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Utilizing higher-order neural networks in U-model based controllers for stable nonlinear plants

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Abstract

The use of intelligent control schemes in nonlinear model based control (NMBC) has gained widespread popularity. Neural networks, in particular, have been used extensively to model the dynamics of nonlinear plants. However, in most cases, these models do not lend themselves to easy maneuvering for controller design. Therefore, a common need is being felt to develop intelligent control strategies that lead to computationally simple control laws. To address this issue, we recently proposed a U-model based controller utilizing nonlinear adaptive filters. The present work extends that concept further to include higher-order neural networks (HONN) for better approximation. The main feature of the proposed structure is its ability to capture higher-order nonlinear properties of the input pattern space while allowing the synthesis of a simple control law. The effectiveness of the proposed scheme is demonstrated through application to various nonlinear models and a comparison with the Backstepping controller is presented.

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References

  1. M. M. Gupta, L. Jin, and N. Homma, Static And Dynamic Neural Networks, John Wiley and Sons, Inc., Hoboken, NJ, 2003.

    Book  Google Scholar 

  2. M. Norgaard, O. Ravn, N. K. Poulsen, and L. K. Hansen, Neural Networks for Modelling and Contol of Dynamic Systems, A Practitioner’s Handbook, Springer-Verlag, London, 2000.

    Google Scholar 

  3. B. K. Bose, “Neural network applications in power electronics and motor drivesan introduction and perspective,” IEEE Trans. on Industrial Electronics, vol. 54, pp. 14–33, 2007.

    Article  Google Scholar 

  4. X. L. Wei, J. Wang, and Z. X. Yang, “Robust smooth-trajectory control of nonlinear servo systems based on neural networks,” IEEE Trans. on Industrial Electronics, vol. 54, pp. 208–217, 2007.

    Article  Google Scholar 

  5. A. Y. Alanis, E. N. Sanchez, and A. G. Loukianov, “Discrete-time adaptive backstepping nonlinear control via high-order neural networks,” IEEE Trans. on Neural Networks, vol. 18, pp. 1185–1195, 2007.

    Article  Google Scholar 

  6. D. E. Rumelhart and J. L. McClelland, Parallel Distributed Processing: Explorations in the Microstructure of Cognition: Foundations, vol. 1, MIT Press, Cambridge, MA, 1986.

    Google Scholar 

  7. C. L. Giles and T. Maxwell, “Learning invariance and generalization in higher-order networks,” Applied Optics, vol. 26, pp. 4972–4978, 1987.

    Article  Google Scholar 

  8. X. Xu, E. Oja, and C. Y. Suen, “Modified hebbian learning for curve and surface fitting,” Neural Networks, vol. 5, no. 3, pp. 441–457, 1992.

    Article  Google Scholar 

  9. J. G. Taylor and S. Commbes, “Learning higherorder correlations,” Neural Networks, vol. 6, no. 3, pp. 423–428, 1993.

    Article  Google Scholar 

  10. N. Homma and M. M. Gupta, “A general secondorder neural unit,” Bull. Coll. Med. Sci., Tohoku Univ., vol. 11, no. 1, pp. 1–6, 2002.

    Google Scholar 

  11. Z. Lin, D. S. Reay, B. W. Williams, and X. He, “Online modeling for switched reluctance motors using B-spline neural networks,” IEEE Trans. on Industrial Electronics, vol. 54, pp. 3317–3322, 2007.

    Article  Google Scholar 

  12. C. A. Hudson, N. S. Lobo, and R. Krishnan, “Sensorless control of single switch-based switched reluctance motor drive using neural network,” IEEE Trans. on Industrial Electronics, vol. 55, pp. 321–329, 2008.

    Article  Google Scholar 

  13. I. J. Leontarities and S. A. Billings, “Input-output parametric models for nonlinear systems. part I: Deterministic nonlinear systems; part II: Stochastic nonlinear systems,” Int. J. of Control, vol. 41, no. 2, pp. 303–344, 1985.

    Article  Google Scholar 

  14. L. Piroddi and W. Spinelli, “An identification algorithm for polynomial NARX models based on simulation error minimization,” Int. J. of Control, vol. 76, no. 17, pp. 1767–1781, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  15. Q. M. Zhu and L. Z. Guo, “A pole placement controller for nonlinear dynamic plants,” J. Systems and Control Engineering, vol. 216, no. 1, pp. 467–476, 2002.

    Google Scholar 

  16. R. K. Pearson, “Selecting nonlinear model struc tures for computer control,” Journal of Process Control, vol. 13, pp. 1–26, 2003.

    Article  Google Scholar 

  17. K. R. Sales and S. A. Billings, “Self-tuning control of nonlinear ARMAX models,” Int. J. of Control, vol. 51, no. 4, pp. 753–769, January 1990.

    Article  MATH  Google Scholar 

  18. M. Shafiq and M. Haseebuddin, “Internal model control for nonlinear dynamic plants using UModel,” Proc. of the 12th Mediterranean Conference on Control and Automation, Turkey, June 2004.

  19. N. R. Butt and M. Shafiq, “Adaptive tracking of non-linear dynamic plants, using the u-model,” IMechE Journal of Systems and Control Engineering, Proc. IMechE, Part I., vol. 220, no. 6, pp. 473–487, 2006.

    Article  Google Scholar 

  20. A. Datta and J. Ochoa, “Adaptive internal model control: Design and stability analysis,” Automatica, vol. 32, no. 2, pp. 261–266, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  21. C. E. Garcia and M. Morari, “Internal model control. 1.a unifying review and some new results,” Ind. Eng. Chem. Process Des. Dev, vol. 21, pp. 308–323, 1982.

    Article  Google Scholar 

  22. S. C. Patwardhan and K. P. Madhavan, “Nonlinear internal model control using quadratic perturbation models,” Computers and Chemical Engineering, vol. 22, pp. 587–601, 1998.

    Article  Google Scholar 

  23. Q. G. Wang, B. Qiang, and Y. Zhang, “Partial internal model control.” IEEE Trans. on Industrial Electronics, vol. 48, no. 5, pp. 976–982, 2001.

    Article  Google Scholar 

  24. W. F. Xie and A. B. Rad, “Fuzzy adaptive internal model control.” IEEE Trans. on Industrial Electronics, vol. 47, no. 1, pp. 193–202, 2000.

    Article  Google Scholar 

  25. M. Shafiq and S. H. Riyaz, “Internal model control structure using adaptive inverse control strategy,” Proc. of the 4th Int. Conf. on Control and Automation, p. 59, 2003.

  26. C. G. Economou, M. Morari, and B. O. Palsson, “Internal model control. 5. extension to nonlinear systems,” Ind. Eng. Chem. Process Des. Dev., vol. 25, no. 1, pp. 403–411, 1986.

    Article  Google Scholar 

  27. M. Morari and E. Zafiriou, Robust Process Control. Prentice Hall, NJ, 1989.

  28. N. R. Butt, M. Shafiq, and T. Khan, “An adaptive root-solving controller for tracking of nonlinear dynamic plants,” Proc. of International Conference on Industrial Electronics and Control Applications, Ecuador, vol. 1, pp. 144–149, November 2005.

    Google Scholar 

  29. Q. M. Zhu, K. Warwick, and J. L. Douce, “Adaptive general predictive controller for nonlinear systems,” IEE Proc. Control Theory Applic., vol. 138, no. 1, pp. 33–40, 1991.

    Article  MATH  Google Scholar 

  30. A. Rubaai and R. Kotaru, “Online identification and control of a dc motor using learning adaptation of neural networks,” IEEE Trans. on Industry Applications, vol. 36, no. 3, pp. 935–942, May/June 2000.

    Article  Google Scholar 

  31. M. Krstic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design, John Wiley & Sons, New York, 1995.

    Google Scholar 

Download references

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Correspondence to Muhammed Shafiq.

Additional information

Recommended by Editor Hyun Seok Yang. We acknowledge support of Sulatan Qaboos University, Muscat, Oman for this research work.

Muhammad Shafiq received his BE degree in Electronic Engineering from NED University, Karachi, Pakistan in 1989. He completed his PhD studies in information and computer engineering at Chiba University, Chiba, Japan in 1997. He worked as technical manager at Thalus, Sauadai Arabai. He served King Fahd University of Petroleum and Minerals as faculty member. He worked as a professor under higher education commission at GIKI and IIUI, Pakistan. Presently, he is working as faculty member in ECE, SQU, Oman.He worked with Pakistan Engineering Council as a member of accreditation teams formed for accreditating several electrical, electronic and mechatronics engineering programs in Pakistan. He was member of national curriculum development committee for communication systems under HEC, Pakistan. He has supervised serveral MS and PhD thesis. He is among the authors of more than eight journal and conference papers. His research interests include applied nonlinear control, adaptive control, and soft computing techniques applied to control systems.

Naveed R. Butt received his B.S. degree in Lasers and Optoelectronics from the GIK Institute, Pakistan, in 2002. He received his Master’s degree in Systems Engineering (Automation and Control) in 2006 from KFUPM, Saudi Arabia. He is currently working towards a Ph.D. degree with Lund University, Sweden. He was previously a Research Assistant with KFUPM in 2004. His research interests include: statistical signal processing, system identification, and intelligent systems.

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Shafiq, M., Butt, N.R. Utilizing higher-order neural networks in U-model based controllers for stable nonlinear plants. Int. J. Control Autom. Syst. 9, 489–496 (2011). https://doi.org/10.1007/s12555-011-0308-y

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