Guaranteed nonlinear state estimator for cooperative systems

Numerical Algorithms

Volumn 37, Issue 1-4 SPEC. ISS., 2004, Pages 187-198

  Kieffer, Michel ^a   Walter, Eric ^a  

^a UNIV PARIS SUD   (France)

Author keywords

bounded errors; cooperative models; interval observer; nonlinear models; set estimator; state estimator

Indexed keywords

EID: 10044224900     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:NUMA.0000049466.96588.a6     Document Type: Conference Paper

References (23)

1. V. Alcaraz-González, A. Genovesi, J. Harmand, A. González, A. Rapaport and J. Steyer, Robust exponential nonlinear interval observer for a class of lumped models useful in chemical and biochemical engineering. Application to a wastewater treatment process, in: Proc. of MISC'99 Workshop on Applications of Interval Analysis to Systems and Control, Girona, 24-26 February 1999, pp. 225-235.
2. F.L. Chernousko, State Estimation for Dynamic Systems (CRC Press, Boca Raton, 1994).
3. A. Gelb, Applied Optimal Estimation (MIT Press, Cambridge, 1974).
4. J.L. Gouzé, A. Rapaport and Z.M. Hadj-Sadok, Interval observers for uncertain biological systems, J. Ecological Modelling 133 (2000) 45-56.
5. Z.M. Hadj-Sadok, Modélisation et estimation dans les bioréacteurs; prise en compte des incertitudes: application au traitement de l'eau, Ph.D. thesis, Université de Nice, Sophia Antipolis (1999).
6. Z.M. Hadj-Sadok, J.L. Gouzé and A. Rapaport, State observers for uncertain models of activated sludge processes, in: CD-ROM of the IFAC-EurAgEng Internat. Workshop on Decision and Control in Waste Bio-Processing, Narbonne, 25-27 February 1998.
7. J. Hoefkens, M. Berz and K. Makino, Efficient high-order methods for ODEs and DAEs, in: Automatic Differentiation: From Simulation to Optimization, eds. G. Corliss, C. Faure and A. Griewank (Springer, New York, 2001) pp. 341-351.
8. J. Hoefkens, M. Berz and K. Makino, Verified high-order integration of DAEs and ODEs, in: Scientific Computing, Validated Numerics, Interval Methods, eds. W. Kraemer and J.W. von Gudenberg (Kluwer, Boston, 2001) pp. 281-292.
9. L. Jaulin, Nonlinear bounded-error state estimation of continuous-time systems, Automatica 38 (2002) 1079-1082.
10. L. Jaulin, M. Kieffer, I. Braems and E. Walter, Guaranteed nonlinear estimation using constraint propagation on sets, Internat. J. Control 74(18) (2001) 1772-1782.
11. L. Jaulin, M. Kieffer, O. Didrit and E. Walter, Applied Interval Analysis (Springer, London, 2001).
12. L. Jaulin and E. Walter, Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis, Math. Comput. Simulation 35(2) (1993) 123-137.
13. L. Jaulin and E. Walter, Set inversion via interval analysis for nonlinear bounded-error estimation, Automatica 29(4) (1993) 1053-1064.
14. M. Kieffer, Estimation ensembliste par analyse par intervalles, application à la localisation d'un véhicule, Ph.D. thesis, Université Paris-Sud, Orsay, France (1999).
15. M. Kieffer, L. Jaulin, I. Braems and E. Walter, Guaranteed set computation with subpavings, in: Scientific Computing, Validated Numerics, Interval Methods, eds. W. Kraemer and J.W. von Gudenberg (Kluwer, Boston, 2001) pp. 167-178.
16. M. Kieffer, L. Jaulin and E. Walter, Guaranteed recursive nonlinear state bounding using interval analysis, Internat. J. Adaptative Control Signal Process. 6(3) (2002) 193-218.
17. A. Kurzhanski and I. Valyi, Ellipsoidal Calculus for Estimation and Control (Birkhäuser, Boston, MA, 1997).
18. R. Lohner, Enclosing the solutions of ordinary initial and boundary value problems, in: Computer Arithmetic: Scientific Computation and Programming Languages, eds. E. Kaucher, U. Kulisch and C. Ullrich (BG Teubner, Stuttgart, 1987) pp. 255-286.
19. R. Lohner, Computation of guaranteed enclosures for the solutions of ordinary initial and boundary value-problem, in: Computational Ordinary Differential Equations, eds. J.R. Cash and I. Gladwell (Clarendon Press, Oxford, 1992) pp. 425-435.
20. M. Milanese, J. Norton, H. Piet-Lahanier and E. Walter, eds., Bounding Approaches to System Identification (Plenum Press, New York, 1996).
21. N.S. Nedialkov and K.R. Jackson, Methods for initial value problems for ordinary differential equations, in: Perspectives on Enclosure Methods (Springer, Vienna, 2001) pp. 219-264.
22. H.L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs, Vol. 41 (Amer. Math. Soc., Providence, 1995).
23. G. Stephanopoulos, Chemical Process Control. An Introduction to Theory and Practice (Prentice-Hall, Englewood Cliffs, 1984).