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Mathematical Problems in Engineering
Volume 2015, Article ID 982041, 10 pages
http://dx.doi.org/10.1155/2015/982041
Research Article

Fast Model Predictive Control Combining Offline Method and Online Optimization with K-D Tree

National Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China

Received 26 April 2015; Revised 5 July 2015; Accepted 22 July 2015

Academic Editor: Jean J. Loiseau

Copyright © 2015 Yi Ding 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. S. J. Wright, “Applying new optimization algorithms to model predictive control,” in Chemical Process Control-V, vol. 93 of CACHE, AIChE Symposium Series no. 316, pp. 147–155, American Institute of Chemical Engineers, New York, NY, USA, 1997. View at Google Scholar
  2. C. V. Rao, S. J. Wright, and J. B. Rawlings, “Application of interior-point methods to model predictive control,” Journal of Optimization Theory and Applications, vol. 99, no. 3, pp. 723–757, 1998. View at Publisher · View at Google Scholar · View at Scopus
  3. Y. Wang and S. Boyd, “Fast model predictive control using online optimization,” IEEE Transactions on Control Systems Technology, vol. 18, no. 2, pp. 267–278, 2010. View at Publisher · View at Google Scholar · View at Scopus
  4. R. A. Bartlett, L. T. Biegler, J. Backstrom, and V. Gopal, “Quadratic programming algorithms for large-scale model predictive control,” Journal of Process Control, vol. 12, no. 7, pp. 775–795, 2002. View at Publisher · View at Google Scholar · View at Scopus
  5. H. J. Ferreau, H. G. Bock, and M. Diehl, “An online active set strategy to overcome the limitations of explicit MPC,” International Journal of Robust and Nonlinear Control, vol. 18, no. 8, pp. 816–830, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. P. Patrinos, P. Sopasakis, and H. Sarimveis, “A global piecewise smooth Newton method for fast large-scale model predictive control,” Automatica, vol. 47, no. 9, pp. 2016–2022, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. P. Patrinos and A. Bemporad, “An accelerated dual gradient-projection algorithm for embedded linear model predictive control,” IEEE Transactions on Automatic Control, vol. 59, no. 1, pp. 18–33, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. A. Bemporad, M. Morari, V. Dua, and E. N. Pistikopoulos, “The explicit linear quadratic regulator for constrained systems,” Automatica, vol. 38, no. 1, pp. 3–20, 2002. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Bemporad and C. Filippi, “Suboptimal explicit receding horizon control via approximate multiparametric quadratic programming,” Journal of Optimization Theory and Applications, vol. 117, no. 1, pp. 9–38, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. C. N. Jones and M. Morari, “Polytopic approximation of explicit model predictive controllers,” IEEE Transactions on Automatic Control, vol. 55, no. 11, pp. 2542–2553, 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. F. J. Christophersen, M. N. Zeilinger, C. N. Jones, and M. Morari, “Controller complexity reduction for piecewise affine systems through safe region elimination,” in Proceedings of the 46th IEEE Conference on Decision and Control (CDC '07), pp. 4773–4778, December 2007. View at Publisher · View at Google Scholar · View at Scopus
  12. G. Pannocchia, J. B. Rawlings, and S. J. Wright, “Fast, large-scale model predictive control by partial enumeration,” Automatica, vol. 43, no. 5, pp. 852–860, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. P. Tøndel, T. A. Johansen, and A. Bemporad, “An algorithm for multi-parametric quadratic programming and explicit MPC solutions,” Automatica, vol. 39, no. 3, pp. 489–497, 2003. View at Publisher · View at Google Scholar · View at Scopus
  14. P. Tøndel, T. A. Johansen, and A. Bemporad, “Evaluation of piecewise affine control via binary search tree,” Automatica, vol. 39, no. 5, pp. 945–950, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  15. F. Bayat, T. A. Johansen, and A. A. Jalali, “Using hash tables to manage the time-storage complexity in a point location problem: application to explicit model predictive control,” Automatica, vol. 47, no. 3, pp. 571–577, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. T. A. Johansen, “Approximate explicit receding horizon control of constrained nonlinear systems,” Automatica, vol. 40, no. 2, pp. 293–300, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. M. N. Zeilinger, C. N. Jones, and M. Morari, “Real-time suboptimal model predictive control using a combination of explicit MPC and online optimization,” IEEE Transactions on Automatic Control, vol. 56, no. 7, pp. 1524–1534, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. J. L. Bentley, “Multidimensional binary search trees used for associative searching,” Communications of the ACM, vol. 18, no. 9, pp. 509–517, 1975. View at Publisher · View at Google Scholar · View at Scopus
  19. J. H. Friedman, J. L. Bentley, and R. A. Finkel, “An algorithm for finding best matches in logarithmic expected time,” ACM Transactions on Mathematical Software, vol. 3, no. 3, pp. 209–226, 1977. View at Publisher · View at Google Scholar
  20. D. T. Lee and C. K. Wong, “Worst-case analysis for region and partial region searches in multidimensional binary search trees and balanced quad trees,” Acta Informatica, vol. 9, no. 1, pp. 23–29, 1977. View at Publisher · View at Google Scholar · View at Scopus
  21. S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge, UK, 2004. View at Publisher · View at Google Scholar · View at MathSciNet