Parameter estimation for a special class of nonlinear systems by using the over-parameterisation method and the linear filter

ABSTRACT This paper studies the parameter estimation issues of a special class of nonlinear systems (i.e. bilinear-in-parameter systems) utilising the measurement input-output data. The estimation idea is based on the data filtering technique and the over-parameterisation method to represent the system as a linearly parameterised form. Then, by means of the filtered model and the noise model, a filtering based over-parameterisation generalised extended gradient iterative (F-O-GEGI) algorithm is developed for estimating all the parameters. For purpose of improving the precision of parameter estimation, a filtering based over-parameterisation generalised extended least squares iterative (F-O-GELSI) algorithm is derived by formulating and minimising two separate criterion functions. By these foundations, the F-O-GEGI algorithm and the F-O-GELSI algorithm with finite measurement data are presented. The simulation example is provided to test and compare the presented approaches.

[1]  Ling Xu,et al.  A proportional differential control method for a time-delay system using the Taylor expansion approximation , 2014, Appl. Math. Comput..

[2]  Yinghong Wen,et al.  Performance Evaluation with Improved Receiver Design for Asynchronous Coordinated Multipoint Transmissions , 2016 .

[3]  Wei Li,et al.  Control Algorithms of Magnetic Suspension Systems Based on the Improved Double Exponential Reaching Law of Sliding Mode Control , 2018, International Journal of Control, Automation and Systems.

[4]  Brian K. Weaver,et al.  Model-based interpolation-iteration method for bearing coefficients identification of operating flexible rotor-bearing system , 2017 .

[5]  Min Liu,et al.  Research on a handwritten character recognition algorithm based on an extended nonlinear kernel residual network , 2018, KSII Trans. Internet Inf. Syst..

[6]  Long Chen,et al.  On Some Separated Algorithms for Separable Nonlinear Least Squares Problems , 2018, IEEE Transactions on Cybernetics.

[7]  Ling Xu.  The parameter estimation algorithms based on the dynamical response measurement data , 2017 .

[8]  Jiling Ding,et al.  The Hierarchical Iterative Identification Algorithm for Multi-Input-Output-Error Systems with Autoregressive Noise , 2017, Complex..

[9]  Feng Ding,et al.  Hierarchical Newton and least squares iterative estimation algorithm for dynamic systems by transfer functions based on the impulse responses , 2018, Int. J. Syst. Sci..

[10]  Yongji Wang,et al.  Review of rational (total) nonlinear dynamic system modelling, identification, and control , 2015, Int. J. Syst. Sci..

[11]  Zhizhong Mao,et al.  Bias compensation principle based recursive least squares identification method for Hammerstein nonlinear systems , 2017, J. Frankl. Inst..

[12]  Yuan Cao,et al.  Research on dynamic nonlinear input prediction of fault diagnosis based on fractional differential operator equation in high-speed train control system. , 2019, Chaos.

[13]  Ling Xu,et al.  The damping iterative parameter identification method for dynamical systems based on the sine signal measurement , 2016, Signal Process..

[14]  Jian Pan,et al.  Adaptive Gradient-Based Iterative Algorithm for Multivariable Controlled Autoregressive Moving Average Systems Using the Data Filtering Technique , 2018, Complex..

[15]  F. Alsaadi,et al.  Recursive parameter identification of the dynamical models for bilinear state space systems , 2017 .

[16]  T. Hayat,et al.  Hierarchical Parameter Estimation for the Frequency Response Based on the Dynamical Window Data , 2018, International Journal of Control, Automation and Systems.

[17]  Yu Guo,et al.  Robust adaptive parameter estimation of sinusoidal signals , 2015, Autom..

[18]  Feng Ding,et al.  Modified Gram–Schmidt Method-Based Variable Projection Algorithm for Separable Nonlinear Models , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[19]  Shaoxue Jing,et al.  Variable knot-based spline approximation recursive Bayesian algorithm for the identification of Wiener systems with process noise , 2017 .

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

[21]  Feng Ding,et al.  Decomposition-based recursive least squares identification methods for multivariate pseudo-linear systems using the multi-innovation , 2018, Int. J. Syst. Sci..

[22]  Erfu Yang,et al.  Gradient‐based iterative parameter estimation for bilinear‐in‐parameter systems using the model decomposition technique , 2018, IET Control Theory & Applications.

[23]  Feng Ding,et al.  A recursive least squares parameter estimation algorithm for output nonlinear autoregressive systems using the input-output data filtering , 2017, J. Frankl. Inst..

[24]  Yu Guo,et al.  Robust adaptive estimation of nonlinear system with time‐varying parameters , 2015 .

[25]  Ling Xu,et al.  Application of the Newton iteration algorithm to the parameter estimation for dynamical systems , 2015, J. Comput. Appl. Math..

[26]  Yide Wang,et al.  A M-EKF fault detection strategy of insulation system for marine current turbine , 2019, Mechanical Systems and Signal Processing.

[27]  C. L. Philip Chen,et al.  A Regularized Variable Projection Algorithm for Separable Nonlinear Least-Squares Problems , 2019, IEEE Transactions on Automatic Control.

[28]  Maamar Bettayeb,et al.  Nonlinear system identification of fractional Wiener models , 2018 .

[29]  Hao Jiang,et al.  Convergence of Proximal Iteratively Reweighted Nuclear Norm Algorithm for Image Processing , 2017, IEEE Transactions on Image Processing.

[30]  Feng Ding,et al.  Some new results of designing an IIR filter with colored noise for signal processing , 2018, Digit. Signal Process..

[31]  Dingli Yu,et al.  An enhanced linear Kalman filter (EnLKF) algorithm for parameter estimation of nonlinear rational models , 2017, Int. J. Syst. Sci..

[32]  Feng Ding,et al.  A novel parameter separation based identification algorithm for Hammerstein systems , 2016, Appl. Math. Lett..

[33]  Feng Ding,et al.  Parameter estimation algorithms for dynamical response signals based on the multi-innovation theory and the hierarchical principle , 2017, IET Signal Process..

[34]  Feng Ding,et al.  Iterative Parameter Estimation for Signal Models Based on Measured Data , 2018, Circuits Syst. Signal Process..

[35]  M. Crow,et al.  A Chain Method for Preconditioned Iterative Linear Solvers for Power System Matrices , 2018, IEEE Transactions on Power Systems.

[36]  Feng Ding,et al.  Hierarchical gradient parameter estimation algorithm for Hammerstein nonlinear systems using the key term separation principle , 2014, Appl. Math. Comput..

[37]  Feng Liu,et al.  Boundedness and continuity of Marcinkiewicz integrals associated to homogeneous mappings on Triebel-Lizorkin spaces , 2019, Frontiers of Mathematics in China.

[38]  Jiling Ding,et al.  Recursive and Iterative Least Squares Parameter Estimation Algorithms for Multiple-Input–Output-Error Systems with Autoregressive Noise , 2018, Circuits Syst. Signal Process..

[39]  Tao Han,et al.  Optimal modified performance of MIMO networked control systems with multi-parameter constraints. , 2019, ISA transactions.

[40]  Rui Liu,et al.  Monitoring strategy for relay incentive mechanism in cooperative communication networks , 2017, Comput. Electr. Eng..

[41]  Laila Kadi,et al.  Frequency identification of Hammerstein-Wiener systems with backlash input nonlinearity , 2017 .

[42]  F. Ding,et al.  Performance analysis of the generalised projection identification for time-varying systems , 2016 .

[43]  Feng Ding,et al.  Parameter estimation for control systems based on impulse responses , 2017 .

[44]  Yuquan Chen,et al.  Identification for Hammerstein nonlinear ARMAX systems based on multi-innovation fractional order stochastic gradient , 2018, Signal Process..

[45]  Yasser Shekofteh,et al.  A New Chaotic System with a Self-Excited Attractor: Entropy Measurement, Signal Encryption, and Parameter Estimation , 2018, Entropy.

[46]  Koen Tiels,et al.  Identification of block-oriented nonlinear systems starting from linear approximations: A survey , 2016, Autom..

[47]  Er-Wei Bai.  An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems , 1998, Autom..

[48]  Biao Huang,et al.  Survey on the theoretical research and engineering applications of multivariate statistics process monitoring algorithms: 2008-2017 , 2018, The Canadian Journal of Chemical Engineering.

[49]  Feng Ding,et al.  Iterative Identification Algorithms for Bilinear-in-parameter Systems by Using the Over-parameterization Model and the Decomposition , 2018 .

[50]  Erfu Yang,et al.  State filtering‐based least squares parameter estimation for bilinear systems using the hierarchical identification principle , 2018, IET Control Theory & Applications.

[51]  Michel Verhaegen,et al.  Subspace Identification of Individual Systems Operating in a Network (SI $^2$ON) , 2018, IEEE Transactions on Automatic Control.

[52]  Peng Li,et al.  Parallel processing algorithm for railway signal fault diagnosis data based on cloud computing , 2018, Future Gener. Comput. Syst..

[53]  Feng Ding,et al.  Iterative identification algorithms for bilinear-in-parameter systems with autoregressive moving average noise , 2017, J. Frankl. Inst..

[54]  Weihai Zhang,et al.  Global stabilization for a class of stochastic nonlinear systems with SISS‐like conditions and time delay , 2018 .

[55]  Feng Liu.  Boundedness and continuity of maximal operators associated to polynomial compound curves on Triebel-Lizorkin spaces , 2019, Mathematical Inequalities & Applications.

[56]  Ling Xu,et al.  Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration , 2015 .

[57]  Feng Ding,et al.  A filtering based multi-innovation gradient estimation algorithm and performance analysis for nonlinear dynamical systems , 2017 .

[58]  Xia Zhang,et al.  Standard Analysis for Transfer Delay in CTCS-3 , 2017 .

[59]  Mirosław Pawlak,et al.  Hammerstein System Identification With the Nearest Neighbor Algorithm , 2017, IEEE Transactions on Information Theory.

[60]  Jacob Benesty,et al.  On the Identification of Bilinear Forms With the Wiener Filter , 2017, IEEE Signal Processing Letters.

[61]  Baolin Liu,et al.  Recursive Extended Least Squares Parameter Estimation for Wiener Nonlinear Systems with Moving Average Noises , 2013, Circuits, Systems, and Signal Processing.

[62]  Liang Liang,et al.  Optimization of Information Interaction Protocols in Cooperative Vehicle-Infrastructure Systems , 2018 .

[63]  Changfeng Ma,et al.  The relaxed gradient-based iterative algorithms for a class of generalized coupled Sylvester-conjugate matrix equations , 2018, J. Frankl. Inst..

[64]  Wen-Qin Wang,et al.  Sparsity-aware transmit beamspace design for FDA-MIMO radar , 2018, Signal Process..

[65]  Feng Liu,et al.  Boundedness and continuity of maximal singular integrals and maximal functions on Triebel-Lizorkin spaces , 2020 .

[66]  Er-Wei Bai,et al.  Least squares solutions of bilinear equations , 2006, Syst. Control. Lett..

[67]  Feng Ding,et al.  Joint state and multi-innovation parameter estimation for time-delay linear systems and its convergence based on the Kalman filtering , 2017, Digit. Signal Process..