Non-asymptotic state estimation for a class of linear time-varying systems with unknown inputs

D. Y. Liu; T. M. Laleg-Kirati; W. Perruquetti; O. Gibaru

doi:10.3182/20140824-6-za-1003.02036

Non-asymptotic state estimation for a class of linear time-varying systems with unknown inputs

D. Y. Liu, T. M. Laleg-Kirati, W. Perruquetti, O. Gibaru

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

46 Scopus citations

Abstract

In this paper, we extend the modulating functions method to estimate the state and the unknown input of a linear time-varying system defined by a linear differential equation. We first estimate the unknown input by taking a truncated Jacobi orthogonal series expansion with unknown coefficients which can be estimated by the modulating functions method. Then, we estimate the state by using extended modulating functions and the estimated input. Both input and state estimators are given by exact integral formulae involving modulating functions and the noisy output. Hence, estimations at different instants can be non-asymptotically obtained using a sliding window of finite length. Numerical results are given to show the accuracy and the robustness of the proposed estimators against corrupting noises.

Original language	English (US)
Title of host publication	19th IFAC World Congress IFAC 2014, Proceedings
Editors	Edward Boje, Xiaohua Xia
Publisher	IFAC Secretariat
Pages	3732-3738
Number of pages	7
ISBN (Electronic)	9783902823625
DOIs	https://doi.org/10.3182/20140824-6-za-1003.02036
State	Published - 2014
Event	19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014 - Cape Town, South Africa Duration: Aug 24 2014 → Aug 29 2014

Publication series

Name	IFAC Proceedings Volumes (IFAC-PapersOnline)
Volume	19
ISSN (Print)	1474-6670

Other

Other	19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014
Country/Territory	South Africa
City	Cape Town
Period	08/24/14 → 08/29/14

Bibliographical note

Publisher Copyright:
© IFAC.

Keywords

Linear time-varying systems
Modulating functions method
Non-asymptotic estimation
State estimation
Unknown input

ASJC Scopus subject areas

Control and Systems Engineering

Access to Document

10.3182/20140824-6-za-1003.02036

Cite this

Liu, D. Y., Laleg-Kirati, T. M., Perruquetti, W., & Gibaru, O. (2014). Non-asymptotic state estimation for a class of linear time-varying systems with unknown inputs. In E. Boje, & X. Xia (Eds.), 19th IFAC World Congress IFAC 2014, Proceedings (pp. 3732-3738). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 19). IFAC Secretariat. https://doi.org/10.3182/20140824-6-za-1003.02036

@inproceedings{3094be21c9234d798f220a3dd6598056,

title = "Non-asymptotic state estimation for a class of linear time-varying systems with unknown inputs",

abstract = "In this paper, we extend the modulating functions method to estimate the state and the unknown input of a linear time-varying system defined by a linear differential equation. We first estimate the unknown input by taking a truncated Jacobi orthogonal series expansion with unknown coefficients which can be estimated by the modulating functions method. Then, we estimate the state by using extended modulating functions and the estimated input. Both input and state estimators are given by exact integral formulae involving modulating functions and the noisy output. Hence, estimations at different instants can be non-asymptotically obtained using a sliding window of finite length. Numerical results are given to show the accuracy and the robustness of the proposed estimators against corrupting noises.",

keywords = "Linear time-varying systems, Modulating functions method, Non-asymptotic estimation, State estimation, Unknown input",

author = "Liu, {D. Y.} and Laleg-Kirati, {T. M.} and W. Perruquetti and O. Gibaru",

note = "Publisher Copyright: {\textcopyright} IFAC.; 19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014 ; Conference date: 24-08-2014 Through 29-08-2014",

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Liu, DY, Laleg-Kirati, TM, Perruquetti, W & Gibaru, O 2014, Non-asymptotic state estimation for a class of linear time-varying systems with unknown inputs. in E Boje & X Xia (eds), 19th IFAC World Congress IFAC 2014, Proceedings. IFAC Proceedings Volumes (IFAC-PapersOnline), vol. 19, IFAC Secretariat, pp. 3732-3738, 19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014, Cape Town, South Africa, 08/24/14. https://doi.org/10.3182/20140824-6-za-1003.02036

Non-asymptotic state estimation for a class of linear time-varying systems with unknown inputs. / Liu, D. Y.; Laleg-Kirati, T. M.; Perruquetti, W. et al.
19th IFAC World Congress IFAC 2014, Proceedings. ed. / Edward Boje; Xiaohua Xia. IFAC Secretariat, 2014. p. 3732-3738 (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 19).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - In this paper, we extend the modulating functions method to estimate the state and the unknown input of a linear time-varying system defined by a linear differential equation. We first estimate the unknown input by taking a truncated Jacobi orthogonal series expansion with unknown coefficients which can be estimated by the modulating functions method. Then, we estimate the state by using extended modulating functions and the estimated input. Both input and state estimators are given by exact integral formulae involving modulating functions and the noisy output. Hence, estimations at different instants can be non-asymptotically obtained using a sliding window of finite length. Numerical results are given to show the accuracy and the robustness of the proposed estimators against corrupting noises.

AB - In this paper, we extend the modulating functions method to estimate the state and the unknown input of a linear time-varying system defined by a linear differential equation. We first estimate the unknown input by taking a truncated Jacobi orthogonal series expansion with unknown coefficients which can be estimated by the modulating functions method. Then, we estimate the state by using extended modulating functions and the estimated input. Both input and state estimators are given by exact integral formulae involving modulating functions and the noisy output. Hence, estimations at different instants can be non-asymptotically obtained using a sliding window of finite length. Numerical results are given to show the accuracy and the robustness of the proposed estimators against corrupting noises.

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Non-asymptotic state estimation for a class of linear time-varying systems with unknown inputs

Abstract

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Bibliographical note

Keywords

ASJC Scopus subject areas

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