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.
Mots-clés : Parameter estimation, system identification, back and forth nudging, output error minimization
@article{COCV_2018__24_1_265_0,
author = {Aalto, Atte},
title = {Iterative observer-based state and parameter estimation for linear systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {265--288},
publisher = {EDP-Sciences},
volume = {24},
number = {1},
year = {2018},
doi = {10.1051/cocv/2017005},
mrnumber = {3843185},
zbl = {1396.93114},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2017005/}
}
TY - JOUR AU - Aalto, Atte TI - Iterative observer-based state and parameter estimation for linear systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 265 EP - 288 VL - 24 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2017005/ DO - 10.1051/cocv/2017005 LA - en ID - COCV_2018__24_1_265_0 ER -
%0 Journal Article %A Aalto, Atte %T Iterative observer-based state and parameter estimation for linear systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 265-288 %V 24 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2017005/ %R 10.1051/cocv/2017005 %G en %F COCV_2018__24_1_265_0
Aalto, Atte. Iterative observer-based state and parameter estimation for linear systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 1, pp. 265-288. doi : 10.1051/cocv/2017005. http://archive.numdam.org/articles/10.1051/cocv/2017005/
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