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.
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References
Maciejowski, J.M.: Predictive Control with Constraints. Prentice-Hall, Englewood Cliffs (2002)
Bemporad, A., Morari, M., Dua, V., Pistikopoulos, E.N.: The explicit linear quadratic regulator for constrained systems. Automatica 38(1), 3–20 (2002)
Tøndel, P., Johansen, T.A., Bemporad, A.: An algorithm for mpqp and explicit mpc solutions. Automatica 39(3), 489–497 (2003)
Mayne, D., Rawlings, J., Rao, C., Scokaert, P.: Constrained model predictive control: Stability and optimality. Automatica 36, 789–814 (2000)
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)
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)
Blanchini, F.: Set invariance in control. Automatica 35(11), 1747–1767 (1999)
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)
Benlaoukli, H., Olaru, S.: Computation and bounding of robust invariant sets for uncertain systems. In: Proceedings of the IFAC World Congress, Seoul, Korea (2008)
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)
de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry, Algorithms and Applications. Springer, Heidelberg (2000)
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)
Kvasnica, M., Grieder, P., Baotić, M.: Multi-parametric toolbox (mpt) (2004)
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Benlaoukli, H., Olaru, S. (2009). Model Predictive Control – Numerical Methods for the Invariant Sets Approximation. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_19
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DOI: https://doi.org/10.1007/978-3-642-00464-3_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00463-6
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