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The Potential of Interpolation for Simplifying Predictive Control and Application to LPV Systems

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Book cover Assessment and Future Directions of Nonlinear Model Predictive Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 358))

Abstract

This paper first introduces several interpolation schemes, which have been derived for the linear time invariant case, but with an underlying objective of trading off performance for online computational simplicity. It is then shown how these can be extended to linear parameter varying systems, with a relatively small increase in the online computational requirements. Some illustrations are followed with a brief discussion on areas of potential development.

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References

  1. M. Bacic, M. Cannon, Y. I. Lee, and B. Kouvaritakis. General interpola-tion in MPC and its advantages. IEEE Transactions on Automatic Control, 48(6):1092–1096, 2003.

    Article  MathSciNet  Google Scholar 

  2. F. Blanchini. Set invariance in control. Automatica, 35:1747–1767, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  3. F. Blanchini, S. Miani, and C. Savorgnan. Polyhedral lyapunov functions com-putation for robust and gain scheduled design. In Proceedings of the Symposium on nonlinear Control Systems (NOLGOS), Stuttgart, Germany, 2004.

    Google Scholar 

  4. F. Borrelli. Constrained Optimal Control for Linear and Hybrid Systems. Springer-Verlag, Berlin, 2003.

    Google Scholar 

  5. A. Casavola, F. Domenico, and F. Giuseppe. Predictive control of constrained nonlinear systems via lpv linear embeddings. International Journal of Robust and Nonlinear Control, 13:281–294, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  6. L. Chisci, P. Falugi, and G. Zappa. Gain-scheduling MPC of nonlinear systems. International Journal of Robust and Nonlinear Control, 13:295–308, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  7. E.G. Gilbert and K. T. Tan. Linear systems with state and control constraints: The theory and application of maximal output admissible sets. IEEE Transactions on Automatic Control, 36(9):1008–1020, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  8. L. Imsland and J.A. Rossiter. Time varying terminal control. In Proceedings of the IFAC World Congress 2005, Prague, Czech Republic, 2005.

    Google Scholar 

  9. M. V. Kothare, V. Balakrishnan, and M. Morari. Robust constrained model pre-dictive control using linear matrix inequalities. Automatica, 32:1361–1379, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  10. B. Kouvaritakis, J.A. Rossiter, and J. Schuurmans. Efficient robust predictive control. IEEE Transactions on Automatic Control, 45(8):1545–1549, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  11. B. Pluymers, J. A. Rossiter, J. A. K. Suykens, and B. De Moor. The efficient computation of polyhedral invariant sets for linear systems with polytopic uncertainty description. In Proceedings of the American Control Conference (ACC), Portland, USA, pages 804–809, 2005.

    Google Scholar 

  12. B. Pluymers, J. A. Rossiter, J. A. K. Suykens, and B. De Moor. Interpolation based MPC for LPV systems using polyhedral invariant sets. In Proceedings of the American Control Conference (ACC), Portland, USA, pages 810–815, 2005.

    Google Scholar 

  13. B. Pluymers, J. A. Rossiter, J. A. K. Suykens, and B. De Moor. A simple algorithm for robust MPC. In Proceedings of the IFAC World Congress 2005, Prague, Czech Republic, 2005.

    Google Scholar 

  14. B. Pluymers, J. A. K. Suykens, and B. De Moor. Construction of reduced complex-ity polyhedral invariant sets for LPV systems using linear programming. Submitted for publication, 2005, (http://www.esat.kuleuven.be/~sistawww/cgi-bin/pub.pl).

  15. J. A. Rossiter, Y. Ding, B. Pluymers, J. A. K. Suykens, and B. De Moor. Interpolation based MPC with exact constraint handling: the uncertain case. In Proceedings of the joint European Control Conference & IEEE Conference on Decision and Control, Seville, Spain, 2005.

    Google Scholar 

  16. J. A. Rossiter and P. Grieder. Using interpolation to improve efficiency of multiparametric predictive control. Automatica, 41(4), 2005.

    Google Scholar 

  17. J. A. Rossiter, B. Kouvaritakis, and M. Bacic. Interpolation based computationally efficient predictive control. International Journal of Control, 77(3):290–301, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  18. J. A. Rossiter, M. J. Rice, and B. Kouvaritakis. A numerically robust state-space approach to stable predictive control strategies. Automatica, 34:65–73, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  19. P. O. M. Scokaert and J. B. Rawlings. Constrained linear quadratic regulation. IEEE Transactions on Automatic Control, 43(8):1163–1168, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  20. Z. Wan and M. V. Kothare. An efficient off-line formulation of robust model pre-dictive control using linear matrix inequalities. Automatica, 39(5):837–846, 2003.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, S1 3JD, UK

    John Anthony Rossiter

  2. Department of Electrical Engineering, ESAT-SCD-SISTA, Kasteelpark Arenberg, 10, Katholieke Universiteit Leuven, B-3001, Heverlee, Leuven, Belgium

    Bert Pluymers & Bart De Moor

Authors
  1. John Anthony Rossiter
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  2. Bert Pluymers
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  3. Bart De Moor
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Editor information

Editors and Affiliations

  1. Institute for Systems Theory and Automatic Control, University of Stuttgart, Pfaffenwaldring 9, 70550, Stuttgart, Germany

    Rolf Findeisen  & Frank Allgöwer  & 

  2. Chemical Engineering Department, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Lorenz T. Biegler

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© 2007 Springer-Verlag Berlin Heidelberg

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Rossiter, J.A., Pluymers, B., De Moor, B. (2007). The Potential of Interpolation for Simplifying Predictive Control and Application to LPV Systems. In: Findeisen, R., Allgöwer, F., Biegler, L.T. (eds) Assessment and Future Directions of Nonlinear Model Predictive Control. Lecture Notes in Control and Information Sciences, vol 358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72699-9_5

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  • DOI: https://doi.org/10.1007/978-3-540-72699-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72698-2

  • Online ISBN: 978-3-540-72699-9

  • eBook Packages: EngineeringEngineering (R0)

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