Abstract
This article presents an optimal estimator for discrete-time systems disturbed by output white noise, where the proposed algorithm identifies the parameters of a Multiple Input Single Output LPV State Space model. This is an LPV version of a class of algorithms proposed elsewhere for identifying LTI systems. These algorithms use the matchable observable linear identification parameterization that leads to an LTI predictor in a linear regression form, where the ouput prediction is a linear function of the unknown parameters. With a proper choice of the predictor parameters, the optimal prediction error estimator can be approximated. In a previous work, an LPV version of this method, that also used an LTI predictor, was proposed; this LTI predictor was in a linear regression form enablin, in this way, the model estimation to be handled by a Least-Squares Support Vector Machine approach, where the kernel functions had to be filtered by an LTI 2D-system with the predictor dynamics. As a result, it can never approximate an optimal LPV predictor which is essential for an optimal prediction error LPV estimator. In this work, both the unknown parameters and the state-matrix of the output predictor are described as a linear combination of a finite number of basis functions of the scheduling signal; the LPV predictor is derived and it is shown to be also in the regression form, allowing the unknown parameters to be estimated by a simple linear least squares method. Due to the LPV nature of the predictor, a proper choice of its parameters can lead to the formulation of an optimal prediction error LPV estimator. Simulated examples are used to assess the effectiveness of the algorithm. In future work, optimal prediction error estimators will be derived for more general disturbances and the LPV predictor will be used in the Least-Squares Support Vector Machine approach.
| Original language | English (US) |
|---|---|
| Title of host publication | 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 4626-4631 |
| Number of pages | 6 |
| Volume | 2018-January |
| ISBN (Electronic) | 9781509028733 |
| DOIs | |
| State | Published - Jan 18 2018 |
| Event | 56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia Duration: Dec 12 2017 → Dec 15 2017 |
Other
| Other | 56th IEEE Annual Conference on Decision and Control, CDC 2017 |
|---|---|
| Country | Australia |
| City | Melbourne |
| Period | 12/12/17 → 12/15/17 |
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ASJC Scopus subject areas
- Decision Sciences (miscellaneous)
- Industrial and Manufacturing Engineering
- Control and Optimization
Cite this
LPV system identification using the matchable observable linear identification approach. / Dos Santos, P. Lopes; Romano, R.; Azevedo-Perdicoulis, T. P.; Rivera, Daniel; Ramos, J. A.
2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Vol. 2018-January Institute of Electrical and Electronics Engineers Inc., 2018. p. 4626-4631.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - LPV system identification using the matchable observable linear identification approach
AU - Dos Santos, P. Lopes
AU - Romano, R.
AU - Azevedo-Perdicoulis, T. P.
AU - Rivera, Daniel
AU - Ramos, J. A.
PY - 2018/1/18
Y1 - 2018/1/18
N2 - This article presents an optimal estimator for discrete-time systems disturbed by output white noise, where the proposed algorithm identifies the parameters of a Multiple Input Single Output LPV State Space model. This is an LPV version of a class of algorithms proposed elsewhere for identifying LTI systems. These algorithms use the matchable observable linear identification parameterization that leads to an LTI predictor in a linear regression form, where the ouput prediction is a linear function of the unknown parameters. With a proper choice of the predictor parameters, the optimal prediction error estimator can be approximated. In a previous work, an LPV version of this method, that also used an LTI predictor, was proposed; this LTI predictor was in a linear regression form enablin, in this way, the model estimation to be handled by a Least-Squares Support Vector Machine approach, where the kernel functions had to be filtered by an LTI 2D-system with the predictor dynamics. As a result, it can never approximate an optimal LPV predictor which is essential for an optimal prediction error LPV estimator. In this work, both the unknown parameters and the state-matrix of the output predictor are described as a linear combination of a finite number of basis functions of the scheduling signal; the LPV predictor is derived and it is shown to be also in the regression form, allowing the unknown parameters to be estimated by a simple linear least squares method. Due to the LPV nature of the predictor, a proper choice of its parameters can lead to the formulation of an optimal prediction error LPV estimator. Simulated examples are used to assess the effectiveness of the algorithm. In future work, optimal prediction error estimators will be derived for more general disturbances and the LPV predictor will be used in the Least-Squares Support Vector Machine approach.
AB - This article presents an optimal estimator for discrete-time systems disturbed by output white noise, where the proposed algorithm identifies the parameters of a Multiple Input Single Output LPV State Space model. This is an LPV version of a class of algorithms proposed elsewhere for identifying LTI systems. These algorithms use the matchable observable linear identification parameterization that leads to an LTI predictor in a linear regression form, where the ouput prediction is a linear function of the unknown parameters. With a proper choice of the predictor parameters, the optimal prediction error estimator can be approximated. In a previous work, an LPV version of this method, that also used an LTI predictor, was proposed; this LTI predictor was in a linear regression form enablin, in this way, the model estimation to be handled by a Least-Squares Support Vector Machine approach, where the kernel functions had to be filtered by an LTI 2D-system with the predictor dynamics. As a result, it can never approximate an optimal LPV predictor which is essential for an optimal prediction error LPV estimator. In this work, both the unknown parameters and the state-matrix of the output predictor are described as a linear combination of a finite number of basis functions of the scheduling signal; the LPV predictor is derived and it is shown to be also in the regression form, allowing the unknown parameters to be estimated by a simple linear least squares method. Due to the LPV nature of the predictor, a proper choice of its parameters can lead to the formulation of an optimal prediction error LPV estimator. Simulated examples are used to assess the effectiveness of the algorithm. In future work, optimal prediction error estimators will be derived for more general disturbances and the LPV predictor will be used in the Least-Squares Support Vector Machine approach.
UR - http://www.scopus.com/inward/record.url?scp=85046150123&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85046150123&partnerID=8YFLogxK
U2 - 10.1109/CDC.2017.8264342
DO - 10.1109/CDC.2017.8264342
M3 - Conference contribution
AN - SCOPUS:85046150123
VL - 2018-January
SP - 4626
EP - 4631
BT - 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
PB - Institute of Electrical and Electronics Engineers Inc.
ER -