189
Views
13
CrossRef citations to date
0
Altmetric
Original Articles

Model predictive control for uncertain max–min-plus-scaling systems

, , &
Pages 701-713 | Received 15 Feb 2006, Accepted 31 Oct 2006, Published online: 08 Apr 2008

References

  • Baccelli , F , Cohen , G and Olsder , G . 1992 . J. Quadrat, Synchronization and Linearity , New York : John Wiley & Sons .
  • Bemporad , A and Morari , M . 1999 . Control of systems integrating logic, dynamics, and constraints . Automatica , 35 : 407 – 427 .
  • Borrelli , F , Bemporad , A and Morari , M . 2003 . A geometric algorithm for multi-parametric linear programming . J. Optimiz. Theory App. , 118 : 515 – 540 .
  • Cassandras , C , Pepyne , D and Wardi , Y . 2001 . Optimal control of a class of hybrid systems . IEEE Trans. Automat. Contr. , 46 : 398 – 415 .
  • Cottenceau , B , Hardouin , L , Boimond , J and Ferrier , J . 2001 . Model reference control for timed event graphs in dioid . Automatica , 37 : 1451 – 1458 .
  • Cuninghame-Green , R . 1979 . Minimax Algebra, Vol. 166 of Lecture Notes in Economics and Mathematical Systems , Berlin, , Germany : Springer-Verlag .
  • De Schutter , B and van den Boom , T . 2001 . Model predictive control for max-plus-linear discrete event systems . Automatica , 37 : 1049 – 1056 .
  • De Schutter , B and van den Boom , T . 2004 . MPC for continuous piecewise-affine systems . Syst. Contr. Lett. , 52 : 179 – 192 .
  • Diehl , M and Björnberg , J . 2004 . Robust dynamic programming for min–max model predictive control of constrained uncertain systems . IEEE Trans. Automat. Contr. , 49 : 2253 – 2257 .
  • Gal , T . 1995 . Postoptimal Analyses, Parametric Programming, and Related Topics , Berlin : de Gruyter .
  • Goodman , J and O’Rourke , J . 1997 . Handbook of Discrete and Computational Geometry, Discrete Mathematics and Its Applications , Boca Raton : CRC Press .
  • Goulart , P , Kerrigan , E and Maciejowski , J . 2006 . Optimization over state feedback policies for robust control with constraints . Automatica , 42 : 523 – 533 .
  • Heemels , W , De Schutter , B and Bemporad , A . 2001 . Equivalence of hybrid dynamical models . Automatica , 37 : 1085 – 1091 .
  • Heidergott , B , Olsder , G and Woude , J . 2005 . Max Plus at Work , Princeton : Princeton University Press .
  • Johansson , M . 2003 . Piecewise Linear Control Systems, Vol. 284 of Lecture Notes in Control and Information Sciences , Berlin, , Germany : Springer .
  • Kerrigan , E and Mayne , D . 2002 . “ Optimal control of constrained, piecewise affine systems with bounded disturbances ” . In Proceedings of the 2002 IEEE Conference on Decision and Control 1552 – 1557 . Las Vegas, Nevada
  • Kvasnica , M , Grieder , P and Baotić , M . Multi-Parametric Toolbox (MPT) Available online at http://control.ee.ethz.ch/mpt/
  • Lofberg , J . 2003 . “ Approximations of closed-loop MPC ” . In Proceedings of the 42th IEEE Conference on Decision and Control 1438 – 1442 . Maui, Hawaii, , USA
  • Maciejowski , J . 2002 . Predictive Control with Constraints , Harlow, , England : Prentice Hall .
  • Mayne , D , Rawlings , J , Rao , C and Scokaert , P . 2000 . Constrained model predictive control: stability and optimality . Automatica , 36 : 789 – 814 .
  • Menguy , E , Boimond , J and Hardouin , L . 1998 . “ Optimal control of discrete event systems in case of updated reference input ” . In Proceedings of the IFAC Conference on System Structure and Control (SSC’98) 601 – 607 . Nantes, , France
  • Motzkin , T , Raiffa , H , Thompson , G and Thrall , R . 1953 . “The double description method” . In Contributions to the Theory of Games, no. 28 in Annals of Mathematics Studies , Edited by: Kuhn , H. and Tucker , A. 51 – 73 . Princeton, , New Jersey : Princeton University Press .
  • Necoara , I . 2006 . “ Model predictive control for max-plus-linear and piecewise affine systems ” . In PhD thesis , The Netherlands : Delft Centre for Systems and Control, Delft University of Technology .
  • Necoara , I , De Schutter , B , van den Boom , T and Hellendoorn , J . 2004 . “ Model predictive control for perturbed continuous piecewise affline systems with bounded disturbances ” . In Proceedings of the 43rd IEEE Conference on Decision and Control 1848 – 1853 . Paradise Island, , The Bahamas
  • Necoara , I , Kerrigan , E , De Schutter , B and van den Boom , T . 2005 . “ Finite-horizon min–max control of max-plus-linear systems ” . In Tech. Rep. 06-002 , The Netherlands : Delft Centre for Systems and Control, Delft University of Technology . (Provisionally accepted for IEEE Transactions on Automatic Control)
  • Olsder , G . 1994 . “ On structural properties of min–max systems ” . In Proceedings of the 11th International Conference on Analysis and Optimization of Systems Sophia-Antipolis, France, Jun. 1994, Vol. 199 of Lecture Notes in Control and Information Sciences , Edited by: Cohen , G and Quadrat , J . 237 – 246 . London : Springer-Verlag .
  • Pardalos , P and Resende , M . 2002 . Handbook of Applied Optimization , Oxford, , UK : Oxford University Press .
  • Rakovic , SV , Kerrigan , EC and Mayne , DQ . 2004 . “ Optimal control of constrained piecewise affine systems with state-and input-dependent disturbances ” . In Proceedings 16th International Symposium on Mathematical Theory of Networks and Systems , Belgium : Katholieke Universiteit Leuven, (Paper MP8–01.25) .
  • Spjøtvold , J , Tøndel , P and Johansen , TA . 2005 . “ Unique polyhedral representations to continuous selections for convex multi-parametric quadratic programs ” . In Proceedings 2005 American Control Conference 816 – 821 . Portland, Oregon, , USA
  • van Egmond , R , Olsder , G and van Zuylen , H . 1999 . “ A new way to optimise network traffic control using maxplus algebra ” . In Proceedings of the 78th Annual Meeting of the Transportation Research Board Washington, DC paper 660

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.