Nonlinear Parameter and State Estimation for Cooperative Systems in a Bounded-Error Context

This paper is about guaranteed nonlinear parameter and state estimation. Sets are computed that contain all possible values of the parameter (or state) vector given bounds on the acceptable errors. The main requirement is that the dynamical equations describing the evolution of the model can be bounded between cooperatives models, i.e., models such that the off-diagonal entries of their Jacobian matrix remain positive. The performances and limitations of the techniques proposed are illustrated on a nonlinear compartmental model.

[1]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[2]  Fred C. Schweppe,et al.  Uncertain dynamic systems , 1973 .

[3]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .

[4]  Y. F. Huang,et al.  On the value of information in system identification - Bounded noise case , 1982, Autom..

[5]  Editors , 1986, Brain Research Bulletin.

[6]  E. Walter,et al.  Exact recursive polyhedral description of the feasible parameter set for bounded-error models , 1989 .

[7]  S. Häkkinen.  7 – Models and Their Applications to Polar Oceanography , 1990 .

[8]  Eldon Hansen,et al.  Global optimization using interval analysis , 1992, Pure and applied mathematics.

[9]  F. Chernousko.  State Estimation for Dynamic Systems , 1993 .

[10]  Eric Walter,et al.  Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis , 1993 .

[11]  Eric Walter,et al.  Set inversion via interval analysis for nonlinear bounded-error estimation , 1993, Autom..

[12]  Hal L. Smith,et al.  Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith , 1995 .

[13]  A. Kurzhanski,et al.  Ellipsoidal Calculus for Estimation and Control , 1996 .

[14]  Eric Walter,et al.  Identification of Parametric Models: from Experimental Data , 1997 .

[15]  Witold Pedrycz,et al.  Bounding approaches to system identification , 1997 .

[16]  Michel Kieffer,et al.  Estimation ensembliste par analyse par intervalles Application à la localisation d'un véhicule , 1999 .

[17]  J. Gouzé,et al.  Interval observers for uncertain biological systems , 2000 .

[18]  M. Berz,et al.  Efficient high-order methods for ODEs and DAEs , 2000 .

[19]  Eric Walter,et al.  Guaranteed Set Computation with Subpavings , 2001 .

[20]  Luc Jaulin,et al.  Applied Interval Analysis , 2001, Springer London.

[21]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[22]  Martin Berz,et al.  Verified High-Order Integration of DAEs and Higher-Order ODEs , 2001 .

[23]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[24]  Eric Walter,et al.  Guaranteed non-linear estimation using constraint propagation on sets , 2001 .

[25]  Luc Jaulin,et al.  Nonlinear bounded-error state estimation of continuous-time systems , 2002, Autom..

[26]  Eric Walter,et al.  Guaranteed recursive non‐linear state bounding using interval analysis , 2002 .

[27]  Eric Walter,et al.  Guaranteed Nonlinear State Estimator for Cooperative Systems , 2004, Numerical Algorithms.