An infinite horizon predictive control algorithm based on multivariable input-output models

Maciej Ławryńczuk; Piotr Tatjewski

International Journal of Applied Mathematics and Computer Science (2004)

  • Volume: 14, Issue: 2, page 167-180
  • ISSN: 1641-876X

Abstract

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In this paper an infinite horizon predictive control algorithm, for which closed loop stability is guaranteed, is developed in the framework of multivariable linear input-output models. The original infinite dimensional optimisation problem is transformed into a finite dimensional one with a penalty term. In the unconstrained case the stabilising control law, using a numerically reliable SVD decomposition, is derived as an analytical formula, calculated off-line. Considering constraints needs solving on-line a quadratic programming problem. Additionally, it is shown how free and forced responses can be calculated without the necessity of solving a matrix Diophantine equation.

How to cite

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Ławryńczuk, Maciej, and Tatjewski, Piotr. "An infinite horizon predictive control algorithm based on multivariable input-output models." International Journal of Applied Mathematics and Computer Science 14.2 (2004): 167-180. <http://eudml.org/doc/207688>.

@article{Ławryńczuk2004,
abstract = {In this paper an infinite horizon predictive control algorithm, for which closed loop stability is guaranteed, is developed in the framework of multivariable linear input-output models. The original infinite dimensional optimisation problem is transformed into a finite dimensional one with a penalty term. In the unconstrained case the stabilising control law, using a numerically reliable SVD decomposition, is derived as an analytical formula, calculated off-line. Considering constraints needs solving on-line a quadratic programming problem. Additionally, it is shown how free and forced responses can be calculated without the necessity of solving a matrix Diophantine equation.},
author = {Ławryńczuk, Maciej, Tatjewski, Piotr},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {infinite horizon; model predictive control; quadratic programming; singular-value decomposition; stability; predictive control; input-output models; matrix Diophantine equations; constrained control; response calculation},
language = {eng},
number = {2},
pages = {167-180},
title = {An infinite horizon predictive control algorithm based on multivariable input-output models},
url = {http://eudml.org/doc/207688},
volume = {14},
year = {2004},
}

TY - JOUR
AU - Ławryńczuk, Maciej
AU - Tatjewski, Piotr
TI - An infinite horizon predictive control algorithm based on multivariable input-output models
JO - International Journal of Applied Mathematics and Computer Science
PY - 2004
VL - 14
IS - 2
SP - 167
EP - 180
AB - In this paper an infinite horizon predictive control algorithm, for which closed loop stability is guaranteed, is developed in the framework of multivariable linear input-output models. The original infinite dimensional optimisation problem is transformed into a finite dimensional one with a penalty term. In the unconstrained case the stabilising control law, using a numerically reliable SVD decomposition, is derived as an analytical formula, calculated off-line. Considering constraints needs solving on-line a quadratic programming problem. Additionally, it is shown how free and forced responses can be calculated without the necessity of solving a matrix Diophantine equation.
LA - eng
KW - infinite horizon; model predictive control; quadratic programming; singular-value decomposition; stability; predictive control; input-output models; matrix Diophantine equations; constrained control; response calculation
UR - http://eudml.org/doc/207688
ER -

References

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  1. Bitmead R.R., Gevers M. and Wertz V. (1990): Adaptive Optimal Control-The Thinking Man's GPC. - Englewood Cliffs: Prentice Hall. Zbl0751.93052
  2. Camacho E.F. and Bordons C. (1999): Model Predictive Control. - London: Springer. 
  3. Chisci L. and Mosca E. (1994): Stabilizing I-O receding horizon control of CARMA plants. - IEEE Trans. Automat. Contr., Vol. 39, No. 3, pp. 614-618. Zbl0814.93058
  4. Clarke D.W. and Scattolini R. (1991): Constrained receding-horizon predictive control. - Proc. IEE, Part D, Vol. 138, No. 4, pp. 347-354. Zbl0743.93063
  5. Clarke D.W. and Mohtadi C. (1989): Properties ofgeneralized predictive control. - Automatica, Vol. 25, No. 6, pp. 859-875. Zbl0699.93028
  6. Clarke D.W., Mohtadi C. and Tuffs P.S. (1987a): Generalized predictive control - I. The basic algorithm. -Automatica, Vol. 23, No. 2, pp. 137-148. Zbl0621.93032
  7. Clarke D.W., Mohtadi C. and Tuffs P.S. (1987b): Generalized predictive control - II. Extensions and interpretations.- Automatica, Vol. 23, No. 2, pp. 149-160. Zbl0621.93033
  8. Cutler C.R. and Ramaker B.L. (1980): Dynamic matrix control - A computer control algorithm. - Proc. Joint. Automat. Contr. Conf., San Francisco. 
  9. Golub G.H. and Van Loan C.F. (1989): Matrix Computations. - Baltimore: The Johns Hopkins University Press. 
  10. Gutman P. and Hagander P. (1985): A new design of constrained controllers for linear systems. - IEEE Trans.Automat. Contr., Vol. 30, No. 1, pp. 22-33. Zbl0553.93052
  11. Henson M.A. (1998): Nonlinear model predictive control: current status and future directions. - Comput.Chem. Eng., Vol. 23, No. 2, pp. 187-202. 
  12. Kailath T. (1980): Linear Systems. - Englewood Cliffs: Prentice Hall. Zbl0454.93001
  13. Kwon W.H. and Byun D.G. (1989): Receding horizon tracking control as a predictive control and its stability properties. -Int. J. Contr., Vol. 50, No. 5, pp. 1807-1824. Zbl0688.93020
  14. Maciejowski J.M. (2002): Predictive Control with Constraints. - Englewood Cliffs: Prentice Hall. Zbl0978.93002
  15. Mayne D.Q. (2001): Control of constrained dynamic systems. - Europ. J. Contr., Vol. 7, Nos. 2-3, pp. 87-99. Zbl1293.93299
  16. Mayne D.Q., Rawlings J.B., Rao C.V. and Scokaert P.O.M. (2000): Constrained model predictive control: Stability and optimality. - Automatica, Vol. 36, No. 6, pp. 789-814. Zbl0949.93003
  17. Morari M. and Lee J.H. (1999): Model predictive control: past, present and future. - Comput. Chem. Eng., Vol. 23, No. 45, pp. 667-682. 
  18. Muske K.R. and Rawlings J.B. (1993): Model predictive control with linear models. - AIChE J., Vol. 39, No. 2, pp. 262-287. 
  19. Ordys W.A., Hangstrup M.E. and Grimble M.J. (2000): Dynamic algorithm for linear quadratic Gaussian predictive control.- Int. J. Appl. Math. Comput. Sci., Vol. 10, No. 2, pp. 227-244. Zbl0981.93026
  20. Rawlings J.B. and Muske K.R. (1993): The stability of constrained receding horizon control. - IEEE Trans.Automat. Contr., Vol. 38, No. 10, pp. 1512-1516. Zbl0790.93019
  21. Rouhani R. and Mehra R.K. (1982): Model algoritmic control (MAC); Basic theoretical properties. - Automatica, Vol. 18, No. 4, pp. 401-414. Zbl0483.93045
  22. Scattolini R. and Bittanti S. (1990): On the choice of the horizon in long-range predictive control - some simple criteria. - Automatica, Vol. 26, No. 5, pp. 915-917. Zbl0701.93033
  23. Scokaert P.O.M. (1997): Infinite horizon generalized predictive control. - Int. J. Contr., Vol. 66, No. 1, pp. 161-175. Zbl0873.93033
  24. Scokaert P.O.M. and Clarke D. W. (1994): Stabilising properties of constrained predictive control.- Proc. IEE, Part D, Vol. 141, No. 5, pp. 295-304. Zbl0925.93555
  25. Sznaier M. and Damborg M.J. (1990): Heuristically enhanced feedback control of constrained discrete-time linear systems. - Automatica, Vol. 26, No. 3, pp. 521-532. Zbl0713.93023
  26. Tatjewski P. (2002): Advanced Control of Industrial Processes, Structures and Algorithms. - Warszawa: Akademicka Oficyna Wydawnicza Exit (in Polish). 
  27. Zafiriou E. (1990): Robust model predictive control of processes with hard constraints. - Comput. Chem. Eng., Vol. 14, Nos. 45, pp. 359-371. 
  28. Zafiriou E. and Marchal A.L. (1991): Stability of SISO quadratic dynamic matrix control with hard output constraints. - AIChE J., Vol. 37, No. 10, pp. 1550-1560. 

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