Order and structural dependence selection of LPV-ARX models revisited

Accurate parametric identification of Linear Parameter-Varying (LPV) systems requires an optimal prior selection of model order and a set of functional dependencies for the parameterization of the model coefficients. In order to address this problem for linear regression models, a regressor shrinkage method, the Non-Negative Garrote (NNG) approach, has been proposed recently. This approach achieves statistically efficient order and structural coefficient dependence selection using only measured data of the system. However, particular drawbacks of the NNG are that it is not applicable for large-scale over-parameterized problems due to computational limitations and that adequate performance of the estimator requires a relatively large data set compared to the size of the parameterization used in the model. To overcome these limitations, a recently introduced L1 sparse estimator approach, the so-called SPARSEVA method, is extended to the LPV case and its performance is compared to the NNG.

[1]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[2]  Lennart Ljung,et al.  System identification toolbox for use with MATLAB , 1988 .

[3]  L. Breiman.  Better subset regression using the nonnegative garrote , 1995 .

[4]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[5]  Bassam Bamieh,et al.  Identification of linear parameter varying models , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[6]  Lennart Ljung,et al.  System identification (2nd ed.): theory for the user , 1999 .

[7]  Michel Verhaegen,et al.  Subspace identification of multivariable linear parameter-varying systems , 2002, Autom..

[8]  H. Zou,et al.  Regularization and variable selection via the elastic net , 2005 .

[9]  L. Mohammadi,et al.  On nonnegative garrote estimator in a linear regression model , 2006 .

[10]  M. Yuan,et al.  On the non‐negative garrotte estimator , 2007 .

[11]  Jacob Roll,et al.  The use of nonnegative garrote for order selection of ARX models , 2008, 2008 47th IEEE Conference on Decision and Control.

[12]  Tyrone L. Vincent,et al.  Nonparametric methods for the identification of linear parameter varying systems , 2008, 2008 IEEE International Conference on Computer-Aided Control Systems.

[13]  Alexandre S. Bazanella,et al.  Informative data: How to get just sufficiently rich? , 2008, 2008 47th IEEE Conference on Decision and Control.

[14]  Michel Verhaegen,et al.  Subspace identification of Bilinear and LPV systems for open- and closed-loop data , 2009, Autom..

[15]  Roland Tóth,et al.  Asymptotically optimal orthonormal basis functions for LPV system identification , 2009, Autom..

[16]  Roland Tóth,et al.  Order and structural dependence selection of LPV-ARX models using a nonnegative garrote approach , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[17]  Roland Toth,et al.  Modeling and Identification of Linear Parameter-Varying Systems , 2010 .

[18]  Sk Satyajit Wattamwar,et al.  Identification of low-order parameter-varying models for large-scale systems , 2010 .

[19]  Hugues Garnier,et al.  Refined instrumental variable methods for identification of LPV Box-Jenkins models , 2010, Autom..

[20]  Håkan Hjalmarsson,et al.  Sparse estimation based on a validation criterion , 2011, IEEE Conference on Decision and Control and European Control Conference.

[21]  Wei Xing Zheng,et al.  Model structure learning: A support vector machine approach for LPV linear-regression models , 2011, IEEE Conference on Decision and Control and European Control Conference.

[22]  Biao Huang,et al.  Multiple model LPV approach to nonlinear process identification with EM algorithm , 2011 .

[23]  Tyrone L. Vincent,et al.  Compressive System Identification in the Linear Time-Invariant framework , 2011, IEEE Conference on Decision and Control and European Control Conference.

[24]  H. Hjalmarsson,et al.  Sparse Estimation of Rational Dynamical Models , 2012 .

[25]  Håkan Hjalmarsson,et al.  Sparse estimation of polynomial dynamical models , 2012 .

[26]  Alex Simpkins,et al.  System Identification: Theory for the User, 2nd Edition (Ljung, L.; 1999) [On the Shelf] , 2012, IEEE Robotics & Automation Magazine.