| Issue |
ESAIM: COCV
Volume 24, Number 1, January-March 2018
|
|
|---|---|---|
| Page(s) | 265 - 288 | |
| DOI | https://doi.org/10.1051/cocv/2017005 | |
| Published online | 22 January 2018 | |
Iterative observer-based state and parameter estimation for linear systems★
1
Inria, Université Paris–Saclay,
1 rue Honoré d’Estienne d’Orves ;
91120
Palaiseau, France
2
LMS, École Polytechnique,
CNRS, Université Paris–Saclay, France
a Corresponding author: atte.ej.aalto@gmail.com
Received:
22
September
2016
Accepted:
19
January
2017
We propose an iterative method for joint state and parameter estimation using measurements on a time interval [0, T] for systems that are backward output stabilizable. Since this time interval is fixed, errors in initial state may have a big impact on the parameter estimate. We propose to use the back and forth nudging (BFN) method for estimating the system’s initial state and a Gauss–Newton step between BFN iterations for estimating the system parameters. Taking advantage of results on the optimality of the BFN method, we show that for systems with skew-adjoint generators, the initial state and parameter estimate minimizing an output error cost functional is an attractive fixed point for the proposed method. We treat both linear source estimation and bilinear parameter estimation problems.
Mathematics Subject Classification: 93B30 / 35R30 / 93C05
Key words: Parameter estimation / system identification / back and forth nudging / output error minimization
© EDP Sciences, SMAI 2018
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