Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 897853, 13 pages
http://dx.doi.org/10.1155/2015/897853
Research Article

Optimal Control Algorithm of Constrained Fuzzy System Integrating Sliding Mode Control and Model Predictive Control

Department of Information Science and Engineering, Northeastern University, Liaoning 110004, China

Received 26 September 2014; Accepted 25 December 2014

Academic Editor: Bo Shen

Copyright © 2015 Chonghui Song. 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. L. X. Wang, A Course in Fuzzy Systems and Control, Printice Hall, Upper Saddle River, NJ, USA, 1997.
  2. H. G. Zhang, M. Li, J. Yang, and D. D. Yang, “Fuzzy model-based robust networked control for a class of nonlinear systems,” IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans, vol. 39, no. 2, pp. 437–447, 2009. View at Publisher · View at Google Scholar · View at Scopus
  3. K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, John Wiley & Sons, New York, NY, USA, 2001.
  4. L.-X. Wang and J. M. Mendel, “Fuzzy basis functions, universal approximation, and orthogonal least-squares learning,” IEEE Transactions on Neural Networks, vol. 3, no. 5, pp. 807–814, 1992. View at Publisher · View at Google Scholar · View at Scopus
  5. H. G. Zhang, Y. Wang, and D. Liu, “Delay-dependent guaranteed cost control for uncertain stochastic fuzzy systems with multiple time delays,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 38, no. 1, pp. 126–140, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. S. G. Cao, N. W. Rees, and G. Feng, “Analysis and design for a class of complex control systems. I. Fuzzy modelling and identification,” Automatica, vol. 33, no. 6, pp. 1017–1028, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  7. H. G. Zhang and X. P. Xie, “Relaxed stability conditions for continuous-time T-S fuzzy-control systems via augmented multi-indexed matrix approach,” IEEE Transactions on Fuzzy Systems, vol. 19, no. 3, pp. 478–492, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. Y. Wang, H. G. Zhang, X. Y. Wang, and D. S. Yang, “Networked synchronization control of coupled dynamic networks with time-varying delay,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 40, no. 6, pp. 1468–1479, 2010. View at Publisher · View at Google Scholar · View at Scopus
  9. H. G. Zhang, S. X. Lun, and D. Liu, “Fuzzy H filter design for a class of nonlinear discrete-time systems with multiple time delays,” IEEE Transactions on Fuzzy Systems, vol. 15, no. 3, pp. 453–469, 2007. View at Publisher · View at Google Scholar · View at Scopus
  10. S. J. Wu and C. T. Lin, “Optimal fuzzy controller design: local concept approach,” IEEE Transactions on Fuzzy Systems, vol. 8, no. 2, pp. 171–185, 2000. View at Publisher · View at Google Scholar · View at Scopus
  11. S. J. Wu and C. T. Lin, “Optimal fuzzy controller design in continuous fuzzy system: global concept approach,” IEEE Transactions on Fuzzy Systems, vol. 8, no. 6, pp. 713–729, 2000. View at Publisher · View at Google Scholar · View at Scopus
  12. C. H. Song and T. Y. Chai, “Comment on ‘Discrete-time optimal fuzzy controller design: global concept approach’,” IEEE Transactions on Fuzzy Systems, vol. 13, no. 2, pp. 285–286, 2005. View at Publisher · View at Google Scholar · View at Scopus
  13. C. H. Song, J. C. Ye, D. R. Liu, and Q. Kang, “Generalized receding horizon control of fuzzy systems based on numerical optimization algorithm,” IEEE Transactions on Fuzzy Systems, vol. 17, no. 6, pp. 1336–1352, 2009. View at Publisher · View at Google Scholar · View at Scopus
  14. C. H. Song, C. Y. Bian, X. Zhang, and C. L. Shi, “Numerical optimization method for HJI equations derived from robust receding horizon control schemes and controller design,” Science China. Information Sciences, vol. 55, no. 1, pp. 214–227, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. C. H. Song and J. C. Ye, “Robust receding horizon control of uncertain fuzzy systems,” Neural Computing and Applications, vol. 22, no. 2, pp. 237–247, 2013. View at Publisher · View at Google Scholar · View at Scopus
  16. C. H. Song, “Numerical optimization method for HJB equations with its application to receding horizon control schemes,” in Proceedings of the 48th IEEE Conference on Decision and Control Held Jointly with the 28th Chinese Control Conference (CDC/CCC '09), pp. 333–338, Shanghai, China, December 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. G. Barles and P. E. Souganidis, “Convergence of approximation schemes for fully nonlinear second order equations,” Asymptotic Analysis, vol. 4, no. 3, pp. 271–283, 1991. View at Google Scholar · View at MathSciNet
  18. J. C. Ye, Optimal life insurance purchase, consumption and portfolio under an uncertain life [Ph.D. Dissertation], Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, Ill, USA, 2006.
  19. H. J. Kushner and P. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time, Springer, New York, NY, USA, 2nd edition, 2001.
  20. Q. S. Song, “Convergence of Markov chain approximation on generalized HJB equation and its applications,” Automatica, vol. 44, no. 3, pp. 761–766, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. W. Fleming and H. Soner, Controlled Markov Processes and Viscosity Solutions, Springer, New York, NY, USA, 2nd edition, 2006. View at MathSciNet
  22. H. G. Zhang, F. S. Yang, X. D. Liu, and Q. L. Zhang, “Stability analysis for neural networks with time-varying delay based on quadratic convex combination,” IEEE Transactions on Neural Networks and Learning Systems, vol. 24, no. 4, pp. 513–521, 2013. View at Publisher · View at Google Scholar · View at Scopus
  23. F.-Y. Wang, H. G. Zhang, and D. Liu, “Adaptive dynamic programming: an introduction,” IEEE Computational Intelligence Magazine, vol. 4, no. 2, pp. 39–47, 2009. View at Publisher · View at Google Scholar · View at Scopus
  24. H. Zhang, Y. Luo, and D. Liu, “Neural-network-based near-optimal control for a class of discrete-time affine nonlinear systems with control constraints,” IEEE Transactions on Neural Networks, vol. 20, no. 9, pp. 1490–1503, 2009. View at Publisher · View at Google Scholar · View at Scopus
  25. H. Zhang, Q. Wei, and Y. Luo, “A novel infinite-time optimal tracking control scheme for a class of discrete-time nonlinear systems via the greedy HDP iteration algorithm,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 38, no. 4, pp. 937–942, 2008. View at Publisher · View at Google Scholar · View at Scopus
  26. C. E. García, D. M. Prett, and M. Morari, “Model predictive control: theory and practice—a survey,” Automatica, vol. 25, no. 3, pp. 335–348, 1989. View at Publisher · View at Google Scholar · View at Scopus
  27. R. R. Bitmead, M. Gevers, and V. Wertz, Adaptive Optimal Control: The Thinking Man's GPC, Prentice Hall, Englewood Cliffs, NJ, USA, 1990.
  28. M. Morari and J. H. Lee, “Model predictive control: past, present and future,” Computers and Chemical Engineering, vol. 23, no. 4-5, pp. 667–682, 1999. View at Publisher · View at Google Scholar · View at Scopus
  29. H. Chen and F. Allgöwer, “A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability,” Automatica, vol. 34, no. 10, pp. 1205–1217, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  30. J. B. Rawlings and K. R. Muske, “The stability of constrained receding horizon control,” IEEE Transactions on Automatic Control, vol. 38, no. 10, pp. 1512–1516, 1993. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. J. Rawling, E. Meadows, and K. Muske, “Nonlinear model predictive control: a tutorial and survey,” in Proceeding of the International Symposium on Advanced Control of Chemical Processes (IFAC ADCHEM '94), pp. 185–197, 1994.
  32. J. Richalet, A. Rault, J. L. Testud, and J. Papon, “Model predictive heuristic control: applications to industrial processes,” Automatica, vol. 14, no. 5, pp. 413–428, 1978. View at Publisher · View at Google Scholar · View at Scopus
  33. J. Richalet, “Industrial applications of model based predictive control,” Automatica, vol. 29, no. 5, pp. 1251–1274, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  34. E. Polak and T. H. Yang, “Moving horizon control of linear systems with input saturation and plant uncertainty. I. Robustness,” International Journal of Control, vol. 58, no. 3, pp. 613–638, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  35. D. Q. Mayne and H. Michalska, “Receding horizon control of nonlinear systems,” IEEE Transactions on Automatic Control, vol. 35, no. 7, pp. 814–824, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  36. H. Michalska and D. Q. Mayne, “Robust receding horizon control of constrained nonlinear systems,” IEEE Transactions on Automatic Control, vol. 38, no. 11, pp. 1623–1633, 1993. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  37. P. Mhaskar, N. H. El-Farra, and P. D. Christofides, “Predictive control of switched nonlinear systems with scheduled mode transitions,” IEEE Transactions on Automatic Control, vol. 50, no. 11, pp. 1670–1680, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  38. M. A. Henson, “Nonlinear model predictive control: current status and future directions,” Computers & Chemical Engineering, vol. 23, no. 2, pp. 187–202, 1998. View at Publisher · View at Google Scholar · View at Scopus
  39. V. I. Utkin, “Variable structure systems with sliding modes,” IEEE Transactions on Automatic Control, vol. 22, no. 2, pp. 212–222, 1977. View at Google Scholar · View at MathSciNet
  40. V. I. Utkin, “Sliding mode control design principles and applications to electric drives,” IEEE Transactions on Industrial Electronics, vol. 40, no. 1, pp. 23–36, 1993. View at Publisher · View at Google Scholar · View at Scopus
  41. K. D. Young, V. I. Utkin, and Ü. Özgüner, “A control engineer's guide to sliding mode control,” IEEE Transactions on Control Systems Technology, vol. 7, no. 3, pp. 328–342, 1999. View at Publisher · View at Google Scholar · View at Scopus
  42. Y. Cao and W. Ren, “Distributed coordinated tracking with reduced interaction via a variable structure approach,” IEEE Transactions on Automatic Control, vol. 57, no. 1, pp. 33–48, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  43. A. Isidori, Nonlinear Control Systems: An Introduction, Springer, New York, NY, USA, 2nd edition, 1989.