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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 240352, 8 pages
http://dx.doi.org/10.1155/2013/240352
Research Article

Feedback Control Method Using Haar Wavelet Operational Matrices for Solving Optimal Control Problems

Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia

Received 4 April 2013; Revised 27 June 2013; Accepted 1 July 2013

Academic Editor: Shawn X. Wang

Copyright © 2013 Waleeda Swaidan and Amran Hussin. 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. R. W. Beard and T. W. McLain, “Successive Galerkin approximation algorithms for nonlinear optimal and robust control,” International Journal of Control, vol. 71, no. 5, pp. 717–743, 1998. View at Scopus
  2. Y. Feng, B. D. O. Anderson, and M. Rotkowitz, “A game theoretic algorithm to compute local stabilizing solutions to HJBI equations in nonlinear H control,” Automatica, vol. 45, no. 4, pp. 881–888, 2009. View at Publisher · View at Google Scholar · View at Scopus
  3. J. Huang and C.-F. Lin, “Numerical approach to computing nonlinear H control laws,” Journal of Guidance, Control, and Dynamics, vol. 18, no. 5, pp. 989–996, 1995. View at Scopus
  4. M. D. S. Aliyu, “An approach for solving the Hamilton-Jacobi-Isaacs equation (HJIE) in nonlinear control,” Automatica, vol. 39, no. 5, pp. 877–884, 2003. View at Publisher · View at Google Scholar · View at Scopus
  5. M. Abu-Khalaf, F. L. Lewis, and J. Huang, “Policy iterations on the Hamilton-Jacobi-Isaacs equation for H state feedback control with input saturation,” IEEE Transactions on Automatic Control, vol. 51, no. 12, pp. 1989–1995, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. S. T. Glad, “Robustness of nonlinear state feedback—a survey,” Automatica, vol. 23, no. 4, pp. 425–435, 1987. View at Scopus
  7. O. von Stryk and R. Bulirsch, “Direct and indirect methods for trajectory optimization,” Annals of Operations Research, vol. 37, no. 1, pp. 357–373, 1992. View at Publisher · View at Google Scholar · View at Scopus
  8. R. W. Beard, G. N. Saridis, and J. T. Wen, “Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation,” Automatica, vol. 33, no. 12, pp. 2159–2176, 1997. View at Scopus
  9. H. M. Jaddu, Numerical methods for solving optimal control problems using Chebyshev polynomials [Ph.D. thesis], School of Information Science, Japan Advanced Institute of Science and Technology, 1998.
  10. S. C. Beeler, H. T. Tran, and H. T. Banks, “Feedback control methodologies for nonlinear systems,” Journal of Optimization Theory and Applications, vol. 107, no. 1, pp. 1–33, 2000. View at Scopus
  11. C. Park and P. Tsiotras, “Approximations to optimal feedback control using a successive wavelet collocation algorithm,” in Proceedings of the American Control Conference, vol. 3, pp. 1950–1955, June 2003. View at Scopus
  12. C. F. Chen and C. H. Hsiao, “Haar wavelet method for solving lumped and distributed parameter systems,” IEE Proceeding on Control Theory and Application, vol. 144, no. 1, pp. 87–94, 1997. View at Publisher · View at Google Scholar
  13. C. H. Hsiao and W. J. Wang, “Optimal control of linear time-varying systems via Haar wavelets,” Journal of Optimization Theory and Applications, vol. 103, no. 3, pp. 641–655, 1999. View at Scopus
  14. R. Dai and J. E. Cochran Jr., “Wavelet collocation method for optimal control problems,” Journal of Optimization Theory and Applications, vol. 143, no. 2, pp. 265–278, 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. J. W. Curtis and R. W. Beard, “Successive collocation: an approximation to optimal nonlinear control,” in Proceeding of the American Control Conference, vol. 5, pp. 3481–3485, June 2001. View at Scopus
  16. C. H. Hsiao and S. P. Wu, “Numerical solution of time-varying functional differential equations via Haar wavelets,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 1049–1058, 2007. View at Publisher · View at Google Scholar · View at Scopus
  17. J. W. Brewer, “Kronecker products and matrix calculus in system theory,” IEEE Transactions on Circuits and Systems, vol. 25, no. 9, pp. 772–781, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. P. Courrieu, “Fast computation of Moore-Penrose inverse matrices,” Neural Information Processing-Letters and Reviews, vol. 8, no. 2, pp. 25–29, 2005.
  19. J.-J. Slotine and W. Li, Applied Nonlinear Control, Prentice-Hall, Englewood Cliffs, NJ, USA, 1991.
  20. A. Isidori, Nonlinear Control Systems, Communication and Control Engineering, Springer, New York, NY, USA, 2nd edition, 1989.