Soft constrained model predictive control with robust stability guarantees

IEEE Transactions on Automatic Control

Volumn 59, Issue 5, 2014, Pages 1190-1202

  Zeilinger, Melanie N ^a,b   Morari, Manfred ^c   Jones, Colin N ^d  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b MAX PLANCK INSTITUTE FOR INTELLIGENT SYSTEMS   (Germany)

^c ETH ZURICH   (Switzerland)

^d EPFL   (Switzerland)

Author keywords

Model Predictive Control; Soft constraints

Indexed keywords

ASYMPTOTIC STABILITY; CONSTRAINED OPTIMIZATION; CONTROL THEORY; MODEL PREDICTIVE CONTROL;

ADDITIVE DISTURBANCE; CLOSED LOOP STABILITY; CONSTRAINED METHOD; CONSTRAINED MODEL PREDICTIVE CONTROL; INPUT-TO-STATE STABILITY; OPTIMAL PERFORMANCE; SOFT CONSTRAINT; TERMINAL CONSTRAINT;

PREDICTIVE CONTROL SYSTEMS;

EID: 84899643785     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2014.2304371     Document Type: Article

References (32)

1. D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, "Constrainedmodel predictive control: Stability and optimality," Automatica,vol. 36, no. 6, pp. 789-814, 2000. (Pubitemid 30587683)
2. E. Zafiriou and H.-W. Chiou, "Output constraint softening for SISO modelpredictive control," in Proc. Amer. Control Conf., 1993, pp. 372-376.
3. A. Zheng and M. Morari, "Stability of model predictive control withmixed constraints," IEEE Trans. Autom. Control, vol. 40, no. 10,pp. 1818-1823, 1995.
4. P. O. M. Scokaert and J. B. Rawlings, "Feasibility issues in linear modelpredictive control," AIChE J., vol. 45, pp. 1649-1659, 1999. (Pubitemid 29382580)
5. N. M. C. de Oliveira and L. T. Biegler, "Constraint handling and stabilityproperties of model-predictive control," AIChE J., vol. 40, pp. 1138-1155,July 1994.
6. E. C. Kerrigan and J. M. Maciejowski, "Soft constraints and exactpenalty functions in model predictive control," in Proc. UKACC Int. Conf.(Control), Cambridge, U.K., Sep. 2000.
7. S. C. Thomsen, H. Niemann, and N. K. Poulsen, "Robust stability inpredictive control with soft constraints," in Proc. Amer. Control Conf.,2010, pp. 6280-6285.
8. A. G. Wills and W. P. Heath, "Barrier function based model predictivecontrol," Automatica, vol. 40, pp. 1415-1422, 2004.
9. D. Limon, I. Alvarado, T. Alamo, and E. F. Camacho, "MPC for trackingpiecewise constant references for constrained linear systems," Automatica,vol. 44, pp. 2382-2387, 2008.
10. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.:Cambridge Univ. Press, 2004.
11. M. Andersen, J. Dahl, Z. Liu, and L. Vandenberghe, "Interior-point methodsfor large-scale cone programming," in Optimization for MachineLearning. Cambridge, MA: MIT Press, 2011, pp. 55-83.
12. E. D. Andersen, C. Roos, and T. Terlaky, "On implementing a primal-dualinterior-point method for conic quadratic optimization," MathematicalProgramming, vol. 95, pp. 249-277, 2003. (Pubitemid 44757855)
13. A. Domahidi, E. Chu, and S. Boyd, "ECOS: An SOCP solver for embeddedsystems," in Proc. Eur. Control Conf., Jul. 2013, pp. 3071-3076.
14. M. N. Zeilinger, C. N. Jones, and M. Morari, "Robust stability propertiesof soft constrained MPC," in Proc. 49th IEEE Conf. Decision Control,2010, pp. 5276-5282.
15. M. Vidyasagar, Nonlinear Systems Analysis, 2nd ed. Englewood Cliffs,NJ: Prentice-Hall, 1993.
16. F. Blanchini, "Set invariance in control," Automatica, vol. 35, pp. 1747-1767, 1999. (Pubitemid 32078089)
17. Z.-P. Jiang and Y. Wang, "Input-to-state stability for discrete-time nonlinearsystems," Automatica, vol. 37, pp. 857-869, 2001.
18. E. D. Sontag and Y. Wang, "New characterizations of input-to-state stability,"IEEE Trans. Autom. Control, vol. 41, pp. 1283-1294, 1999.
19. D. Limon, T. Alamo, D. M. Raimondo, D. Mu noz de la Pe na, J.M. Bravo,A. Ferramosca, and E. F. Camacho, "Input-to-state stability: A unifyingframework for robust model predictive control," Lecture Notes ControlInform. Sci., vol. 384, pp. 1-26, 2009.
20. J. B. Rawlings and D. Q. Mayne, Model Predictive Control: Theory andDesign. Madison, WI: Nob Hill Publishing, 2009.
21. J. Maciejowski, Predictive Control With Constraints. Englewood Cliffs,NJ: Prentice-Hall, 2000.
22. A. Ferramosca, D. Limon, I. Alvarado, T. Alamo, and E. F. Camacho,"MPC for tracking with optimal closed-loop performance," Automatica,vol. 45, pp. 1975-1978, Aug. 2009.
23. D. Limon, I. Alvarado, T. Alamo, and E. F. Camacho, "Robust tubebasedMPC for tracking of constrained linear systems with additivedisturbances," J. Process Control, vol. 20, no. 3, pp. 248-260,Mar. 2010.
24. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear MatrixInequalities in System and Control Theory, vol. 15. Philadelphia, PA:SIAM, Jun. 1994, ser. Studies in Applied Mathematics.
25. R. Fletcher, Practical Methods of Optimization, 2nd ed. New York:Wiley, 1987.
26. M. N. Zeilinger, D. M. Raimondo, A. Domahidi, M. Morari, andC. N. Jones, "On Real-time Robust Model Predictive Control," Automatica,vol. 50, no. 3, pp. 683-694, 2014.
27. G. Grimm, M. J. Messina, S. E. Tuna, and A. R. Teel, "Examples whennonlinear model predictive control is nonrobust," Automatica, vol. 40,no. 10, pp. 1729-1738, 2004.
28. D. Q. Mayne, M. M. Seron, and S. V. Rakovic, "Robust model predictivecontrol of constrained linear systems with bounded disturbances,"Automatica, vol. 41, no. 2, pp. 219-234, 2005.
29. B. Bank, J. Guddat, D. Klatte, B. Kummer, and K. Tammer, Non-LinearParametric Optimization. Berlin, Germany: Akademie-Verlag, 1982.
30. M. N. Zeilinger, "Real-Time Model Predictive Control," Ph.D. dissertation,ETH Zurich, Zurich, Switzerland, 2011.
31. J. Löfberg, "YALMIP: A Toolbox for Modeling and Optimization inMATLAB," in Proc. IEEE Int. Symp. Computer Aided Control Syst.Design, 2004, pp. 284-289. (Pubitemid 40788529)
32. M. Kvasnica, Real-Time Model Predictive Control via Multi- ParametricProgramming: Theory and Tools. Saarbrücken, Germany: VDM Verlag,2009.