Interval analysis for guaranteed nonlinear parameter estimation

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 36, Issue 16, 2003, Pages 249-260

  Walter, Eric ^a   Kieffer, Michel ^a  

^a UNIV PARIS SUD   (France)

Author keywords

compartmental models; cooperativity; global optimization; identifiability; interval analysis; nonlinear estimation; parameter bounding

Indexed keywords

COST FUNCTIONS; GLOBAL OPTIMIZATION; ITERATIVE METHODS; NONLINEAR ANALYSIS;

COMPARTMENTAL MODEL; COOPERATIVITY; IDENTIFIABILITY; INTERVAL ANALYSIS; NON-LINEAR ESTIMATION; PARAMETER BOUNDING;

PARAMETER ESTIMATION;

EID: 17744389539     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1016/S1474-6670(17)34770-5     Document Type: Conference Paper

References (30)

1. E. Davis Constraint propagation with interval labels Artificial Intelligence 32 3 1987 281 331
2. K. Godfrey Compartimental Models and Their Application 1983 Academic Press London
3. J.L. Gouzé, A. Rapaport, and Z.M. Hadj-Sadok Interval observers for uncertain biological systems Journal of Ecological Modelling 133 2000 45 56
4. A. Griewank, and G.F. Corliss Automatic Differentiation of Algorithms: Theory, Implementation and Applications 1991 SIAM Philadelphia, PA
5. R. Hammer, M. Hocks, U. Kulisch, and D. Ratz C++ Toolbox for Verified Computing 1995 Springer-Verlag Berlin
6. E.R. Hansen On solving systems of equations using interval arithmetic Mathematical Computing 22 1968 374 384
7. E.R. Hansen Global Optimization Using Interval Analysis 1992 Marcel Dekker New York, NY
8. J. Hoefkens, M. Berz, and K. Makino Efficient high-order methods for ODEs and DAEs G. Corliss, C. Faure, A. Griewank, Automatic Differentiation: From Simulation to Optimization 2001 Springer-Verlag New-York, NY. 341 351
9. E. Hyvönen Constraint reasoning based on interval arithmetic: the tolerance propagation approach Artificial Intelligence 58 1-3 1992 71 112
10. L. Jaulin Nonlinear bounded-error state estimation of continuous-time systems Automatica 38 2002 1079 1082
11. L. Jaulin, and E. Walter Set inversion via interval analysis for nonlinear bounded-error estimation Automatica 29 4 1993 1053 1064
12. L. Jaulin, M. Kieffer, I. Braems, and E. Walter Guaranteed nonlinear estimation using constraint propagation on sets International Journal of Control 74 18 2001 1772 1782
13. L. Jaulin, M. Kieffer, O. Didrit, and E. Walter Applied Interval Analysis 2001 Springer-Verlag London
14. R.B. Kearfott Rigorous Global Search: Continuous Problems 1996 Kluwer Dordrecht, the Netherlands
15. M. Kieffer, and E. Walter Interval analysis for guaranteed nonlinear parameter estimation A.C. Atkinson, L. Pronzato, H.P. Wynn, MODA 5-Advances in Model-Oriented Data Analysis and Experiment Design 1998 Physica-Verlag Heidelberg 115 125
16. M. Kieffer, L. Jaulin, and E. Walter Guaranteed recursive nonlinear state estimation using interval analysis Proceedings of the 37th IEEE Conference on Decision and Control Tampa, FL. 1998 3966 3971
17. R. Lohner Computation of guaranteed enclosures for the solutions of ordinary initial an boundary value-problem J.R. Cash, I. Gladwell, Computational Ordinary Differential Equations 1992 Clarendon Press Oxford 425 435
18. M. Milanese, J. Norton, H. Piet-Lahanier, and E. Walter Bounding Approaches to System Identification 1996 Plenum Press New York, NY
19. R.E. Moore Automatic error analysis in digital computation Technical Report LMSD-48421 Palo Alto, CA. 1959 Lockheed Missiles and Space Co
20. R.E. Moore Methods and Applications of Interval Analysis 1979 SIAM Philadelphia, PA
21. N.S. Nedialkov, and K.R. Jackson Methods for initial value problems for ordinary differential equations U. Kulisch, R. Lohner, A. Facius, Perspectives on Enclosure Methods 2001 Springer-Verlag Vienna 219 264
22. A. Neumaier Interval Methods for Systems of Equations 1990 Cambridge University Press Cambridge, UK
23. L.B. Rall Automatic Differentiation: Techniques and Applications Lecture Notes in Computer Science 120 1981 Springer-Verlag Berlin of
24. L.B. Rall, and G.F. Corliss Automatic differentiation: Point and interval AD P.M. Pardalos, C.A. Floudas, Encyclopedia of Optimization 1999 Kluwer Dordrecht, the Netherlands
25. H. Ratschek, and J. Rokne Computer Methods for the Range of Functions 1984 Ellis Horwood Chichester, UK
26. H. Ratschek, and J. Rokne New Computer Methods for Global Optimization 1988 Ellis Horwood Chichester, UK
27. D.J. Sam-Haroud, and B. Faltings Consistency techniques for continuous constraints Constraints 1 1-2 1996 85 118
28. H.L. Smith Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems Mathematical Surveys and Monographs 41 1995 American Mathematical Society Providence, RI of
29. P. van Hentenryck, L. Michel, and F. Benhamou Newton: Constraint programming over nonlinear constraints Science of Computer Programming 30 1-2 1998 83 118
30. E. Walter Identifiability of State Space Models 1982 Springer-Verlag Berlin