Control of Constrained Linear-Time Varying Systems via Kautz Parametrization of Model Predictive Control Scheme

Massoud Hemmasian Ettefagh, José De Doná, Mahyar Naraghi, Farzad Towhidkhah


Kautz parametrization of the Model Predictive Control (MPC) method has shown its ability to reduce the number of decision variables in Linear Time Invariant (LTI) systems. This paper devotes to extend Kautz network to be used in MPC Algorithm for linear time-varying systems. It is shown that Kautz network enables us to maintain a satisfactory performance while the number of decision variables are reduced considerably. Stability of the algorithm is studied under the framework of the optimal solution. The proposed method is validated by an illustrative example. In this regard, the performance of unconstrained systems as well as constrained ones is compared.


Model Predictive Control; Kautz Network; Time-Varying Systems.


A. Bemporad, M. Morari, V. Dua, and E. N. Pistikopoulos, “The explicit linear quadratic regulator for constrained systems,” Automatica, vol. 38, no. 1, pp. 3 – 20, 2002.

M. M. Seron, J. A. De Doná, and G. C. Goodwin, “Global analytical model predictive control with input constraints,” in Proceedings of the 39th IEEE Conference on Decision and Control, vol. 1, 2000, pp. 154–159 vol.1.

L. Wang, “Continuous time model predictive control design using orthonormal functions,” International Journal of Control, vol. 74, no. 16, pp. 1588–1600, 2001.

L. Wang, “Discrete model predictive controller design using Laguerre functions,” Journal of Process Control, vol. 14, no. 2, pp. 131 – 142, 2004.

Wang, Liuping. Model predictive control system design and implementation using MATLAB®. Springer Science & Business Media, 2009.

J. Rossiter, L. Wang, and G. Valencia-Palomo, “Efficient algorithms for trading off feasibility and performance in predictive control,” International Journal of Control, vol. 83, no. 4, pp. 789–797, 2010.

G. Valencia-Palomo and J. A. Rossiter, “Novel programmable logic controller implementation of a predictive controller based on Laguerre functions and multi-parametric solutions,” IET Control Theory Applications, vol. 6, no. 8, pp. 1003–1014, May 2012.

B. Khan and J. A. Rossiter, “Robust MPC algorithms using alternative parameterizations,” in International Conference on Control (UKACC). IEEE, 2012, pp. 882–887.

W. Kwon and A. Pearson, “A modified quadratic cost problem and feedback stabilization of a linear system,” IEEE Transactions on Automatic Control, vol. 22, no. 5, pp. 838–842, Oct 1977.

“On feedback stabilization of time-varying discrete linear systems,” IEEE Transactions on Automatic Control, vol. 23, no. 3, pp. 479–481, Jun 1978

W. H. Kwon, A. M. Bruckstein, and T. Kailath, “Stabilizing state-feedback design via the moving horizon method,” International Journal of Control, vol. 37, no. 3, pp. 631–643, 1983.

S. S. Keerthi and E. G. Gilbert, “Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: Stability and moving-horizon approximations,” Journal of Optimization Theory and Applications, vol. 57, no. 2, pp. 265–293, 1988.

D. Q. Mayne and H. Michalska, “Receding horizon control of nonlinear systems,” IEEE Transactions on Automatic Control, vol. 35, no. 7, pp. 814–824, Jul 1990.

G. D. Nicolao, L. Magni, and R. Scattolini, “Stabilizing receding horizon control of nonlinear time-varying systems,” IEEE Transactions on Automatic Control, vol. 43, no. 7, pp. 1030–1036, Jul 1998.

P. Falcone, F. Borrelli, J. Asgari, H. E. Tseng and D. Hrovat, "Predictive Active Steering Control for Autonomous Vehicle Systems," in IEEE Transactions on Control Systems Technology, vol. 15, no. 3, pp. 566-580, May 2007.

E. W. Kamen, The Control Handbook: Control System Advanced Methods, 2nd ed. CRC Press, 2010, Fundamentals of Linear Time-Varying Systems.

Wahlberg, B, “System identification using Kautz models,” IEEE Transactions on Automatic Control, 39(6), 1276-1282, Jun 1994.

Oliveira, G. H., da Rosa, A., Campello, R. J., Machado, J. B., & Amaral, W. C. “An introduction to models based on Laguerre, Kautz and other related orthonormal functions– part i: linear and uncertain models,” International Journal of Modelling, Identification and Control, 14(1-2), 121–132, 2011.

Ninness, B., & Gustafsson, F, “A unifying construction of orthonormal bases for system identification,” IEEE Transactions on Automatic Control, 42(4), 515-521, Apr 1997.

Full Text: PDF

DOI: 10.28991/esj-2017-01117


  • There are currently no refbacks.

Copyright (c) 2017 Massoud Hemmasian Ettefagh, José De Doná, Mahyar Naraghi, Farzad Towhidkhah