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Practical Issues in Nonlinear Model Predictive Control: Real-Time Optimization and Systematic Tuning

  • Toshiyuki Ohtsuka
  • Kohei Ozaki
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 384)

Abstract

In this paper, we discuss two important practical issues in nonlinear model predictive control (NMPC): real-time optimization and systematic tuning. First, we present a couple of efficient algorithms based on the assumption that the sampling period is sufficiently short. Real-time algorithms are obtained in a unified manner as initial-value problems of ordinary differential equations (ODEs) for unknown quantities. A brief survey is given on applications of such ODE-type real-time algorithms in mechanical systems. Furthermore, as a first step toward systematic tuning of a performance index, we propose combining feedback linearization with NMPC. The proposed performance index can be tuned with only one parameter to adjust the output response and the magnitude of the control input. The effectiveness of the proposed method is demonstrated in numerical examples.

Keywords

real-time algorithm continuation method reference input 

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References

  1. 1.
    Cannon, M.: Efficient nonlinear model predictive control algorithms. Annual Reviews in Control 28(2), 229–237 (2004)CrossRefGoogle Scholar
  2. 2.
    DeHaan, D., Guay, M.: A real-time framework for model-predictive control of continuous-time nonlinear systems. IEEE Transactions on Automatic Control 52(11), 2047–2057 (2007)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Diehl, M., Ferreau, H.J., Haverbeke, N.: Efficient numerical methods for nonlinear MPC and moving horizon estimation. In: Keynote, International Workshop on Assessment and Future Directions of NMPC (2008)Google Scholar
  4. 4.
    Zavala, V.M., Biegler, L.T.: Nonlinear programming strategies for state estimation and model predictive control. In: International Workshop on Assessment and Future Directions of NMPC (2008) (invited Paper)Google Scholar
  5. 5.
    Ohtsuka, T., Fujii, H.A.: Real-time optimization algorithm for nonlinear receding-horizon control. Automatica 33(6), 1147–1154 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Ohtsuka, T.: Time-variant receding-horizon control of nonlinear systems. Journal of Guidance, Control, and Dynamics 21(1), 174–176 (1998)zbMATHCrossRefGoogle Scholar
  7. 7.
    Ohtsuka, T.: A continuation/GMRES method for fast computation of nonlinear receding horizon control. Automatica 40(4), 563–574 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Bryson Jr., A.E., Ho, Y.C.: Applied Optimal Control. Hemisphere (1975)Google Scholar
  9. 9.
    Richter, S.L., DeCarlo, R.A.: Continuation methods: Theory and applications. IEEE Transactions on Automatic Control AC-28(6), 660–665 (1983)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Kelley, C.T.: Iterative Methods for Linear and Nonlinear Equations. SIAM, Philadelphia (1995)zbMATHGoogle Scholar
  11. 11.
    Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, 2nd edn. Springer, Heidelberg (1996)zbMATHGoogle Scholar
  12. 12.
    Ohtsuka, T., Fujii, H.A.: Nonlinear receding-horizon state estimation by real-time optimization technique. Journal of Guidance, Control, and Dynamics 19(4), 863–870 (1996)zbMATHCrossRefGoogle Scholar
  13. 13.
    Ohtsuka, T.: Nonlinear receding-horizon state estimation with unknown disturbances. Transactions of the Society of Instrument and Control Engineers 35(10), 1253–1260 (1999)Google Scholar
  14. 14.
    Seguchi, H., Ohtsuka, T.: Nonlinear receding horizon control of an underactuated hovercraft. International Journal of Robust and Nonlinear Control 13(3–4), 381–398 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
  16. 16.
    Kohno, Y., Hamamatsu, M., Nakashima, K., Fujimoto, H., Saito, Y., Ikeda, H., Ohnishi, H.: Development of ship maneuvering control system. In: Proceedings of the 2nd SICE Annual Conference on Control Systems, pp. 441–444 (2002) (in Japanese)Google Scholar
  17. 17.
    Nagatsuka, M., Shishido, N., Sudo, I., Yokoyama, A., Masui, K., Tomita, H.: Flight demonstration for autonomous area avoidance algorithm, using receding horizon control. In: Proceedings of the Aircraft Symposium, pp. 201–205 (2006) (in Japanese)Google Scholar
  18. 18.
    Kawabe, T., Nishira, H., Ohtsuka, T.: An optimal path generator using a receding horizon control scheme for intelligent automobiles. In: Proceedings of the 2004 IEEE International Conference on Control Applications, Taipei, pp. 1597–1602 (2004)Google Scholar
  19. 19.
    Okazaki, M., Ohtsuka, T.: Switching control for guaranteeing the safety of a tethered satellite. Journal of Guidance, Control, and Dynamics 29(4), 822–830 (2006)CrossRefGoogle Scholar
  20. 20.
    Kawai, Y., Hirano, H., Azuma, T., Fujita, M.: Visual feedback control of an unmanned planar blimp system with self-scheduling parameter via receding horizon control. In: Proceedings of the 2004 IEEE International Conference on Control Applications, Taipei, pp. 1603–1608 (2004)Google Scholar
  21. 21.
    Lee, J., Yamakita, M.: Nonlinear model predictive control for constrained mechanical systems with state jump. In: Proceedings of the 2006 IEEE International Conference on Control Applications, Munich, pp. 585–590 (2006)Google Scholar
  22. 22.
    Saffarian, M., Fahimi, F.: Control of helicopters’ formation using non-iterative nonlinear model predictive approach. In: Proceedings of the 2008 American Control Conference, Seattle, pp. 3707–3712 (2008)Google Scholar
  23. 23.
    Soneda, Y., Ohtsuka, T.: Nonlinear moving horizon state estimation with continuation/generalized minimum residual method. Journal of Guidance, Control, and Dynamics 28(5), 878–884 (2005)CrossRefGoogle Scholar
  24. 24.
  25. 25.
    Shimizu, Y., Ohtsuka, T., Diehl, M.: A real-time algorithm for nonlinear receding horizon control using multiple shooting and continuation/Krylov method. In: International Journal of Robust and Nonlinear Control (to appear, 2009)Google Scholar
  26. 26.
    Marquez, H.J.: Nonlinear Control Systems. Wiley Interscience, Hoboken (2003)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Toshiyuki Ohtsuka
    • 1
  • Kohei Ozaki
    • 2
  1. 1.Department of Systems Innovation, Graduate School of Engineering ScienceOsaka University 
  2. 2.Department of Mechanical Engineering, Graduate School of EngineeringOsaka University 

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