A Bayesian approach for estimation of linear-regression LPV models

In this paper, a Bayesian framework for identification of linear parameter-varying (LPV) models with finite impulse response (FIR) dynamic structure is introduced, in which the dependency structure of LPV system on the scheduling variables is identified based on a Gaussian Process (GP) formulation. Using this approach, a GP is employed to describe the distribution of the coefficient functions, that are dependent on the scheduling variables, in LPV linear-regression models. First, a prior distribution over the nonlinear functions representing the unknown coefficient dependencies of the model to be estimated is defined; then, a posterior distribution of these functions is obtained given measured data. The mean value of the posterior distribution is used to provide a model estimate. The approach is formulated with both static and dynamic dependency of the coefficient functions on the scheduling variables. The properties and performance of the proposed method are evaluated using illustrative examples.

[1]  Alessandro Chiuso,et al.  Subspace identification using predictor estimation via Gaussian regression , 2008, 2008 47th IEEE Conference on Decision and Control.

[2]  Jan-Willem van Wingerden,et al.  LPV Identification of Wind Turbine Rotor Vibrational Dynamics Using Periodic Disturbance Basis Functions , 2013, IEEE Transactions on Control Systems Technology.

[3]  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.

[4]  Siep Weiland,et al.  Identification of low order parameter varying models for large scale systems , 2009 .

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

[6]  Lennart Ljung,et al.  Kernel methods in system identification, machine learning and function estimation: A survey , 2014, Autom..

[7]  Giuseppe De Nicolao,et al.  A new kernel-based approach for system identification , 2008, 2008 American Control Conference.

[8]  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.

[9]  Herbert Werner,et al.  Closed-loop system identification of LPV input-output models - application to an arm-driven inverted pendulum , 2008, 2008 47th IEEE Conference on Decision and Control.

[10]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

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

[12]  Guillaume Mercère,et al.  A local approach framework for black-box and gray-box LPV system identification , 2013, 2013 European Control Conference (ECC).

[13]  Alessandro Chiuso,et al.  A Bayesian approach to sparse dynamic network identification , 2012, Autom..

[14]  V. Peterka.  BAYESIAN APPROACH TO SYSTEM IDENTIFICATION , 1981 .

[15]  Wallace E. Larimore,et al.  Identification of linear parameter-varying engine models , 2013, 2013 American Control Conference.

[16]  Alessandro Chiuso,et al.  Bayesian and nonparametric methods for system identification and model selection , 2014, 2014 European Control Conference (ECC).

[17]  Alessandro Chiuso,et al.  Tuning complexity in kernel-based linear system identification: The robustness of the marginal likelihood estimator , 2014, 2014 European Control Conference (ECC).

[18]  Bernhard Schölkopf,et al.  Learning with kernels , 2001 .

[19]  Bassam Bamieh,et al.  Identification of linear parameter varying models , 2002 .

[20]  Giuseppe De Nicolao,et al.  A new kernel-based approach for linear system identification , 2010, Autom..

[21]  Henrik Ohlsson,et al.  On the estimation of transfer functions, regularizations and Gaussian processes - Revisited , 2012, Autom..

[22]  Hossam Seddik Abbas,et al.  An instrumental variable technique for open-loop and closed-loop identification of input-output LPV models , 2009, 2009 European Control Conference (ECC).

[23]  Roland Tóth,et al.  LPV model order selection in an LS-SVM setting , 2013, 52nd IEEE Conference on Decision and Control.

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

[25]  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.

[26]  R. Tóth,et al.  Nonparametric identification of LPV models under general noise conditions : an LS-SVM based approach , 2012 .