Machine learning barycenter approach to identifying LPV state-space models

In this paper an identification method for state-space LPV models is presented. The method is based on a particular parameterization that can be written in linear regression form and enables model estimation to be handled using Least-Squares Support Vector Machine (LS-SVM). The regression form has a set of design variables that act as filter poles to the underlying basis functions. In order to preserve the meaning of the Kernel functions (crucial in the LS-SVM context), these are filtered by a 2D-system with the predictor dynamics. A data-driven, direct optimization based approach for tuning this filter is proposed. The method is assessed using a simulated example and the results obtained are twofold. First, in spite of the difficult nonlinearities involved, the nonparametric algorithm was able to learn the underlying dependencies on the scheduling signal. Second, a significant improvement in the performance of the proposed method is registered, if compared with the one achieved by placing the predictor poles at the origin of the complex plane, which is equivalent to considering an estimator based on an LPV auto-regressive structure.

[1]  Felipe Pait,et al.  Matchable-observable linear models for multivariable identification: Structure selection and experimental results , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[2]  Hossam Seddik Abbas,et al.  On the State-Space Realization of LPV Input-Output Models: Practical Approaches , 2012, IEEE Transactions on Control Systems Technology.

[3]  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.

[4]  F. Pait,et al.  The Barycenter Method for Direct Optimization , 2018, 1801.10533.

[5]  A. A. Bachnas,et al.  A review on data-driven linear parameter-varying modeling approaches: A high-purity distillation column case study , 2014 .

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

[7]  A. Morse,et al.  MIMO Design Models and Internal Regulators for Cyclicly-Switched Parameter-Adaptive Control Systems , 1993, 1993 American Control Conference.

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

[9]  Javad Mohammadpour,et al.  An IV-SVM-based approach for identification of state-space LPV models under generic noise conditions , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[10]  Carlo Novara.  Set membership identification of state-space LPV systems , 2012 .

[11]  John L. Nazareth,et al.  Introduction to derivative-free optimization , 2010, Math. Comput..

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

[13]  A. A. Bachnas,et al.  A review on data-driven linear parameter-varying modeling approaches: A high-purity distillation column case study , 2014 .

[14]  J. W. van Wingerden,et al.  A kernel based approach for LPV subspace identification , 2015 .

[15]  Håkan Hjalmarsson,et al.  Order and structural dependence selection of LPV-ARX models revisited , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[16]  Daniel E. Rivera,et al.  LPV system identification using a separable least squares support vector machines approach , 2014, 53rd IEEE Conference on Decision and Control.

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

[18]  A smoothly parameterized family of stabilizable, observable linear systems containing realizations of all transfer functions of McMillan degree not exceeding n , 1991 .

[19]  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.

[20]  Carlo Novara,et al.  Linear Parameter-Varying System Identification: New Developments and Trends , 2011 .