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A Multimethod Technique for Solving Optimal Control Problem

  • Alexander I. Tyatyushkin
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 76)

Abstract

A multimethod algorithm for solving optimal control problems is implemented in the form of parallel optimization processes with the choice of the best approximation. The multimethod algorithm based on a sequence of different methods is to provide fast convergence to an optimal solution. Such a technology allows one to take into account some particularities of the problem at all stages of its solving and improve the efficiency of optimal control search.

Key words

Optimal control Multimethod algorithms Parallel computations Software packages Numerical methods 

References

  1. 1.
    Evtushenko, Yu.G.: Methods of solving of extremal problems and its application. Nauka, Moscow (1982).Google Scholar
  2. 2.
    Gurman, V.I., Dmitri’ev, M.G., Osipov, G.S.: Intellectual multimethod’s technology for solving and analysis of control problems: Preprint of Institute of programmed systems of RAS. Pereslavl–Zallesskii (1996).Google Scholar
  3. 3.
    Ling, L., Xue G.: Optimization of Molecular Similarity Index with Applications to Biomolecules. J. Glob. Optim. 14(3), 299–312 (1999)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Lyubushin, A.A., Chernous’ko, F.L.: The method of successive approximations for computation of optimal control. Izv. AN SSSR. Tehn. kibernetika. 2, 141–159 (1983).Google Scholar
  5. 5.
    Morzhin, O.V., Tyatyushkin, A.I.: An algorithm of the section method and program tools for reachable sets approximating. J. of Computer and Systems Sciences International. 47(1), 1–7 (2008).MathSciNetCrossRefGoogle Scholar
  6. 6.
    Tyatyushkin, A.I.: Package KONUS for optimization of continuous controlled systems. The packages of applied softwares: The experience of using. Nauka, Moscow (1989).Google Scholar
  7. 7.
    Tyatyushkin, A.I.: Numerical methods and software for optimization of controlled systems. Nauka, Novosibirsk (1992).Google Scholar
  8. 8.
    Tyatyushkin, A.I.: Numerical methods for optimization of controlled systems. J. Stability and control: Theory and Appl. 3(2), 150–174 (2000)MathSciNetGoogle Scholar
  9. 9.
    Tyatyushkin, A.I.: Parallel computations in Optimal control problems. Siberian J. of Number.Mathematics (Sib.Branch of Russ. Acad. of Sci). 3(2), 181–190, Novosibirsk (2000).Google Scholar
  10. 10.
    Tyatyushkin, A.I.: Many-Method Technique of Optimization of Control Systems. Nauka, Novosibirsk (2006).Google Scholar
  11. 11.
    Tyatyushkin, A.I., Zholudev, A.I., Erinchek, N.M.: The program system for solving optimal control problems with phase constraints. Intern. J. of Software Engineering and Knowledge Engineering. 3(4), 487–497 (1993).CrossRefGoogle Scholar
  12. 12.
    Vasil’ev, O.V., Tyatyushkin, A.I.: On some method of solving of optimal control problems based on maximum principle. J. vychisl. matem. i mat. fiziki. 21(6), 1376–1384 (1981).Google Scholar
  13. 13.
    Yuan, G.: Modified nonlinear conjugate gradient methods with sufficient descent property for large-scale optimization problems. Optim. Lett. 3(1), 11–21 (2009).MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Zholudev, A.I., Tyatyushkin, A.I., Erinchek, N.M.: Numerical optimization methods of controlled systems. Izv. AN SSSR. Tehn. kibernetika. 4, 14–31 (1989).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institute for System Dynamics and Control Theory SB RASIrkutskRussia

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