Every continuous nonlinear control system can be obtained by parametric convex programming

IEEE Transactions on Automatic Control

Volumn 53, Issue 8, 2008, Pages 1963-1967

  Baes, Michel ^a   Diehl, Moritz ^a   Necoara, Ion ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Continuous feedback laws; Model predictive control (MPC); Parametric convex programming (PCP)

Indexed keywords

CONTROL SYSTEMS; FEEDBACK; NONLINEAR CONTROL SYSTEMS; PREDICTIVE CONTROL SYSTEMS;

CONSTRUCTIVE PROOFS; CONTINUOUS; CONTINUOUS FEEDBACK LAWS; CONVEX ANALYSES; CONVEX PROGRAMMINGS; EXTENDING; FEEDBACK LAWS; PARAMETRIC CONVEX PROGRAMMING (PCP);

MODEL PREDICTIVE CONTROL;

EID: 54049142898     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2008.928131     Document Type: Article

References (18)

1. A. Fiacco, Introduction to Sensitivity and Stability Analysis in Nonlinear Programming. London, U.K: Academic, 1983.
2. T. Gal, Postoptimal Analyses, Parametric Programming, and Related Topics. Berlin, Germany: De Gruyter, 1995.
3. F. Borrelli, Constrained Optimal Control of Linear and Hybrid Systems ser. Lecture Notes in Control and Information Sciences. Berlin, Germany: Springer, 2003, vol. 290.
4. A. Bemporad, M. Morari, V. Dua, and E. Pistikopoulos, "The explicit linear quadratic regulator for constrained systems," Automatica, vol. 38, no. 1, pp. 3-20, Jan. 2002.
5. M. Diehl and J. Björnberg, "Robust dynamic programming for min-max model predictive control of constrained uncertain systems," IEEE Trans. Automat. Control, vol. 49, no. 12, pp. 2253-2257, Dec. 2004.
6. P. Tondel, T. Johansen, and A. Bemporad, "An algorithm for multiparametric quadratic programming and explicit MPC solutions," Automatica, vol. 39, no. 3, pp. 489-497, Mar. 2003.
7. E. Kerrigan and J. Maciejowski, "Feedback min-max MPC using a single linear program: Robust stability and the explicit solution," Int. J. Robust Nonlin. Control, vol. 13, no. 3-4, pp. 1-18, 2003.
8. J. Maciejowski, Predictive Control With Constraints. Harlow, U.K.: Prentice-Hall, 2002.
9. D. Mayne, J. Rawlings, C. Rao, and P. Scokaert, "Constrained model predictive control: Stability and optimality," Automatica, vol. 36, no. 7, pp. 789-814, Jun. 2000.
10. C. García, D. Prett, and M. Morari, "Model predictive control: Theory and practice - A survey," Automatica, vol. 25, no. 3, pp. 335-348, May 1989.
11. B. Bank, J. Guddat, D. Klatte, B. Kummer, and K. Tammer, Non-Linear Parametric Optimization. Berlin, Germany: Akademie-Verlag, 1982.
12. S. Robinson and R. Day, "A sufficient condition for continuity of optimal sets in mathematical programming," J. Mathemat. Anal. Applic., vol. 45, pp. 506-511, 1974.
13. A. Bemporad and C. Filippi, "Approximate multiparametric convex programming," in Proc. 42nd IEEE Conf. Decision and Control, Maui, HI, Dec. 2003, pp. 3185-3190.
14. J. Björnberg and M. Diehl, "Approximate robust dynamic programming and robustly stable MPC," Automatica, vol. 42, no. 5, pp. 777-782, May 2006.
15. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge University Press, 2004.
16. A. Barvinok, A Course in Convexity, sen. Graduate Studies in Mathematics. Providence, RI: AMS, 2002, vol. 54.
17. R. T. Rockafellar, Convex Analysis, ser. Princeton Mathematics Series. Princeton, U.K.: Princeton University Press, 1970, vol. 28.
18. R. Kalman, "When is a linear control system optimal?," Trans. ASME, J. Basic Eng., ser. D, vol. 88, pp. 51-60, Mar. 1964.