Page 586 - Mathematical Techniques of Fractional Order Systems

556 Mathematical Techniques of Fractional Order Systems

techniques for the parameters estimation of the commensurate and incom-
mensurate fractional order models. Consequently, with the aid of these tech-
niques, an accurate and fast prediction for the chaotic behavior parameters in
the motor is achieved and that may help in controlling the system and may
protect the motor from damage.

REFERENCES

Alam, D.F., Yousri, D.A., Eteiba, M.B., 2015. Flower pollination algorithm based solar PV
parameter estimation. Energy Convers. Manage. 101, 410 422.
Alatas, B., 2010a. Chaotic harmony search algorithms. Appl. Math. Comput. 216 (9),
2687 2699. Available from: https://doi.org/10.1016/j.amc.2010.03.114.
Alatas, B., 2010b. Expert Systems with Applications Chaotic bee colony algorithms for global
numerical optimization. Exp. Syst. Applicat. 37 (8), 5682 5687. Available from: https://doi.
org/10.1016/j.eswa.2010.02.042.
Allam, D., Yousri, D.A., Eteiba, M.B., 2016. Parameters extraction of the three diode model for
the multi-crystalline solar cell / module using Moth-Flame Optimization Algorithm. Energy
Convers. Manage. 123, 535 548. Available from: https://doi.org/10.1016/j.
enconman.2016.06.052.
Ataei, M., Kiyoumarsi, A., Ghorbani, B., 2010. Control of chaos in permanent magnet synchro-
nous motor by using optimal lyapunov exponents placement. Phys. Lett. A 374 (41),
4226 4230. Available from: https://doi.org/10.1016%2Fj.physleta.2010.08.047.
Chaos Modeling and Control Systems Design. In: Azar, A.T., Vaidyanathan, S. (Eds.), Springer
International Publishing. Available from: https://doi.org/10.1007%2F978-3-319-13132-0.
Azar, A.T., Vaidyanathan, S. (Eds.), 2015b. Computational Intelligence Applications in
Modeling and Control. Springer International Publishing. Available from: https://doi.org/
10.1007%F2978-3-319-11017-2.
Azar, A.T., Vaidyanathan, S. (Eds.), 2016. Advances in Chaos Theory and Intelligent Control.
Springer International Publishing. Available from: https://doi.org/10.1007%F978-3-319-
30340-6.
Azar, A.T., Vaidyanathan, S., Ouannas, A. (Eds.), 2017. Fractional Order Control and
Synchronization of Chaotic Systems. Springer International Publishing. Available from:
https://doi.org/10.1007%F978-3-319-50249-6.
Boulkroune, A., Bouzeriba, A., Bouden, T., Azar, A.T., 2016a. Fuzzy adaptive synchronization
of uncertain fractional-order chaotic systems. Advances in Chaos Theory and Intelligent
Control. Springer International Publishing, pp. 681 697. Available from: https://doi.org/
10.1007%2F978-3-319-30340-6_28.
Boulkroune, A., Hamel, S., Azar, A.T., Vaidyanathan, S., 2016b. Fuzzy control-based function
synchronization of unknown chaotic systems with dead-zone input. Advances in Chaos
Theory and Intelligent Control. Springer International Publishing, pp. 699 718. Available
from: https://doi.org/10.1007%2F978-3-319-30340-6_29.
Debnath, L., 2003. Recent applications of fractional calculus to science and engineering. Int. J.
Math. Sci. 2003 (54), 3413 3442. Available from: http://www.hindawi.com/journals/ijmms/
2003/753601/abs/.
Debnath, L., 2004. A brief historical introduction to fractional calculus. Int. J. Math. Edu. Sci.
Tech. 35 (4), 487 501. Available from: http://www.tandfonline.com/doi/abs/10.1080/
00207390410001686571.