Prediction error method for identification of LPV models

Abstract This paper is concerned with identification of linear parameter varying (LPV) systems in an input–output setting with Box–Jenkins (BJ) model structure. Classical linear time invariant prediction error method (PEM) is extended to the LPV PEM. Under the new LPV framework, identification of two types of input–output LPV models is considered: one is based on parameter interpolation and the other is based on model interpolation. The effectiveness of the proposed solution is validated by comparison with other existing LPV identification approaches through simulation examples and demonstrated by experiment studies.

[1]  M. Lovera,et al.  Identification for gain-scheduling: a balanced subspace approach , 2007, 2007 American Control Conference.

[2]  Biao Huang,et al.  Dynamic Modeling, Predictive Control and Performance Monitoring: A Data-driven Subspace Approach , 2008 .

[3]  M. Sznaier,et al.  An LMI approach to control oriented identification of LPV systems , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[4]  Mi Friswell,et al.  17th IFAC World Congress , 2008 .

[5]  Bassam Bamieh,et al.  Identification for a general class of LPV Models , 2000 .

[6]  Yucai Zhu,et al.  LPV Model Identification Using Blended Linear Models with Given Weightings , 2009 .

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

[8]  Jan Swevers,et al.  Identification of Interpolating Affine LPV Models for Mechatronic Systems with one Varying Parameter , 2008, Eur. J. Control.

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

[10]  Lawton H. Lee,et al.  Identification of Linear Parameter-Varying Systems Using Nonlinear Programming , 1999 .

[11]  Michel Verhaegen,et al.  Subspace identification of MIMO LPV systems using a periodic scheduling sequence , 2007, Autom..

[12]  Alireza Karimi,et al.  On the Consistency of Certain Identification Methods for Linear Parameter Varying Systems , 2008 .

[13]  L. Ljung Prediction error estimation methods , 2002 .

[14]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[15]  M. Lovera,et al.  Identification of non-linear parametrically varying models using separable least squares , 2004 .

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

[17]  A. Karimi,et al.  Data‐driven tuning of linear parameter‐varying precompensators , 2009 .

[18]  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.

[19]  S. Billings,et al.  Piecewise linear identification of non-linear systems , 1987 .

[20]  Gustavo Belforte,et al.  Optimal worst case estimation for LPV-FIR models with bounded errors , 2004, Syst. Control. Lett..

[21]  Roland Tóth,et al.  LPV system identification with globally fixed orthonormal basis functions , 2007, 2007 46th IEEE Conference on Decision and Control.

[22]  Michel Verhaegen,et al.  A class of subspace model identification algorithms to identify periodically and arbitrarily time-varying systems , 1995, Autom..

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

[24]  Vincent Verdult,et al.  Kernel methods for subspace identification of multivariable LPV and bilinear systems , 2005, Autom..

[25]  Lawton Hubert Lee,et al.  Identification and Robust Control of Linear Parameter-Varying Systems , 1997 .

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

[27]  Jixin Qian,et al.  A Two-Stage Method for Identification of Dual-Rate Systems with Fast Input and Very Slow Output , 2009 .

[28]  Michèle Hibon,et al.  Exponential smoothing: The effect of initial values and loss functions on post-sample forecasting accuracy , 1991 .

[29]  Yucai Zhu,et al.  Multivariable System Identification For Process Control , 2001 .

[30]  M. Lovera,et al.  Identification of a class of linear models with nonlinearly varying parameters , 1999, 1999 European Control Conference (ECC).

[31]  Vito Cerone,et al.  Set-membership identification of LPV models with uncertain measurements of the time-varying parameter , 2008, 2008 47th IEEE Conference on Decision and Control.

[32]  Biao Huang,et al.  Minimum Variance Control and Performance Assessment of Time-Variant Processes , 2000 .

[33]  Wilson J. Rugh,et al.  Research on gain scheduling , 2000, Autom..

[34]  Marco Lovera,et al.  Identification of a class of non-linear parametrically varying models , 2003 .

[35]  Yucai Zhu,et al.  Nonlinear MPC using an identified LPV model , 2009 .

[36]  Okko H. Bosgra,et al.  LPV control for a wafer stage: beyond the theoretical solution , 2005 .

[37]  Yucai Zhu,et al.  Estimation of an N-L-N Hammerstein-Wiener model , 2002, Autom..

[38]  Kanat Camlibel,et al.  Proc. of the 47th IEEE Conference on Decision and Control , 2008 .

[39]  L. Ljung,et al.  Identification of composite local linear state-space models using a projected gradient search , 2002 .

[40]  Psc Peter Heuberger,et al.  An LPV identification Framework Based on Orthonormal Basis Functions , 2009 .

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

[42]  F. Bianchi,et al.  Robust identification / invalidation in an LPV framework , 2010 .

[43]  Roderick Murray-Smith,et al.  Multiple Model Approaches to Modelling and Control , 1997 .

[44]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[45]  P.M.J. Van den Hof,et al.  Modeling and Identification of Linear Parameter-Varying Systems, an Orthonormal Basis Function Approach , 2004 .

[46]  Michel Verhaegen,et al.  Identification of fully parameterized linear and nonlinear state-space systems by projected gradient search , 2003 .

[47]  Y. Arkun,et al.  Estimation of nonlinear systems using linear multiple models , 1997 .