Free access
Issue
ESAIM: COCV
Volume 15, Number 1, January-March 2009
Page(s) 189 - 204
DOI http://dx.doi.org/10.1051/cocv:2008025
Published online 23 January 2009
  1. F. Blanchini, Set invariance in control. Automatica 35 (1999) 1747–1767. [CrossRef] [MathSciNet]
  2. J.M. Bravo, D. Limon, T. Alamo and E.F. Camacho, On the computation of invariant sets for constrained nonlinear systems: An interval arithmetic approach. Automatica 41 (2005) 1583–1589. [CrossRef] [MathSciNet]
  3. M. Cannon, V. Deshmukh and B. Kouvaritakis, Nonlinear model predictive control with polytopic invariant sets. Automatica 39 (2003) 1487–1494. [CrossRef] [MathSciNet]
  4. H. Chen and F. Allgower, A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica 34 (1998) 1205–1217. [CrossRef] [MathSciNet]
  5. E. Gardenes, M.A. Sainz, L. Jorba, R. Calm, R. Estela, H. Mielgo and A. Trepat, Modal intervals. Reliab. Comput. 7 (2001) 77–111. [CrossRef] [MathSciNet]
  6. E. Hansen, Global Optimization Using Interval Analysis. Marcel Dekker, New York (1992).
  7. P. Herrero, M.A. Sainz, J. Vehí and L. Jaulin, Quantified set inversion algorithm with applications to control. Reliab. Comput. 11 (2005) 369–382. [CrossRef] [MathSciNet]
  8. L. Jaulin, M. Kieffer, O. Didrit and E. Walter, Applied Interval Analysis. Springer, London (2001).
  9. E. Kaucher, Interval analysis in the extended interval space IR, Comput. Suppl. 2. Springer, Heidelberg (1980) 33–49.
  10. E.C. Kerrigan, Robust Constraint Satisfaction: Invariant Sets and Predictive Control. Ph.D. thesis, University of Cambridge, USA (2000).
  11. J. Klamaka, Controllability of nonlinear discrete systems. Internat. J. Appl. Math. Comput. Sci. 12 (2002) 173–180.
  12. W. Kühn, Rigorously computed orbits of dynamical systems without the wrapping effect. Computing 61 (1998) 47–67. [CrossRef] [MathSciNet]
  13. D. Limon, T. Alamo and E.F. Camacho, Robust MPC control based on a contractive sequence of sets, in Proc. 42nd IEEE Conf. Dec. Control (2003) 3706–3711.
  14. D.Q. Mayne and W.R. Schroeder, Robust time-optimal control of constrained linear systems. Automatica 33 (1997) 2103–2118. [CrossRef] [MathSciNet]
  15. R. Moore, Interval Analysis. Prentice Hall, Englewood Cliffs, NJ (1966).
  16. S.V. Rakovic, E.C. Kerrigan and D.Q. Mayne, Reachability computations for constrained discrete-time systems with state- and input-dependent disturbances, in Proc. 42nd IEEE Conf. Dec. Control (2003) 3905–3910.
  17. S.P. Shary, A new technique in systems analysis under interval uncertainty and ambiguity. Reliab. Comput. 8 (2002) 321–418. [CrossRef] [MathSciNet]
  18. A.N. Sirotin and A.M. Formal'skii, Reachability and controllability of discrete-time systems under control actions bounded in magnitude and norm. Autom. Remote Control 64 (2003) 1844–1857. [CrossRef] [MathSciNet]