no. 2
Instrumental variables and LSM in continuous-time parameter estimation
Escobar, Jesica1 ; Enqvist, Martin2
1 School of Mechanical and Electrical Engineering, National Polytechnic Institute, Department of Control Automatics, Av. IPN Col. Lindavista 07738 Mexico City, Mexico.
2 Division of Automatic Control, University of Linköping, 581 83 Linköping, Sweden.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 2, pp. 427-442.

In this paper the main goal is to compare the instrumental variables and the least squares methods applied to parameter estimation in continuous-time systems, avoiding any preliminary discretization of the process, and to analyse which method is more suitable for estimation in continuous-time under stochastic perturbations. A numerical example illustrates the effectiveness of the algorithms.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2015052
Classification : 93E03, 60H10, 93E10
Mots clés : Parameter estimation, continuous-time, stochastic systems, instrumental variable
Escobar, Jesica 1 ; Enqvist, Martin 2

1 School of Mechanical and Electrical Engineering, National Polytechnic Institute, Department of Control Automatics, Av. IPN Col. Lindavista 07738 Mexico City, Mexico.
2 Division of Automatic Control, University of Linköping, 581 83 Linköping, Sweden. 
@article{COCV_2017__23_2_427_0,
     author = {Escobar, Jesica and Enqvist, Martin},
     title = {Instrumental variables and {LSM} in continuous-time parameter estimation},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {427--442},
     publisher = {EDP-Sciences},
     volume = {23},
     number = {2},
     year = {2017},
     doi = {10.1051/cocv/2015052},
     mrnumber = {3608087},
     zbl = {1358.93159},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv/2015052/}
}
TY  - JOUR
AU  - Escobar, Jesica
AU  - Enqvist, Martin
TI  - Instrumental variables and LSM in continuous-time parameter estimation
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2017
SP  - 427
EP  - 442
VL  - 23
IS  - 2
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/cocv/2015052/
DO  - 10.1051/cocv/2015052
LA  - en
ID  - COCV_2017__23_2_427_0
ER  - 
%0 Journal Article
%A Escobar, Jesica
%A Enqvist, Martin
%T Instrumental variables and LSM in continuous-time parameter estimation
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2017
%P 427-442
%V 23
%N 2
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/cocv/2015052/
%R 10.1051/cocv/2015052
%G en
%F COCV_2017__23_2_427_0
Escobar, Jesica; Enqvist, Martin. Instrumental variables and LSM in continuous-time parameter estimation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 2, pp. 427-442. doi : 10.1051/cocv/2015052. http://www.numdam.org/articles/10.1051/cocv/2015052/

R. Bowden and A. Darrel, Instrumental Variables. Cambridge University Press (1984). | Zbl

I. Chairez, Differential neuro-fuzzy controller for uncertain nonlinear systems. IEEE Trans. Fuzzy Systems 21 (2013) 369–384. | DOI

J. Davila, L. Fridman and A. Levant, Second-Order Sliding-Mode Observers for Mechanical Systems. IEEE Trans. Autom. Control 50 (2005) 1785–1789. | DOI | MR | Zbl

M.H.A. Davis, Linear Estimation and Stochastic Control. Chapman and Hall, London (1977). | MR | Zbl

C. Edwards, S. Spurgeon, Sliding Mode Control. Taylor and Francis, London (1998).

J. Escobar and A. Poznyak, Time-varying matrix estimation in stochastic continuous-time models under colored noise using LSM with forgetting factor. Int. J. Syst. Sci. 42 (2011) 2009–2020. | DOI | MR | Zbl

J. Escobar and A. Poznyak, Robust Continuous-Time Matrix Estimation under Dependent Noise Perturbations: Sliding Modes Filtering and LSM with Forgetting. Circuits Syst. Signal Process. 28 (2009) 257–282. | DOI | MR | Zbl

T. Gard, Introduction to Stochastic Differential Equations. Marcel Dekker, New York (1988). | MR | Zbl

M. Gilson, H. Garnier and Van Den P. Hof, Instrumental variable methods for continuous-time identification in closed-loop. Proc. Amer. Control Conf. 3 (2004) 2846–2851.

P. Kumar and P. Varaiya, Stochastic Systems: Estimation, Identification and Adaptive Control. Prentice Hall, Englewood Cliffs, NJ (1986). | Zbl

J.-N. Juan, Applied System Identification. Prentice Hall, Englewood Cliffs, New Jersey (1994). | Zbl

X. Liu, J. Wang and W.X. Zheng, Convergence analysis of refined instrumental variable method for continuous-time system identification. IET Control Theory Appl. 5 (2011) 868–877. | DOI | MR

L. Ljung, System Identification: Theory for the User. Prentice Hall, Upper Saddle River, NJ (1999). | Zbl

M. Mossberg, High-Accuracy Instrumental Variable Identification of Continuous-Time Autoregressive Processes From Irregularly Sampled Noisy Data. IEEE Trans. Signal Process. 56 (2008) 4087–4091. | DOI | MR | Zbl

R. Pintelon and J. Schoukens, System Identification, A Frequency Domain Approach. IEEE Press (2001).

A. Poznyak, J. Escobar and Y. Shtessel, Sliding modes time varying matrix identification for stochastic systems. Int. J. Syst. Sci. 38 (2007) 847–859. | DOI | MR | Zbl

D.I. Rosas Almeida, J. Alvarez and L. Fridman, Robust observation and Identification of nDOF Lagrangian systems. Int. J. Robust Nonlin. Control 17 (2007) 842–861. | DOI | MR | Zbl

V. Utkin, Sliding Modes Control and their Applications to Variable Structure Systems. MIR (1978).

V. Utkin, Sliding Modes in Control and Optimization. Springer-Verlag, Berlin, Heidelberg (1992). | MR | Zbl

Cité par Sources :