, Autom. Remote Control, 67:7 (2006), 1082–1092  mathnet  crossref  mathscinet  zmath
    20. V. Yu. Tertychny-Dauri, “Solution of Variational Dynamic Problems under Parametric Uncertainty”, Problems Inform. Transmission, 41:1 (2005), 45–58  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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