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 |
Optimal Control Problem, Classical Quasi-Newton Method, New Quasi-Newton Method, Control Operator
| [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. |
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
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
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
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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}
}
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 -
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