Inf-sup control of discontinuous piecewise affine systems

2007 European Control Conference, ECC 2007

Volumn , Issue , 2007, Pages 3344-3350

  Spjotvold, J ^a   Kerrigan, E C ^b   Rakovic, S V ^c   Mayne, D Q ^b   Johansen, T A ^a  

^a NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

^c ETH ZURICH   (Switzerland)

Author keywords

Approximate solutions to inf sup problems; Optimal control; Parametric programming; Piecewise affine systems

Indexed keywords

CONTROL THEORY; COST FUNCTIONS; DYNAMIC PROGRAMMING; LINEAR PROGRAMMING; OPTIMAL CONTROL SYSTEMS;

APPROXIMATE SOLUTION; EXPLICIT CONTROL LAW; OPTIMAL CONTROL PROBLEM; OPTIMAL CONTROLS; PARAMETRIC PROGRAMMING; PIECEWISE AFFINE SYSTEMS; PIECEWISE AFFINES; SUBOPTIMAL SOLUTION;

DISCRETE TIME CONTROL SYSTEMS;

EID: 84927739915     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.23919/ecc.2007.7068858     Document Type: Conference Paper

References (18)

1. F. Borrelli, M. Baotíc, A. Bemporad, and M. Morari, "Dynamic programming for constrained optimal control of discrete-time linear hybrid systems," Automatica, vol. 41, pp. 1709-1721, 2005.
2. S. V. Rakovíc, E. C. Kerrigan, and D. Q. Mayne, "Optimal control of constrained piecewise affine systems with state-and input-dependent disturbances," in Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems, Katholieke Universiteit Leuven, Belgium, 2004.
3. D. Q. Mayne and S. V. Rakovíc, "Optimal control of constrained piecewise affine systems using reverse transformation," in Proceedings of the 41st IEEE Conference on Decision and Control, vol. 2, Las Vegas, USA, 2002, pp. 1546-1551.
4. A. Bemporad, F. Borrelli, and M. Morari, "Piecewise linear optimal controllers for hybrid systems," in Proc. American Contr. Conf., Chicago, IL, 2000, pp. 1190-1194.
5. -, "Optimal Controllers for Hybrid Systems: Stability and Piecewise Linear Explicit Form," in IEEE Conference on Decision and Control, Sydney, Australia, 2000.
6. F. Borrelli, "Discrete time constrained optimal control," Ph. D. Dissertation, Swiss Federal Institute of Technology, 2002.
7. 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 of the 43rd IEEE Conference on Decision and Control, Paradise Island, Bahamas, 2002.
8. M. Diehl and J. Björnberg, "Robust dynamic programming for minmax model predictive control of constrained uncertain systems," IEEE Trans. Automatic Control, vol. 49, no. 12, pp. 2253-2257, 2004.
9. A. Bemporad and M. Morari, "Control of systems integrating logic, dynamics, and constraints," Automatica, vol. 35, no. 3, pp. 407-427, 1999.
10. R. Goebel and A. R. Teel, "Solutions to hybrid inclusions via set and graphical convergence with stability theory applications," Automatica, vol. 42, pp. 573-587, 2006.
11. R. T. Rockafellar and R. J.-B. Wets, Variational Analysis, ser. Grundlehren der mathematischen Wissenschaften. Berlin: Springer-Verlag, 1998, vol. 317.
12. H. Jeffreys and B. S. Jeffreys, Upper and Lower Bounds, 3rd ed. Cambridge, England: Cambridge University Press, 1988.
13. T. Gal and J. Nedoma, "Multiparametric linear programming," Management Science, vol. 18, pp. 406-442, 1972.
14. B. Bank, J. Guddat, D. Klatte, B. Kummer, and K. Tammer, Non-linear Parametric Optimization. Berlin: Birkhäuser, 1983.
15. 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.
16. F. Borrelli, A. Bemporad, and M. Morari, "A geometric algorithm for multi-parametric linear programming," Journal of Optimization Theory and Applications, vol. 118, no. 3, pp. 515-540, 2003.
17. R. T. Rockafellar, Convex Analysis. Princeton, New Jersey: Princeton Univeristy Press, 1972.
18. S. V. Rakovíc, E. C. Kerrigan, D. Q. Mayne, and J. Lygeros, "Reachability analysis of discrete-time systems with disturbances," IEEE Transactions on Automatic Control, vol. 51, pp. 546-561, 2006.