Parameterized tube model predictive control

IEEE Transactions on Automatic Control

Volumn 57, Issue 11, 2012, Pages 2746-2761

  Rakovic, Saša V ^a   Kouvaritakis, Basil ^b   Cannon, Mark ^b   Panos, Christos ^c   Findeisen, Rolf ^d  

^a UNIVERSITY OF MARYLAND   (United States)

^b UNIVERSITY OF OXFORD   (United Kingdom)

^c IMPERIAL COLLEGE LONDON   (United Kingdom)

^d OTTO VON GUERICKE UNIVERSITY   (Germany)

Author keywords

Constrained control; convex programming; robust control; set dynamics; tube model predictive control

Indexed keywords

COMPUTATIONALLY EFFICIENT; CONSTRAINED CONTROLS; CONTROL POLICY; DEGREE OF NON-LINEARITY; LINEAR PROGRAMS; MINKOWSKI; ONLINE USE; PARAMETERIZED; SET-DYNAMICS; STATE OF THE ART; SYNTHESIS METHOD; TUBE MODEL;

CONVEX PROGRAMMING; MODEL PREDICTIVE CONTROL; PARAMETERIZATION; ROBUST CONTROL; TUBES (COMPONENTS);

PREDICTIVE CONTROL SYSTEMS;

EID: 84867086490     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2012.2191174     Document Type: Article

References (23)

1. J. B. Rawlings and D. Q. Mayne, Model Predictive Control: Theory and Design. Madison, WI: Nob Hill, 2009.
2. R. E. Bellman, Dynamic Programming. Princeton, NJ: Princeton Univ. Press, 1957.
3. D. P. Bertsekas, Dynamic Programming and Optimal Control, 3rd ed. Nashua, NH: Athena Scientific, 2007, vol. I and II.
4. F. Blanchini and S. Miani, Set-Theoretic Methods in Control, ser. Systems & Control: Foundations & Applications. Boston, Basel, Berlin: Birkhäuser, 2008.
5. 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. (Pubitemid 128737398)
6. E. C. Kerrigan and J. M. Maciejowski, "Robustly stable feedback min-max model predictive control," in Proc. Amer. Control Conf. (ACC '03), Denver, CO, Jun. 2003.
7. D. Q.Mayne, M. Seron, and S. V. Rakovi, "Robust model predictive control of constrained linear systems with bounded disturbances," Automatica, vol. 41, pp. 219-224, 2005. (Pubitemid 41536571)
8. D. Q. Mayne, S. V. Rakovi, R. Findeisen, and F. Allgöwer, "Robust output feedback model predictive control of constrained linear systems: Time varying case," Automatica, vol. 45, pp. 2082-2087, 2009.
9. F. Blanchini, "Control synthesis of discrete time systems with control and state bounds in the presence of disturbance," J. Optimiz. Theory Applicat., vol. 65, no. 1, pp. 29-40, 1990. (Pubitemid 20698833)
10. Y. I. Lee and B. Kouvaritakis, "Constrained receding horizon predictive control for systems with disturbances," Int. J. Control, vol. 72, no. 11, pp. 1027-1032, 1999.
11. S. V. Rakovi, B. Kouvaritakis, R. Findeisen, and M. Cannon, "Homothetic tube model predictive control," Automatica, 2012, to be published.
12. J. Löfberg, "Minimax approaches to robust model predictive control," Ph.D. dissertation, Dept. of Elect. Eng., Linköping Univ., Linköping, Sweden, 2003.
13. J. Löfberg, "Approximations of closed-loop minimax mpc," in Proceedings of 42nd IEEE Conference on Decision and Control, CDC 2003, Maui, HI, Dec. 2003, vol. 2, pp. 1438-1442.
14. P. J. Goulart, E. C. Kerrigan, and J. M. Maciejowski, "Optimization over state feedback policies for robust control with constraints," Automatica, vol. 42, no. 4, pp. 523-533, 2006. (Pubitemid 43267647)
15. B.Bank, J.Guddat,D.Klatte, B. Kummer, andK. Tammer, Non-Linear Parametric Optimization. Basel, Boston, Stuttgart: Birkhäuser, 1983.
16. I. V. Kolmanovsky and E. G. Gilbert, "Theory and computation of disturbance invariant sets for discrete time linear systems," Math. Problems in Eng.: Theory, Methods, Applicat., vol. 4, pp. 317-367, 1998. (Pubitemid 128557716)
17. S. V. Rakovi, "Minkowski algebra and banach contraction principle in set invariance for linear discrete time systems," in Proc. 46th IEEE Conf. Decision Control (CDC '07), New Orleans, LA, Dec. 2007, pp. 2169-2174.
18. S. V. Rakovi and M. Bari, "Parameterized robust control invariant sets for linear systems: Theoretical advances and computational remarks," IEEE Trans. Autom. Control, vol. 55, no. 7, pp. 1599-1614, Jul. 2010.
19. S. V. Rakovi, B. Kouvaritakis, M. Cannon, C. Panos, and R. Findeisen, "Parameterized tube model predictive control," Univ. of Oxford, Dept. of Eng. Sci., 2010, Tech. Rep. OUEL 2315/10.
20. R. T. Rockafellar, Convex Analysis. Princeton, NJ: Princeton Univ. Press, 1970.
21. R. Schneider, Convex Bodies: The Brunn-Minkowski Theory. Cambridge, U.K.: Cambridge Univ. Press, 1993, vol. 44.
22. Z. Artstein and S. V. Rakovi, "Feedback and invariance under uncertainty via set iterates," Automatica, vol. 44, no. 2, pp. 520-525, 2008.
23. M. Kvasnica, P. Grieder, and M. Baoti, Multi-Parametric Toolbox (MPT), 2004 [Online]. Available: http://control.ee.ethz.ch/mpt/