A decomposition algorithm for feedback min-max model predictive control

IEEE Transactions on Automatic Control

Volumn 51, Issue 10, 2006, Pages 1688-1692

  Muñoz De La Peña, David ^a   Alamo, T ^a   Bemporad, A ^b   Camacho, E F ^a  

^a UNIVERSITY OF SEVILLE   (Spain)

^b UNIVERSITY OF SIENA   (Italy)

Author keywords

Optimization algorithms; Predictive control for linear systems; Uncertain systems

Indexed keywords

COMPUTER SIMULATION; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; DISCRETE TIME CONTROL SYSTEMS; FEEDBACK; LINEAR CONTROL SYSTEMS; OPTIMIZATION; UNCERTAIN SYSTEMS;

DECOMPOSITION ALGORITHM; DISCRETE-TIME UNCERTAIN LINEAR SYSTEMS; MIN-MAX PROBLEM;

PREDICTIVE CONTROL SYSTEMS;

EID: 33750093111     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2006.883062     Document Type: Article

References (19)

1. T. Alamo, D. Muñoz de la Peña, D. Limon, and E. F. Camacho, "Constrained min-max predictive control: Modifications of the objective function leading to polynomial complexity," IEEE Trans. Autom. Control, vol. 50, no. 5, pp. 710-714, May 2005.
2. J. C. Allwright and G. C. Papavasiliou, "On linear programming and robust model-predictive control using impulse-responses," Syst. Control Lett., vol. 18, pp. 159-164, 1992.
3. A. Bemporad, F. Borreli, and M. Morari, "Min-max control of constrained uncertain discrete-time linear systems," IEEE Trans. Autom. Control, vol. 48, no. 9, pp. 1600-1606, Sep. 2003.
4. J. F. Benders, "Partitioning procedures for solving mixed-variables programming problems," Numer. Math., vol. 4, pp. 238-252, 1962.
5. J. R. Birge and F. V. Louveaux, "A multicut algorithm for twostage stochastic linear programs," Eur. J. Oper. Res., vol. 34, no. 3, pp. 384-392, 1988.
6. J. R. Birge and F. V. Louveaux, Introduction to Stochastic Programming. New York: Springer-Verlag, 1997.
7. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004.
8. P. J. Campo and M. Morari, "Robust model predictive control," in Proc. Amer. Control Conf., 1987, vol. 2, pp. 1021-1026.
9. M. Diehl and J. Björnberg, "Robust dynamic programming for min-max model predictive control of constrained uncertain systems," IEEE Trans. Autom. Control, vol. 49, no. 12, pp. 2253-2257, Dec. 2004.
10. E. C. Kerrigan and J. M. Maciejowski, "Feedback min-max model predictive control using a single linear program: Robust stability and the explicit solution," Int. J. Robust Nonlinear Control, vol. 14, pp. 395-413, 2004.
11. J. Edwards, J. Birge, A. King, and L. Nazareth, "A standard input format for computer codes which solve stochastic programs with recourse and a library of utilities to simplify its use," Working Paper WP-85-03, International Institute for Applied Systems Analysis. Laxenburg, Austria, 1985.
12. H. I. Gassmann, The SMPS format for stochastic linear programs [Online]. Available: http://www.mgmt.dal.ca/sba/profs/hgassmann/SMPS2.htm
13. M. V. Kothare, V. Balakrishnan, and M. Morari, "Robust constrained model predictive control using linear matrix inequalities," Automatica, vol. 32, pp. 1361-1379, 1996.
14. J. H. Lee and Z. Yu, "Worst-case formulations of model predictive control for systems with bounded parameters," Automatica, vol. 33, no. 5, pp. 763-781, 1997.
15. J. Löfberg, "Minimax approaches to robust model predictive control," Ph.D. dissertation, Dept. Elect. Eng., Linköping Univ., Linköping, Sweden, Apr. 2003 [Online]. Available: http://www.control.isy.liu.se/publications/doc?id=1466
16. A. Makhorin, GNU linear programming kit [Online]. Available: http://www.gnu.org/software/glpk 2005
17. A. I. Propoi, "Use of linear programming methods for synthesizing sampled-data automatic systems," Automat. Remote Control, vol. 24, no. 7, pp. 837-844, 1963.
18. P. O. M. Scokaert and D. Q. Mayne, "Min-max feedback model predictive control for constrained linear systems," IEEE Trans. Autom. Control, vol. 43, no. 8, pp. 1136-1142, Aug. 1998.
19. H. S. Witsenhausen, "A min-max control problem for sampled linear systems," IEEE Trans. Autom. Control, vol. AC-13, no. 1, pp. 5-21, Jan. 1968.