Model predictive control based on linear programming - The explicit solution

IEEE Transactions on Automatic Control

Volumn 47, Issue 12, 2002, Pages 1974-1985

  Bemporad, Alberto ^a   Borrelli, Francesco ^b   Morari, Manfred ^b  

^a UNIVERSITY OF SIENA   (Italy)

^b ETH ZURICH   (Switzerland)

Author keywords

Constraints; Linear programming (LP); Model predictive control (MPC); Multiparametric programming; Piecewise linear control

Indexed keywords

ALGORITHMS; FUNCTIONS; LINEAR PROGRAMMING; OPTIMAL CONTROL SYSTEMS;

MULTIPARAMETRIC PROGRAMMING;

PREDICTIVE CONTROL SYSTEMS;

EID: 0036957343     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2002.805688     Document Type: Article

References (44)

1. S. J. Qin and T. A. Badgwell, "An overview of industrial model predictive control technology," in Chemical Process Control-V: AIChe Symp. Series-Amer. Inst. Chem. Eng., 1997, vol. 93, pp. 232-256.
2. J. Richalet, A. Rault, J. L. Testud, and J. Papon, "Model predictive heuristic control-application to industrial processes," Automatica, vol. 14, pp. 413-428, 1978.
3. C. R. Cutler and B. C. Ramaker, "Dynamic matrix control-A computer control algorithm," in Proc. Amer. Control Conf., vol. WP5-B, San Francisco, CA, 1980.
4. C. E. García and A. M. Morshedi, "Quadratic programming solution of dynamic matrix control (QDMC)," Chem. Eng. Commun., vol. 46, pp. 73-87, 1986.
5. D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, "Constrained model predictive control: Stability and optimality," Automatica, vol. 36, pp. 789-814, June 2000.
6. M. Sznaier and M. J. Damborg, "Suboptimal control of linear systems with state and control inequality constraints," in Proc. 26th IEEE Conf. Decision Control, Los Angeles, CA, 1987, pp. 761-762.
7. L. A. Zadeh and L. H. Whalen, "On optimal control and linear programming," IEEE Trans. Automat. Contr., vol. AC-7, pp. 45-46, Jan. 1962.
8. A. I. Propoi, "Use of linear programming methods for synthesizing sampled-data automatic systems," Automat. Rem. Control, vol. 24, no. 7, pp. 837-844, 1963.
9. T. S. Chang and D. E. Seborg, "A linear programming approach for multivariable feedback control with inequality constraints," Int. J. Control, vol. 37, no. 3, pp. 583-597, 1983.
10. P. J. Campo and M. Morari, "Model predictive optimal averaging level control,"AIChE J., vol. 35, no. 4, pp. 579-591, 1989.
11. 1-norm model predictive control," AIChE J., vol. 39, no. 12, pp. 1954-1965, 1993.
12. C. V. Rao and J. B. Rawlings, "Linear programming and model predictive control," J. Process Control, vol. 10, pp. 283-289, 2000.
13. P.O. Gutman, "A linear programming regulator applied to hydroelectric reservoir level control," Automatica, vol. 22, no. 5, pp. 533-541, 1986.
14. P.O. Gutman and M. Cwikel, "Admissible sets and feedback control for discrete-time linear dynamical systems with bounded control and states," IEEE Trans. Automat. Contr., vol. AC-31, pp. 373-376, Apr. 1986.
15. F. Blanchini, "Ultimate boundedness control for uncertain discrete-time systems via set-induced Lyapunov functions," IEEE Trans. Automat. Contr., vol. 39, pp. 428-433, Feb. 1994.
16. 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.
17. T. Gal and J. Nedoma, "Multiparametric linear programming," Manag. Sci., vol. 18, pp. 406-442, 1972.
18. T. Gal, Postoptimal Analyzes, Parametric Programming, and Related Topics, 2nd ed. Berlin, Germany: de Gruyter, 1995.
19. F. Borrelli, A. Bemporad, and M. Morari, "A geometric algorithm for multi-parametric linear programming," J. Optim. Theory, to be published.
20. J. B. Rawlings and K. R. Muske, "The stability of constrained receding-horizon control," IEEE Trans. Automat. Contr., vol. 38, pp. 1512-1516, 1993.
21. A. Zheng and M. Morari, "Stability of model predictive control with mixed constraints," IEEE Trans. Automat. Contr., vol. 40, pp. 1818-1823, 1995.
22. S. S. Keerthi and E. G. Gilbert, "Optimal infinite-horizon feedback control laws for a general class of constrained discrete-time systems: Stability and moving-horizon approximations," J. Opt. Theory Appl., vol. 57, pp. 265-293, 1988.
23. E. G. Gilbert and K. T. Tan, "Linear systems with state and control constraints: The theory and applications of maximal output admissible sets," IEEE Trans. Automat. Contr., vol. 36, pp. 1008-1020, Sept. 1991.
24. A. Bemporad, "Reducing conservativeness in predictive control of constrained systems with disturbances," in Proc. 37th IEEE Conf. Decision Control, Tampa, FL, 1998, pp. 1384-1391.
25. E. C. Kerrigan and J. M. Maciejowski, "Invariant sets for constrained nonlinear discrete-time systems with application to feasibility in model predictive control," in Proc. 39th IEEE Conf. Decision Control, 2000, pp. 4951-4956.
26. A. Bemporad and M. Morari, "Robust model predictive control: A survey," in Robustness in Identification and Control, A. Garulli, A. Tesi, and A. Vicino, Eds. New York: Springer-Verlag, 1999, no. 245 in Lecture Notes in Control and Information Sciences, pp. 207-226.
27. D. Q. Mayne and H. Michalska, "Robust receding horizon control of constrained nonlinear systems," IEEE Trans. Automat. Contr., vol. 38, pp. 1623-1633, Nov. 1993.
28. A. Bemporad, L. Chisci, and E. Mosca, "On the stabilizing property of SIORHC," Automatica, vol. 30, no. 12, pp. 2013-2015, 1994.
29. G. Bitsoris, "On the positive invariance of polyhedral sets for discrete-time systems," Syst. Control Lett., vol. 11, pp. 243-248, 1988.
30. A. Polański, "On infinity norms as Lyapunov functions for linear systems," IEEE Trans. Automat. Contr., vol. 40, pp. 1270-1273, July 1995.
31. H. Kiendl, J. Adamy, and P. Stelzner, "Vector norms as Lyapunov functions for linear systems," IEEE Trans. Automat. Contr., vol. 37, pp. 839-842, June 1992.
32. F. Blanchini, "Set invariance in control," Automatica, vol. 35, pp. 1747-1767, Nov. 1999.
33. C. Filippi, "On the geometry of optimal partition sets in multiparametric linear programming," Dept. Pure Appl. Math., Univ. Padova, Padova, Italy, Tech. Rep. 12, June 1997.
34. M. Schechter, "Polyhedral functions and multiparametric linear programming," J. Optim. Theory Appl., vol. 53, pp. 269-280, May 1987.
35. A. V. Fiacco, Introduction to Sensitivity and Stability Analysis in Nonlinear Programming. London, U.K.: Academic, 1983.
36. V. Dua and E. N. Pistikopoulos, "An algorithm for the solution of multiparametric mixed integer linear programming problems," Ann. Oper. Res., pp. 123-139, 2000.
37. I. Adler and R. D. C. Monteiro, "A geometric view of parametric linear programming," Algorithmica, vol. 8, no. 2, pp. 161-176, 1992.
38. J. E. Goodman and J. O'Rourke, Eds., Handbook of Discrete and Computational Geometry. Boca Raton, FL: CRC Press, 1997, Discrete Mathematics and Its Applications.
39. A. Bemporad, K. Fukuda, and F. D. Torrisi, "Convexity recognition of the union of polyhedra," Comput. Geometry, vol. 18, pp. 141-154, 2001.
40. F. Borrelli, M. Baotic, A. Bemporad, and M. Morari, "Efficient on-line computation of constrained optimal control laws," in Proc. 40th IEEE Conf Decision Control, Orlando, FL, 2001, pp. 1187-1192.
41. P. Tøndel, T. A. Johansen, and A. Bemporad, "Computation and approximation of piecewise affine control via binary search trees," Automatica, to be published.
42. A. Bemporad and M. Morari, "Control of systems integrating logic, dynamics, and constraints," Automatica, vol. 35, pp. 407-427, Mar. 1999.
43. A. Bemporad, F. Borrelli, and M. Morari, "Piecewise linear optimal controllers for hybrid systems," in Proc. Amer. Control Conf., Chicago, IL, 2000, pp. 1190-1194.
44. A. Bemporad, F. Borrelli, and M. Morari, "Min-max control of constrained uncertain discrete-time linear systems," IEEE Trans. Automat. Contr., to be published.