Geodesic
Design of predictive LQ controller
Kybernetika, Tome 35 (1999) no. 4, pp. 459-472 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

A single variable controller is developed in the predictive control framework based upon minimisation of the LQ criterion with infinite output and control horizons. The infinite version of the predictive cost function results in better stability properties of the controller and still enables to incorporate constraints into the control design. The constrained controller consists of two parts: time-invariant nominal LQ controller and time-variant part given by Youla–Kučera parametrisation of all stabilising controllers.
A single variable controller is developed in the predictive control framework based upon minimisation of the LQ criterion with infinite output and control horizons. The infinite version of the predictive cost function results in better stability properties of the controller and still enables to incorporate constraints into the control design. The constrained controller consists of two parts: time-invariant nominal LQ controller and time-variant part given by Youla–Kučera parametrisation of all stabilising controllers.
Classification : 49N10, 93B40, 93B51, 93C55
Keywords: predictive control; LQ controller; discrete-time control system; control design; Youla-Kucera parametrization 
@article{KYB_1999_35_4_a4,
     author = {Fikar, Miroslav and Engell, Sebastian and Dost\'al, Petr},
     title = {Design of predictive {LQ} controller},
     journal = {Kybernetika},
     pages = {459--472},
     year = {1999},
     volume = {35},
     number = {4},
     mrnumber = {1723589},
     zbl = {1274.93089},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1999_35_4_a4/}
}
TY  - JOUR
AU  - Fikar, Miroslav
AU  - Engell, Sebastian
AU  - Dostál, Petr
TI  - Design of predictive LQ controller
JO  - Kybernetika
PY  - 1999
SP  - 459
EP  - 472
VL  - 35
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/KYB_1999_35_4_a4/
LA  - en
ID  - KYB_1999_35_4_a4
ER  - 
%0 Journal Article
%A Fikar, Miroslav
%A Engell, Sebastian
%A Dostál, Petr
%T Design of predictive LQ controller
%J Kybernetika
%D 1999
%P 459-472
%V 35
%N 4
%U http://geodesic.mathdoc.fr/item/KYB_1999_35_4_a4/
%G en
%F KYB_1999_35_4_a4
Fikar, Miroslav; Engell, Sebastian; Dostál, Petr. Design of predictive LQ controller. Kybernetika, Tome 35 (1999) no. 4, pp. 459-472. http://geodesic.mathdoc.fr/item/KYB_1999_35_4_a4/

[1] Clarke D. W., Mohtadi, C., Tuffs P. S.: Generalized predictive control. Part I. The basic algorithm. Automatica 23 (1987), 2, 137–148 | DOI | Zbl

[2] Clarke D. W., Mohtadi, C., Tuffs P. S.: Generalized predictive control. Part II: Extensions and interpretations. Automatica 23 (1987), 2, 149–160 | DOI | Zbl

[3] Clarke D. W., Scattolini R.: Constrained receding–horizon predictive control. IEE Proc. D 138 (1991), 4, 347–354 | DOI | Zbl

[4] Fikar M., Engell S.: Receding horizon predictive control based upon Youla – Kučera parametrization. European J. Control 3 (1997), 4, 304–316 | DOI

[5] Horn R. A., Johnson C. R.: Matrix Analysis. Cambridge University Press 1985 | MR | Zbl

[6] Hunt K. J., Šebek M.: Implied polynomial matrix equations in multivariable stochastic optimal control. Automatica 27 (1991), 2, 395–398 | DOI | MR | Zbl

[7] Kučera V.: Discrete Linear Control: The Polynomial Equation Approach. Wiley, Chichester 1979 | MR | Zbl

[8] Kučera V.: Analysis and Design of Discrete Linear Control Systems. Prentice Hall, Englewood Cliffs, N. J. 1991 | MR | Zbl

[9] McIntosh A. R., Shah S. L., Fisher D. G.: Analysis and tuning of adaptive generalized predictive control. Canad. J. Chem. Engrg. 69 (1991), 97–110 | DOI

[10] Middleton R., Goodwin G. C.: Digital Control and Estimation. A Unified Approach. Prentice Hall, Englewood Cliffs, N. J. 1990 | Zbl

[11] Mosca E., Zhang J.: Stable redesign of predictive control. Automatica 28 (1992), 1229–1233 | DOI | MR | Zbl

[12] Rawlings J. B., Muske K. R.: The stability of constrained receding horizon control. IEEE Trans. Automat. Control 38 (1993), 10, 1512–1516 | DOI | MR | Zbl

[13] Rossiter J. A., Gossner J. R., Kouvaritakis B.: Infinite horizon stable predictive control. IEEE Trans. Automat. Control 41 (1996), 10, 1522–1527 | DOI | MR | Zbl

[14] Rossiter J. A., Kouvaritakis B.: Constrained stable generalised predictive control. IEE Proc. D 140 (1993), 4, 243–254 | Zbl

[15] Rossiter J. A., Kouvaritakis, B., Gossner J. R.: Feasibility and stability results for constrained stable predictive control. Automatica 31 (1995), 3, 863–877 | DOI | MR

[16] Scokaert P. O. M., Clarke D. W.: Stabilizing properties of constrained predictive control. IEE Proc. – Control Theory Appl. 141 (1994), 5, 295–304

[17] Scokaert P. O. M., Rawlings J. B.: Infinite horizon linear quadratic control with constraints. In: 13th Triennal World Congress IFAC, San Francisco 1996, Volume M, pp. 109–114

[18] Šebek M.: Direct polynomial approach to discrete–time stochastic tracking. Problems Control Inform. Theory 12 (1983), 293–302 | MR | Zbl

[19] Zafiriou E., Chiou H. W.: On the dynamic resiliency of constrained processes. Comput. Chem. Engrg. 20 (1996), 4, 347–355 | DOI

[20] Zheng A., Morari M.: Stability of model predictive control with mixed constraints. IEEE Trans. Automat. Control 40 (1995), 10, 1818–1823 | DOI | MR | Zbl