Iterative identification for multiple-input systems with time-delays based on greedy pursuit and auxiliary model

Abstract This paper focuses on the identification of multiple-input single-output output-error systems with unknown time-delays. Since the time-delays are unknown, an identification model with a high dimensional and sparse parameter vector is derived based on overparameterization. Traditional identification methods cannot get sparse solutions and require a large number of observations unless the time-delays are predetermined. Inspired by the sparse optimization and the greedy algorithms, an auxiliary model based orthogonal matching pursuit iterative (AM-OMPI) algorithm is proposed by using the orthogonal matching pursuit, and then based on the gradient search, an auxiliary model based gradient pursuit iterative algorithm is proposed, which is computationally more efficient than the AM-OMPI algorithm. The proposed methods can simultaneously estimate the parameters and time-delays from a small number of sampled data. A simulation example is used to illustrate the effectiveness of the proposed algorithms.

[1]  Feng Ding,et al.  Recursive parameter estimation algorithm for multivariate output-error systems , 2018, J. Frankl. Inst..

[2]  Feng Ding,et al.  Iterative identification algorithms for input nonlinear output error autoregressive systems , 2016 .

[3]  Felipe Pait,et al.  Matchable-Observable Linear Models and Direct Filter Tuning: An Approach to Multivariable Identification , 2017, IEEE Transactions on Automatic Control.

[4]  Yu Zhang,et al.  Decoupling Smith Predictor Design for Multivariable Systems with Multiple Time Delays , 2000 .

[5]  Joel A. Tropp,et al.  Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit , 2007, IEEE Transactions on Information Theory.

[6]  S. Bjorklund,et al.  A review of time-delay estimation techniques , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[7]  Mike E. Davies,et al.  Gradient Pursuits , 2008, IEEE Transactions on Signal Processing.

[8]  Feng Ding,et al.  The auxiliary model based hierarchical gradient algorithms and convergence analysis using the filtering technique , 2016, Signal Process..

[9]  Joel A. Tropp,et al.  Just relax: convex programming methods for identifying sparse signals in noise , 2006, IEEE Transactions on Information Theory.

[10]  Hamid Reza Karimi,et al.  Data-based modeling and estimation of vehicle crash processes in frontal fixed-barrier crashes , 2017, J. Frankl. Inst..

[11]  Murti V. Salapaka,et al.  Model identification of a network as compressing sensing , 2011, Syst. Control. Lett..

[12]  Kamel Abderrahim,et al.  Hierarchical gradient based identification of discrete-time delay systems , 2013, 52nd IEEE Conference on Decision and Control.

[13]  Xingyu Wang,et al.  Decentralized unscented Kalman filter based on a consensus algorithm for multi-area dynamic state estimation in power systems , 2015 .

[14]  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.

[15]  Xiaoping Liu,et al.  Auxiliary model-based interval-varying multi-innovation least squares identification for multivariable OE-like systems with scarce measurements , 2015 .

[16]  Feng Ding,et al.  Combined parameter and output estimation of dual-rate systems using an auxiliary model , 2004, Autom..

[17]  Yuanqing Xia,et al.  Adaptive parameter identification of linear SISO systems with unknown time-delay , 2014, Syst. Control. Lett..

[18]  D. L. Donoho,et al.  Compressed sensing , 2006, IEEE Trans. Inf. Theory.

[19]  F. Ding,et al.  Filtering-based iterative identification for multivariable systems , 2016 .

[20]  Roland Tóth,et al.  An SDP approach for l0-minimization: Application to ARX model segmentation , 2013, Autom..

[21]  Tyrone L. Vincent,et al.  Compressive System Identification of LTI and LTV ARX models , 2011, IEEE Conference on Decision and Control and European Control Conference.

[22]  Feng Ding,et al.  Novel data filtering based parameter identification for multiple-input multiple-output systems using the auxiliary model , 2016, Autom..

[23]  Yanjun Liu,et al.  A CS Recovery Algorithm for Model and Time Delay Identification of MISO-FIR Systems , 2015, Algorithms.

[24]  Fuad E. Alsaadi,et al.  Iterative parameter identification for pseudo-linear systems with ARMA noise using the filtering technique , 2018 .

[25]  Hamid Reza Karimi,et al.  Fault Detection for Linear Discrete Time-Varying Systems With Multiplicative Noise: The Finite-Horizon Case , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[26]  Michael Elad,et al.  From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images , 2009, SIAM Rev..

[27]  Dongqing Wang,et al.  Model recovery for Hammerstein systems using the auxiliary model based orthogonal matching pursuit method , 2018 .

[28]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[29]  Michael Elad,et al.  Sparse and Redundant Representations - From Theory to Applications in Signal and Image Processing , 2010 .

[30]  Feng Ding,et al.  Parameter estimation algorithms for Hammerstein time-delay systems based on the orthogonal matching pursuit scheme , 2017, IET Signal Process..

[31]  Wen-Xu Wang,et al.  Predicting catastrophes in nonlinear dynamical systems by compressive sensing. , 2011, Physical review letters.

[32]  Sheng Chen,et al.  Orthogonal least squares methods and their application to non-linear system identification , 1989 .

[33]  Hamid Reza Karimi,et al.  Resilient Sampled-Data Control for Markovian Jump Systems With an Adaptive Fault-Tolerant Mechanism , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[34]  Douglas Cochran,et al.  Nonlinear system identification using compressed sensing , 2012, 2012 Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR).

[35]  S. Selvanathan,et al.  Time-delay estimation in multivariate systems using Hilbert transform relation and partial coherence functions , 2010 .

[36]  Feng Ding,et al.  Gradient based and least-squares based iterative identification methods for OE and OEMA systems , 2010, Digit. Signal Process..

[37]  T. Hayat,et al.  Parameter estimation for pseudo-linear systems using the auxiliary model and the decomposition technique , 2017 .