RECURRENT REPRESENTATION FOR NON-STATIONARY PARAMETER ESTIMATE OF LEAST SQUARES METHOD WITH LEAST DEVIATIONS FROM "ATTRACTION" POINTS FOR BILINEAR DYNAMIC SYSTEMS

Journal of Numerical and Applied Mathematics ◽

10.17721/2706-9699.2019.2.04 ◽

2019 ◽

pp. 32-38

Author(s):

Alexander Slabospitsky

Keyword(s):

Least Squares ◽

Dynamic Systems ◽

Unknown Parameter ◽

Least Squares Method ◽

Parameter Estimate ◽

Parameter Estimates ◽

Forgetting Factor ◽

Recurrent Algorithm ◽

Discrete Dynamic System ◽

Variable Forgetting Factor

The estimation problem of non-stationary parameter matrices is considered for bilinear discrete dynamic system in the case when for these unknown parameter matrices their ‘attraction’ points are known at any moment. Explicit and recurrent forms of representation are obtained for these parameter estimates of the least squares method with variable forgetting factor and least deviation norm from ‘attraction’ points under non-classical assumptions. The recurrent algorithm is also proposed for corresponding weighted residual sum of squares.

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Recurrent algorithm for non-stationary parameter estimation by least squares method with least deviations from ‘attraction’ points for bilinear discrete dynamic systems

Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics ◽

10.17721/1812-5409.2018/3.10 ◽

2018 ◽

pp. 71-74

Author(s):

A. Slabospitsky

Keyword(s):

Least Squares ◽

Least Squares Method ◽

Inverse Operator ◽

Forgetting Factor ◽

Recurrent Algorithm ◽

Discrete Dynamic ◽

Discrete Dynamic System ◽

Least Squares Estimate ◽

Variable Forgetting Factor ◽

Pseudo Inverse

The estimation problem of slowly time-varying parameter matrices is considered for bilinear discrete dynamic system in the presence of disturbances. The least squares estimate with variable forgetting factor is investigated for this object in non-classical situation when this estimate may be not unique and additionally ‘attraction’ points for unknown parameter matrices are given at any moment. The set of all above-mentioned estimates of these unknown matrices is defined through the Moore-Penrose pseudo-inverse operator. The least squares estimate with variable forgetting factor and least deviation norm from given ‘attraction’ point at any moment is proposed as unique estimate on this set of all estimates. The explicit form of representation is obtained for this unique estimate of the parameter matrices by the least squares method with variable forgetting factor and least deviation norm from given ‘attraction’ points under non-classical assumptions. The recurrent algorithm for this estimate is also derived which does not require the usage of the matrix pseudo-inverse operator.

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State Estimation for Atomic Clocks System under Non-stationary Noise Using Recursive Least-squares Method with Vector-type Variable Forgetting Factor

Transactions of the Society of Instrument and Control Engineers ◽

10.9746/sicetr.56.45 ◽

2020 ◽

Vol 56 (2) ◽

pp. 45-50

Author(s):

Shunichiro MABUCHI ◽

Masato HIRANO ◽

Shuichi ADACHI ◽

Tetsuya IDO ◽

Yuko HANADO

Keyword(s):

Least Squares ◽

State Estimation ◽

Least Squares Method ◽

Recursive Least Squares ◽

Forgetting Factor ◽

Stationary Noise ◽

Vector Type ◽

Type Variable ◽

Recursive Least Squares Method ◽

Variable Forgetting Factor

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Identification of Parameters in Li-Ion Battery Model by Least Squares Method with Variable Forgetting Factor

International Journal of Computational Methods ◽

10.1142/s0219876219500270 ◽

2019 ◽

Vol 17 (07) ◽

pp. 1950027

Author(s):

Xiong Wei ◽

Mo Yimin ◽

Zhang Feng

Keyword(s):

Least Squares ◽

Electric Vehicle ◽

Least Squares Method ◽

Model Parameters ◽

Identification Algorithm ◽

Li Ion Battery ◽

Forgetting Factor ◽

Battery Model ◽

Li Ion ◽

Variable Forgetting Factor

The inaccuracy of the battery model of an electric vehicle will seriously affect the safe operation of the electric vehicle. This paper aims to design a better identification method for Li-ion battery model parameters to improve the accuracy of the model. A least squares method was developed with variable forgetting factor (VFF) to identify the parameters of a second-order resistor-recapacitor (RC) model of Li-ion battery. After using the identified parameters, the battery model can reliably and accurately track the variability of the actual working state of the energy storage system. Results at different values of the forgetting factor were analyzed to determine the principle for selecting the value of the forgetting factor, and disclose the impacts of the factor values on model accuracy. Finally, the proposed identification algorithm was tested through comparison between results of the model simulation and experimental data. This method provides an important basis for subsequent development of accurate state-of-charge (SOC) and state-of-health (SOH) estimation algorithms.

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