We present a necessary optimality conditions for a class of optimal control problems. The dynamical control system involves integer and fractional order derivatives and the final time is free. Optimality conditions are obtained. Feedback control laws for linear dynamic system are obtained.
| Published in |
American Journal of Theoretical and Applied Statistics (Volume 6, Issue 5-1)
This article belongs to the Special Issue Statistical Distributions and Modeling in Applied Mathematics |
| DOI | 10.11648/j.ajtas.s.2017060501.17 |
| Page(s) | 46-50 |
| 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), 2017. Published by Science Publishing Group |
Optimal Control, Fractional Differential Equation, Free Time, Lagrange Multipliers and Feedback Control
| [1] | A. Debbouche and M. M. El-Borai, "Weak almost periodic and optimal mild solutions of fractional evolution equations". Electronic Journal of Differential Equations, vol. 2009, pp. 1-8, (2009). |
| [2] | Mahmoud M. El-Borai, "Some probability densities and fundamental solutions of fractional evolution equations". Chaos, Solitons & Fractals, vol. 14, pp. 433-440, (2002). |
| [3] | Mahmoud. M. El-Borai, Khairia El-Said El-Nadi, and E. G. El-Akabawy, "On some fractional evolution equations". Computers and mathematics with applications, vol. 59, pp. 1352-1355, (2010). |
| [4] | O. P. Agrawal, A general formulation and solution scheme for fractional optimal control problems. Nonlinear Dynam. 38 (2004), no. 1-4, 323-337. |
| [5] | Mahmoud M. El-Borai, W. G. Elsayed and F. N. Ghaffoori, On the Cauchy Problem for Some Parabolic Fractional Partial Differential Equations with Time Delays, J. Math. & System Scie. 6 (2016), 194-199. |
| [6] | Mahmoud M. El-Borai, W. G. Elsayed and R. M. Al-Masroub, Exact Solutions for Some Nonlinear Partial Differential Equations via Extended (G'/G) – Expansion Method, Inter. J. Math. Trends and Tech. (IJMTT) – Vol. 36, No. 1-Aug (2016), 60-71. |
| [7] | O. P. Agrawal, A formulation and numerical scheme for fractional optimal control problems. J. Vib. Control 14 (2008), no. 9-10, 1291-1299. |
| [8] | O. P. Agrawal, O. Defterli and D. Baleanu, Dumitru Fractional optimal control problems with several state and control variables. J. Vib. Control 16 (2010), no. 13, 1967-1976. |
| [9] | G. S. F. Frederico and D. F. M. Torres, Fractional optimal control in the sense of Coputo and the fractional Noether’s theorem. Int. Math. Forum 3 (2008), no. 9-12, 479-493. |
| [10] | G. S. F. Frederico and D. F. M. Torres. Fractional conservation laws in optimal control theory, Nonlinear Dynam. 53 (2008), no. 3, 215-222. |
| [11] | C. Tricaud and Y. Chen. An approximate method for numerically solving fractional order optimal control problems of general form. Comput. Math. Appl. 59 (2010), no. 5, 1644-1655. |
| [12] | A. A. Kilbas, H. M. Srivastava, J. J. Trujillo. Theory and Applications of Fractional Differential Equations. Elsevier, North-Holland Mathematics Studies, (2006), p: 204. |
| [13] | S. G. Samko, A. A. Kibas O. I. Marichev. Fractional Integrals and Derivatives. Gordon and Breach Science Publishers, (2004). |
| [14] | C. Tricaud and Y. Chen. Time Optimal Control of Systems with Fractional Dynamics, Int. J. Differ. Equ. Appl., Volume 2010 (2010). Article ID 461048. |
| [15] | Z. D. Jelicic and N. Petrovacki, Optimality conditions and a solution scheme for fractional optimal control problems, Struct. Multidiscipline. Optimum. 38 (2009), no. 6, 571–581. |
| [16] | Mahmoud M. El-Borai, Khairia El-Said El-Nadi, On the fractional optimal control, Int. J. of Appl. Math. and Mech. (2008), 13-18. |
| [17] | Pontryagin LS, Baltyanskii VG, Gamkrelidze RV, and Mischenko EF (1962). The mathematical theory of optimal process. Inter science publishers Inc, New York. |
APA Style
Mahmoud M. El-borai, Wagdy G. ElSayed, M. A. Abdou, M. Taha E. (2017). On The Fractional Optimal Control Problem with Free End Point. American Journal of Theoretical and Applied Statistics, 6(5-1), 46-50. https://doi.org/10.11648/j.ajtas.s.2017060501.17
ACS Style
Mahmoud M. El-borai; Wagdy G. ElSayed; M. A. Abdou; M. Taha E. On The Fractional Optimal Control Problem with Free End Point. Am. J. Theor. Appl. Stat. 2017, 6(5-1), 46-50. doi: 10.11648/j.ajtas.s.2017060501.17
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Download@article{10.11648/j.ajtas.s.2017060501.17,
author = {Mahmoud M. El-borai and Wagdy G. ElSayed and M. A. Abdou and M. Taha E.},
title = {On The Fractional Optimal Control Problem with Free End Point},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {6},
number = {5-1},
pages = {46-50},
doi = {10.11648/j.ajtas.s.2017060501.17},
url = {https://doi.org/10.11648/j.ajtas.s.2017060501.17},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.s.2017060501.17},
abstract = {We present a necessary optimality conditions for a class of optimal control problems. The dynamical control system involves integer and fractional order derivatives and the final time is free. Optimality conditions are obtained. Feedback control laws for linear dynamic system are obtained.},
year = {2017}
}
TY - JOUR T1 - On The Fractional Optimal Control Problem with Free End Point AU - Mahmoud M. El-borai AU - Wagdy G. ElSayed AU - M. A. Abdou AU - M. Taha E. Y1 - 2017/04/11 PY - 2017 N1 - https://doi.org/10.11648/j.ajtas.s.2017060501.17 DO - 10.11648/j.ajtas.s.2017060501.17 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 46 EP - 50 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.s.2017060501.17 AB - We present a necessary optimality conditions for a class of optimal control problems. The dynamical control system involves integer and fractional order derivatives and the final time is free. Optimality conditions are obtained. Feedback control laws for linear dynamic system are obtained. VL - 6 IS - 5-1 ER -
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