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Model Predictive Control – Numerical Methods for the Invariant Sets Approximation

  • H. Benlaoukli
  • S. Olaru
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5434)

Abstract

This paper deals with the computational issues encountered in the construction of invariant sets for LTI (Linear Time Invariant) systems subject to linear constraints. Three algorithms to compute or approximate the invariant set are presented. Two of theme are based on expansive and contractive strategy, while the third one uses the transition graph over the partition of the closed loop piecewise affine system.

Keywords

Model Predictive Control Linear Time Invariant Predictive Control Generality Positive Invariance Expansive Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Maciejowski, J.M.: Predictive Control with Constraints. Prentice-Hall, Englewood Cliffs (2002)zbMATHGoogle Scholar
  2. 2.
    Bemporad, A., Morari, M., Dua, V., Pistikopoulos, E.N.: The explicit linear quadratic regulator for constrained systems. Automatica 38(1), 3–20 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Tøndel, P., Johansen, T.A., Bemporad, A.: An algorithm for mpqp and explicit mpc solutions. Automatica 39(3), 489–497 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Mayne, D., Rawlings, J., Rao, C., Scokaert, P.: Constrained model predictive control: Stability and optimality. Automatica 36, 789–814 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Limon, D., Alvarado, I., Alamo, T., Camacho, E.F.: Mpc for tracking of piece-wise constant references for constrained linear systems. In: Proceeding 16th IFAC World Congress, Prague (2005)Google Scholar
  6. 6.
    Olaru, S., Dumur, D.: Compact explicit mpc with guarantee of feasibility for tracking. In: Proceedings of the IEEE Conference on Decision and Control and European Control Conference, pp. 969–974 (2005)Google Scholar
  7. 7.
    Blanchini, F.: Set invariance in control. Automatica 35(11), 1747–1767 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Rakovic, S.V., Grieder, P., Kvasnica, M., Mayne, D.Q., Morari, M.: Computation of invariant sets for piecewise affine discrete time systems subject to bounded disturbances. In: Proceeding 43th IEEE Conference on Decision and Control (December 2004)Google Scholar
  9. 9.
    Benlaoukli, H., Olaru, S.: Computation and bounding of robust invariant sets for uncertain systems. In: Proceedings of the IFAC World Congress, Seoul, Korea (2008)Google Scholar
  10. 10.
    Gilbert, E., Tan, K.: Linear systems with state and control constraints, the theory and application of maximal output admissible sets. IEEE Transaction on Automatic Control 36, 1008–1020 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry, Algorithms and Applications. Springer, Heidelberg (2000)zbMATHGoogle Scholar
  12. 12.
    Rakovic, S.V., Kerrigan, E.C., Kouramas, K.I., Mayne, D.Q.: Invariant approximations of the minimal robust positively invariant set. IEEE Transaction on Automatic Control 50, 406–410 (2005)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Kvasnica, M., Grieder, P., Baotić, M.: Multi-parametric toolbox (mpt) (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • H. Benlaoukli
    • 1
  • S. Olaru
    • 1
  1. 1.Automatic Control DepartmentSUPELECGif sur YvetteFrance

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