Interval analysis for guaranteed non-linear parameter and state estimation

Mathematical and Computer Modelling of Dynamical Systems

Volumn 11, Issue 2, 2005, Pages 171-181

  Kieffer, Michel ^a   Walter, Eric ^a  

^a UNIV PARIS SUD   (France)

Author keywords

Bounded errors; Identification; Interval analysis; Non linear estimation; Parameter bounding; State bounding

Indexed keywords

BOUNDED ERRORS; INTERVAL ANALYSIS; NON-LINEAR ESTIMATION; PARAMETER BOUNDING; STATE BOUNDING;

IDENTIFICATION (CONTROL SYSTEMS); STATE ESTIMATION; TOOLS;

PARAMETER ESTIMATION;

EID: 22944455883     PISSN: 13873954     EISSN: None     Source Type: Journal    
DOI: 10.1080/13873950500068807     Document Type: Article

References (23)

1. Milanese, M., Norton, J., Piet-Lahanier, H. and Walter, E. (Eds), 1996, Bounding Approaches to System Identification (New York: Plenum Press).
2. Moore, R.E., 1959, Automatic error analysis in digital computation. Technical Report LMSD-48421, Lockheed Missiles and Space Co., Palo Alto, CA.
3. Neumaier, A., 1990, Interval Methods for Systems of Equations (Cambridge: Cambridge University Press).
4. Hansen, E.R., 1992, Global Optimization Using Interval Analysis (New York: Marcel Dekker).
5. Ratschek, H. and Rokne, J., 1988, New Computer Methods for Global Optimization (Chichester: Ellis Horwood).
6. Jaulin, L. and Walter, E., 1993, Automatica, 29, 1053-1064.
7. Berz, M. and Makino, K., 1998, Reliable Computing, 4, 361-369.
8. Lohner, R., 1992, In J.R. Cash and I. Gladwell (Eds) Computational Ordinary Differential Equations, pages 425-435 (Oxford: Clarendon Press).
9. Moore, R.E., 1979, Methods and Applications of Interval Analysis (Philadelphia: SIAM).
10. Nedialkov, N.S. and Jackson, K.R., 2001, In U. Kulisch, R. Lohner, and A. Facius (Eds) Perspectives on Enclosure Methods, pages 219-264 (Vienna: Springer-Verlag).
11. Kearfott, R.B., 1995, ACM Transactions on Mathematical Software, 21, 63-78.
12. Klatte, R., Kulisch, U., Wieth, A., Lawo, C. and Rauch, M., 1993, C-xsc: A C+ + A Class Library for Extended Scientific Computing (Berlin: Springer-Verlag).
13. Rump, S.M., 2001, In J.∼Grabmeier, E. Kaltofen, and V. Weispfennig (Eds) Handbook of Computer Algebra: Foundations, Applications, Systems (Heidelberg: Springer-Verlag).
14. Jaulin, L., Kieffer, M., Didrit, O. and Walter, E., 2001, Applied Interval Analysis (London: Springer-Verlag).
15. Ratschek, H. and Rokne, J., 1984, Computer Methods for the Range of Functions (Chichester: Ellis Horwood).
16. Chiriaev, D. and Walster, G.W., 1998, Interval arithmetic specification. Available online at: http://www.mscs.edu/globsol/walster-papers.html.
17. Lerch, M. and Wolff von Gudenberg, J., 2000, fi_lib+ +: Specification, implementation and test of a library for extended interval arithmetic. In Proc. 4th Conference on Real Numbers and Computers, Dagstuhl, Germany. Available online at: http://www.imada.sdu.dk/\symbol{126}kornerup/RNC4/papers/p03.ps.
18. Kieffer, M., Jaulin, L. and Walter, E., 2002, International Journal of Adaptative Control and Signal Processing, 6, 193-218.
19. Braems, I., Berthier, F., Jaulin, L., Kieffer, M. and Walter, E., 2001, Journal of Electroanalytical Chemistry, 495, 1-9.
20. Braems, I., Jaulin, L., Kieffer, M., Ramdani, N. and Kieffer, M., 2003, Reliable parameter estimation in presence of uncertain variables that are not estimated. In Proceedings of the 13th IFAC Symposium on System Identification SYSID 2003, Rotterdam, The Netherlands, Elsevier Science Ltd, Oxford, pages 1856-1861.
21. Kieffer, M., Jaulin, L., Walter, E. and Meizel, D., 2000, Reliable Computing, 6, 337-362.
22. Kieffer, M., Jaulin, L., Walter, E. and Meizel, D., 1999, Guaranteed mobile robot tracking using interval analysis. In Proc. MISC'99 Workshop on Applications of Interval Analysis to Systems and Control, pages 347-359, Girona, Spain.
23. Kieffer, M., and Walter, E. 2004, Guaranteed nonlinear state estimator for cooperative systems. Numerical Algorithms, 37, 187-198.