Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013, Article ID 831657, 12 pages
http://dx.doi.org/10.1155/2013/831657
Research Article

A Genetic Algorithm Approach for Prediction of Linear Dynamical Systems

1Department of Mechatronics Engineering, Faculty of Engineering, The University of Jordan, Amman 11942, Jordan
2Department of Electrical Engineering, Faculty of Engineering, The University of Jordan, Amman 11942, Jordan
3Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan
4Department of Mathematics, Faculty of Science, King AbdulAziz University, Jeddah 21589, Saudi Arabia
5Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan

Received 19 June 2013; Accepted 9 October 2013

Academic Editor: Ben T. Nohara

Copyright © 2013 Za'er Abo-Hammour et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. Zivot and J. Wang, Modelling Financial Time Series with S-PLUS, Springer, New York, NY, USA, 2003.
  2. L. D. Landau and G. Zito, Digital Control Systems-Design, Identification, Implementation, Springer, London, UK, 2006.
  3. A. García-Hiernaux, J. Casals, and M. Jerez, “Estimating the system order by subspace methods,” Computational Statistics, vol. 27, no. 3, pp. 411–425, 2012. View at Publisher · View at Google Scholar · View at Scopus
  4. L. Wahlberg, P. Lindskog, and B. Wahlberg, “Applications of Kautz models in system identification,” in Proceedings of the 12th IFAC World Congress, Sydney, Australia, 1993.
  5. H. AbdulRahim, F. Ibrahim, and M. N. Taib, “System identification of nonlinear autoregressive models in monitoring dengue infection,” International Journal on Smart Sensing and Intelligent Systems, vol. 3, no. 4, pp. 783–806, 2010. View at Google Scholar · View at Scopus
  6. A. Dahlen, Identification of stochastic systems: subspace methods and covariance extension [Ph.D. thesis], Royal Institute of Technology, Stockholm, Sweden, 2001.
  7. L. Fenga and D. N. Politis, “Bootstrap-based ARMA order selection,” Journal of Statistical Computation and Simulation, vol. 81, no. 7, pp. 799–814, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. P. M. Broersen and S. de-Waele, “Finite sample properties of ARMA order selection,” IEEE Transactions on Instrumentation and Measurement, vol. 53, no. 3, pp. 645–651, 2004. View at Publisher · View at Google Scholar · View at Scopus
  9. Z. S. Abo-Hammour, O. M. K. Alsmadi, A. M. Al-Smadi, M. I. Zaqout, and M. S. Saraireh, “ARMA model order and parameter estimation using genetic algorithms,” Mathematical and Computer Modelling of Dynamical Systems, vol. 18, no. 2, pp. 201–221, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. A. Al-Smadi and A. Al-Zaben, “ARMA model order determination using edge detection: a new perspective,” Circuits, Systems, and Signal Processing, vol. 24, no. 6, pp. 723–732, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. P. M. Broersen, Automatic Autocorrelation and Spectral Analysis, Springer, London, UK, 2006.
  12. H. Akaike, “Fitting autoregressive models for prediction,” Annals of the Institute of Statistical Mathematics, vol. 21, no. 1, pp. 243–247, 1969. View at Publisher · View at Google Scholar
  13. H. Akaike, “Statistical predictor identification,” Annals of the Institute of Statistical Mathematics, vol. 22, no. 1, pp. 203–217, 1970. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. J. Rissanen, “Modeling by shortest data description,” Automatica, vol. 14, no. 5, pp. 465–471, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  15. E. J. Hannan, “The estimation of the order of an ARMA process,” Annals of Statistics, vol. 8, no. 5, pp. 1071–1081, 1980. View at Publisher · View at Google Scholar
  16. G. Liang, D. M. Wilkes, and J. A. Cadzow, “ARMA model order estimation based on the eigenvalues of the covariance matrix,” IEEE Transactions on Signal Processing, vol. 41, no. 10, pp. 3003–3009, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  17. S. Rolf, J. Sprave, and W. Urfer, “Model identification and parameter estimation of ARMA models by means of evolutionary algorithms,” in Proceedings of the 1997 IEEE/IAFE Conference on Computational Intelligence for Financial Engineering, pp. 237–243, March 1997. View at Scopus
  18. E. Ursu and K. F. Turkman, “Periodic autoregressive model identification using genetic algorithms,” Journal of Time Series Analysis, vol. 33, no. 3, pp. 398–405, 2012. View at Publisher · View at Google Scholar · View at Scopus
  19. R. Baragona, F. Battaglia, and D. Cucina, “Estimating threshold subset autoregressive moving-average models by genetic algorithms,” International Journal of Statistics, vol. 62, no. 1, pp. 39–61, 2004. View at Google Scholar
  20. W. Chang, “Coefficient estimation of IIR filter by a multiple crossover genetic algorithm,” Computers and Mathematics with Applications, vol. 51, no. 9-10, pp. 1437–1444, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  21. A. Al-Smadi, “Automatic identification of ARMA systems,” International Journal of General Systems, vol. 38, no. 1, pp. 29–41, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  22. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, New York, NY, USA, 1989.
  23. Z. S. Abo-Hammour, Advanced continuous genetic algorithms and their applications in the motion planning of robotic manipulators and the numerical solution of boundary value problems [Ph.D. thesis], Quiad-Azam University, Islamabad, Pakistan, 2002.
  24. Z. S. Abo-Hammour, “A novel continuous genetic algorithms for the solution of the cartesian path generation problem of robot manipulators,” in Robot Manipulators: New Research, J. X. Lui, Ed., pp. 133–190, Nova Science, New York, NY, USA, 2005. View at Google Scholar
  25. Z. S. Abo-Hammour, A. G. Asasfeh, A. M. Al-Smadi, and O. M. K. Alsmadi, “A novel continuous genetic algorithm for the solution of optimal control problems,” Optimal Control Applications and Methods, vol. 32, no. 4, pp. 414–432, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  26. Z. S. Abo-Hammour, O. M. Alsmadi, S. I. Bataineh, M. A. Al-Omari, and N. Affach, “Continuous genetic algorithms for collision-free Cartesian path planning of robot manipulators regular paper,” International Journal of Advanced Robotic Systems, vol. 8, no. 6, pp. 14–36, 2011. View at Google Scholar · View at Scopus
  27. Z. S. Abo-Hammour, O. M. K. Alsmadi, and A. M. Al-Smadi, “Multi-time-scale systems model order reduction via genetic algorithms with eigenvalue preservation,” Journal of Circuits, Systems and Computers, vol. 20, no. 7, pp. 1403–1418, 2011. View at Publisher · View at Google Scholar · View at Scopus
  28. Z. S. Abo-Hammour, N. M. Mirza, S. M. Mirza, and M. Arif, “Cartesian path generation of robot manipulators using continuous genetic algorithms,” Robotics and Autonomous Systems, vol. 41, no. 4, pp. 179–223, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  29. Z. S. Abo-Hammour, M. Yusuf, N. M. Mirza, S. M. Mirza, M. Arif, and J. Khurshid, “Numerical solution of second-order, two-point boundary value problems using continuous genetic algorithms,” International Journal for Numerical Methods in Engineering, vol. 61, no. 8, pp. 1219–1242, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  30. O. Abu Arqub, Numerical solution of fuzzy differential equation using continuous genetic algorithms [Ph.D. thesis], University of Jordan, Amman, Jordan, 2008.
  31. O. Abu Arqub, Z. S. Abo-Hammour, and S. Momani, “Application of continuous genetic algorithm for nonlinear system of second-order boundary value problems,” Applied Mathematics and Information Sciences, vol. 8, no. 1, pp. 1–14, 2014. View at Publisher · View at Google Scholar
  32. O. Abu Arqub, Z. S. Abo-Hammour, S. Momani, and N. Shawagfeh, “Solving singular two-point boundary value problems using continuous genetic algorithm,” Abstract and Applied Analysis, vol. 2012, Article ID 205391, 25 pages, 2012. View at Publisher · View at Google Scholar
  33. A. S. Nissinen, H. N. Koivo, and H. Koivisto, “Optimization of neural network topologies using genetic algorithm,” Intelligent Automation and Soft Computing, vol. 5, no. 3, pp. 211–224, 1999. View at Publisher · View at Google Scholar · View at Scopus
  34. A. Al-Smadi and D. M. Wilkes, “Robust and accurate ARX and ARMA model order estimation of non-Gaussian processes,” IEEE Transactions on Signal Processing, vol. 50, no. 3, pp. 759–763, 2002. View at Google Scholar