Optimal control and piecewise parametric programming

2007 European Control Conference, ECC 2007

Volumn , Issue , 2007, Pages 2762-2767

  Mayne, D Q ^a   Rakovic, S V ^b   Kerrigan, E C ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

DECISION MAKING; LINEAR SYSTEMS; OPTIMAL CONTROL SYSTEMS; QUADRATIC PROGRAMMING;

CONSTRAINED OPTIMAL CONTROL PROBLEMS; IMPROVED TECHNIQUES; PARAMETRIC PROGRAMMING; PIECEWISE AFFINE FUNCTIONS; PIECEWISE AFFINE SYSTEMS; PIECEWISE QUADRATIC FUNCTION; PIECEWISE QUADRATIC PROGRAMMING; REVERSE TRANSFORMATION;

DYNAMIC PROGRAMMING;

EID: 84927725687     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.23919/ecc.2007.7068427     Document Type: Conference Paper

References (19)

1. A. Bemporad, F. Borrelli, and M. Morari, "Piecewise linear optimal controllers for hybrid systems," in Proceedings of the American Control Conference, Chicago, 2000, pp. 1190-1194.
2. -, "Optimal controllers for hybrid systems: stability and piecewise linear explicit form," in Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, December 2000.
3. D. Q. Mayne, "Control of constrained dynamic systems," European Journal of Control, vol. 7, pp. 87-99, 2001.
4. D. Ramirez and E. Camacho, "On the piecewise linear nature of min-max model predictive control with bounded uncertainties," in Proceedings of the 40th IEEE 2001 Conference on Decision and Control, Orlando, Florida, USA, 2001, pp. 4845-4850.
5. 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, 2002.
6. F. Borrelli, "Discrete time constrained optimal control," Ph. D. dissertation, Swiss Federal Instritute of Technology, Zurich, 2002.
7. E. C. Kerrigan and D. Q. Mayne, "Optimal control of constrained piecewise affine systems with bounded disturbances," in Proceedings of the 41st IEEE 2002 Conference on Decision and Control, vol. 2, Las Vegas, USA, 2002, pp. 1552-1557.
8. D. Q. Mayne and S. Rakovíc, "Optimal control of constrained piecewise affine discrete-time systems using reverse transformation," in Proceedings of the IEEE 2002 Conference on Decision and Control, vol. 2, Las Vegas, USA, 2002, pp. 1546-1551 vol. 2.
9. -, "Optimal control of constrained piecewise affine discrete-time systems," Journal of Computational Optimization and Applications, vol. 25, no. 1-3, pp. 167-191, 2003.
10. M. M. Seron, G. C. Goodwin, and J. A. D. Doná, "Characterisation of receding horizon control for constrained linear systems," Asian Journal of Control, vol. 5, no. 2, pp. 271-286, June 2003.
11. A. Bemporad, F. Borrelli, and M. Morari, "Min-max control of constrained uncertain discrete-time linear systems," IEEE Transactions on Automatic Control, vol. 48, no. 9, pp. 1600-1606, September 2003.
12. E. C. Kerrigan and J. M. Maciejowski, "Feedback min-max model predictive control using a single linear program: Robust stability and the explicit solution," International Journal of Robust and Nonlinear Control, vol. 14, no. 4, pp. 395-413, March 2004.
13. M. Diehl and J. Bjornberg, "Robust dynamic programming for minmax model predictive control of constrained uncertain systems," IEEE Trans. Automatic Control, vol. 49, no. 12, pp. 2253-2257, December 2004.
14. D. Q. Mayne, "Control of constrained dynamic systems," Imperial College London, Tech. Rep. EEE/C&P/DQM/9/2001, 2001, keynote address, European Control Conference, Oporto, 4-7 September, 2001.
15. D. M. de la Peña, T. Alamo, A. Bemporad, and E. F. Camacho, "A dynamic programming approach for determining the explicit solution of MPC controllers," in Proceedings 43rd IEEE Conference on Decision and Control, Paradise Island, Bahamas, December 2004.
16. D. Q. Mayne, S. V. Rakovíc, R. B. Vinter, and E. C. Kerrigan, "Characterization of the solution to a constrained H∞ optimal control problem," Automatica, vol. 42, pp. 371-382, 2006.
17. B. Bank, J. Guddat, D. Klatte, B. Kummer, and K. Tanner, Non-linear parametric optimization. Basel, Boston, Stuttgart: Birkhäuser Verlag, 1983.
18. G. B. Dantzig, J. Folkman, and N. Z. Shapiro, "On the continuity of the minimum set of a continuous function," Journal of Mathematical Analysis and Applications, vol. 17, no. 3, pp. 519-548, 1967.
19. D. Q. Mayne and S. Rakovíc, "Model predictive control of constrained piecewise affine discrete-time systems," International Journal of Robust and Nonlinear Control, vol. 13, no. 3-4, pp. 261-279, 2003.