| Peer-Reviewed

On Application of a New Quasi-Newton Algorithm for Solving Optimal Control Problems

Received: 25 December 2014     Accepted: 24 February 2015     Published: 4 March 2015
Views:       Downloads:
Abstract

In this work, we review the construction of the linear operator associated with a class of linear regulator problems subject to the state differential equation. The associated linear operator is then utilized in the derivation of a New Quasi-Newton Method (QNM) for solving this class of optimal control problems. Our results show an improvement over the Classical Quasi-Newton Method.

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 2)
DOI 10.11648/j.pamj.20150402.14
Page(s) 52-56
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Optimal Control Problem, Classical Quasi-Newton Method, New Quasi-Newton Method, Control Operator

References
[1] Broyden, C. G., (1965). “A Class of Methods for Solving Nonlinear Simultaneous Equations”, Math. Comp., 19, pp. 577-593.
[2] Davidon, W. C,. (1959). “Variable Metric Method for Minimization”, Rep. ANL-5990 Rev, Argonne National Laboratories, Argonne, I11
[3] Dennis, J. E. JR and More, J. J., (1977). “Quasi Newton Methods, Motivation and Theory”, SIAM Review 19(1), pp 46-89
[4] Fletcher, R., and Powell, M. J. D., (1963), “A rapidly Convergent Descent Method for Minimization.” Comp. J., 6, pp 163-168.
[5] George, M. S. (1996), An Engineering Approach To Optimal Control And Estimation Theory. John Wiley & Sons, Inc.
[6] Ibiejugba, M. A. and Onumanyi, P., (1984), “A Control Operator and Some of its Applications,” Journal of Mathematical Analysis and Applications, Vol. 103, No.1, pp 31-47.
[7] Ibiejugba, M. A., (1980), “Computing Methods in Optimal Control,” Ph. D. Thesis, University of Leeds, Leeds, England.
[8] Igor, G., Stephen, G. N. and Ariella, S., (2009), Linear and Nonlinear Optimization, 2nd edition, George Mason University, Fairfax, Virginia, SIAM, Philadelphia.
[9] Nocedal, J. and Wright, S. J., (2006), Numerical Optimization. 2nd edition. Springer-Verlag, New York.
Cite This Article
  • APA Style

    Felix Makanjuola Aderibigbe, Adejoke O. Dele-Rotimi, Kayode James Adebayo. (2015). On Application of a New Quasi-Newton Algorithm for Solving Optimal Control Problems. Pure and Applied Mathematics Journal, 4(2), 52-56. https://doi.org/10.11648/j.pamj.20150402.14

    Copy | Download

    ACS Style

    Felix Makanjuola Aderibigbe; Adejoke O. Dele-Rotimi; Kayode James Adebayo. On Application of a New Quasi-Newton Algorithm for Solving Optimal Control Problems. Pure Appl. Math. J. 2015, 4(2), 52-56. doi: 10.11648/j.pamj.20150402.14

    Copy | Download

    AMA Style

    Felix Makanjuola Aderibigbe, Adejoke O. Dele-Rotimi, Kayode James Adebayo. On Application of a New Quasi-Newton Algorithm for Solving Optimal Control Problems. Pure Appl Math J. 2015;4(2):52-56. doi: 10.11648/j.pamj.20150402.14

    Copy | Download

  • @article{10.11648/j.pamj.20150402.14,
      author = {Felix Makanjuola Aderibigbe and Adejoke O. Dele-Rotimi and Kayode James Adebayo},
      title = {On Application of a New Quasi-Newton Algorithm for Solving Optimal Control Problems},
      journal = {Pure and Applied Mathematics Journal},
      volume = {4},
      number = {2},
      pages = {52-56},
      doi = {10.11648/j.pamj.20150402.14},
      url = {https://doi.org/10.11648/j.pamj.20150402.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150402.14},
      abstract = {In this work, we review the construction of the linear operator associated with a class of linear regulator problems subject to the state differential equation. The associated linear operator is then utilized in the derivation of a New Quasi-Newton Method (QNM) for solving this class of optimal control problems. Our results show an improvement over the Classical Quasi-Newton Method.},
     year = {2015}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - On Application of a New Quasi-Newton Algorithm for Solving Optimal Control Problems
    AU  - Felix Makanjuola Aderibigbe
    AU  - Adejoke O. Dele-Rotimi
    AU  - Kayode James Adebayo
    Y1  - 2015/03/04
    PY  - 2015
    N1  - https://doi.org/10.11648/j.pamj.20150402.14
    DO  - 10.11648/j.pamj.20150402.14
    T2  - Pure and Applied Mathematics Journal
    JF  - Pure and Applied Mathematics Journal
    JO  - Pure and Applied Mathematics Journal
    SP  - 52
    EP  - 56
    PB  - Science Publishing Group
    SN  - 2326-9812
    UR  - https://doi.org/10.11648/j.pamj.20150402.14
    AB  - In this work, we review the construction of the linear operator associated with a class of linear regulator problems subject to the state differential equation. The associated linear operator is then utilized in the derivation of a New Quasi-Newton Method (QNM) for solving this class of optimal control problems. Our results show an improvement over the Classical Quasi-Newton Method.
    VL  - 4
    IS  - 2
    ER  - 

    Copy | Download

Author Information
  • Department of Mathematical Sciences, Ekiti State University, Ado Ekiti, Nigeria

  • Department of Mathematical Sciences, Ekiti State University, Ado Ekiti, Nigeria

  • Department of Mathematical Sciences, Ekiti State University, Ado Ekiti, Nigeria

  • Sections