Hierarchical maximum likelihood generalized extended stochastic gradient algorithms for bilinear‐in‐parameter systems

In this article, we use the maximum likelihood principle and the multi‐innovation identification theory to study the identification issue of a bilinear‐in‐parameter system with autoregressive moving average noise. A maximum likelihood multi‐innovation stochastic gradient algorithm is derived to estimate the model parameters, which uses not only the current innovation but also the past innovations to improve the parameter estimation accuracy. The maximum likelihood multi‐innovation stochastic gradient algorithm has higher parameter estimation accuracy than the stochastic gradient algorithm. The simulation examples indicate that the proposed methods work well.

[1]  Feng Ding,et al.  Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems , 2009, Autom..

[2]  Feng Ding,et al.  Partially Coupled Stochastic Gradient Identification Methods for Non-Uniformly Sampled Systems , 2010, IEEE Transactions on Automatic Control.

[3]  Feng Ding,et al.  Parameter estimation with scarce measurements , 2011, Autom..

[4]  Feng Ding,et al.  Hierarchical Least Squares Identification for Linear SISO Systems With Dual-Rate Sampled-Data , 2011, IEEE Transactions on Automatic Control.

[5]  Y. Liu,et al.  Gradient-based and least-squares-based iterative estimation algorithms for multi-input multi-output systems , 2012, J. Syst. Control. Eng..

[6]  Feng Ding,et al.  An efficient hierarchical identification method for general dual-rate sampled-data systems , 2014, Autom..

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

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

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

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

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

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

[13]  Feng Ding,et al.  The Gradient-Based Iterative Estimation Algorithms for Bilinear Systems with Autoregressive Noise , 2017, Circuits, Systems, and Signal Processing.

[14]  F. Ding,et al.  Least-squares-based iterative and gradient-based iterative estimation algorithms for bilinear systems , 2017 .

[15]  Jianqiang Pan,et al.  A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems , 2017 .

[16]  Feng Ding,et al.  The maximum likelihood least squares based iterative estimation algorithm for bilinear systems with autoregressive moving average noise , 2017, J. Frankl. Inst..

[17]  R. Mininni,et al.  State and parameter estimation in solenoid nonlinear equations , 2018 .

[18]  Thomas B. Schön,et al.  Maximum likelihood identification of stable linear dynamical systems , 2018, Autom..

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

[20]  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.

[21]  Meihang Li,et al.  The least squares based iterative algorithms for parameter estimation of a bilinear system with autoregressive noise using the data filtering technique , 2018, Signal Process..

[22]  Feng Ding,et al.  Combined state and parameter estimation for a bilinear state space system with moving average noise , 2018, J. Frankl. Inst..

[23]  Feng Ding,et al.  Filtering-Based Maximum Likelihood Gradient Iterative Estimation Algorithm for Bilinear Systems with Autoregressive Moving Average Noise , 2018, Circuits Syst. Signal Process..

[24]  Min Zuo,et al.  CropDeep: The Crop Vision Dataset for Deep-Learning-Based Classification and Detection in Precision Agriculture , 2019, Sensors.

[25]  Feng Ding,et al.  Decomposition- and Gradient-Based Iterative Identification Algorithms for Multivariable Systems Using the Multi-innovation Theory , 2019, Circuits Syst. Signal Process..

[26]  Meihang Li,et al.  Maximum Likelihood Least Squares Based Iterative Estimation for a Class of Bilinear Systems Using the Data Filtering Technique , 2020 .

[27]  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..

[28]  Mohammad Haeri,et al.  LMI‐based cooperative distributed model predictive control for Lipschitz nonlinear systems , 2019, Optimal Control Applications and Methods.

[29]  Feng Ding,et al.  Adaptive RBF-AR Models Based on Multi-Innovation Least Squares Method , 2019, IEEE Signal Processing Letters.

[30]  Yan Ji,et al.  Hierarchical recursive generalized extended least squares estimation algorithms for a class of nonlinear stochastic systems with colored noise , 2019, J. Frankl. Inst..

[31]  Guo Xie,et al.  Fault Diagnosis of Train Plug Door Based on a Hybrid Criterion for IMFs Selection and Fractional Wavelet Package Energy Entropy , 2019, IEEE Transactions on Vehicular Technology.

[32]  Feng Ding,et al.  A Hierarchical Approach for Joint Parameter and State Estimation of a Bilinear System with Autoregressive Noise , 2019, Mathematics.

[33]  Feng Liu,et al.  Bio-Inspired Speed Curve Optimization and Sliding Mode Tracking Control for Subway Trains , 2019, IEEE Transactions on Vehicular Technology.

[34]  Ling Xu,et al.  Highly computationally efficient state filter based on the delta operator , 2019, International Journal of Adaptive Control and Signal Processing.

[35]  F. Ding,et al.  Partially‐coupled least squares based iterative parameter estimation for multi‐variable output‐error‐like autoregressive moving average systems , 2019, IET Control Theory & Applications.

[36]  Feng Ding,et al.  The filtering‐based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle , 2019, International Journal of Adaptive Control and Signal Processing.

[37]  Feng Ding,et al.  State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors , 2019, International Journal of Adaptive Control and Signal Processing.

[38]  Chen Xu,et al.  Hybrid Model Predictive Control Strategy of Supercapacitor Energy Storage System Based on Double Active Bridge , 2019, Energies.

[39]  Ling Xu,et al.  Recursive parameter estimation methods and convergence analysis for a special class of nonlinear systems , 2019, International Journal of Robust and Nonlinear Control.

[40]  Ling Xu,et al.  Hierarchical Multi-Innovation Generalised Extended Stochastic Gradient Methods for Multivariable Equation-Error Autoregressive Moving Average Systems , 2020 .

[41]  Mingcong Deng,et al.  Robust fault tolerant tracking control for the multi-joint manipulator based on operator theory , 2020, J. Frankl. Inst..

[42]  Jing Chen,et al.  Modified Kalman filtering based multi-step-length gradient iterative algorithm for ARX models with random missing outputs , 2020, Autom..

[43]  Wojciech Paszke,et al.  PD-Type Iterative Learning Control for Uncertain Spatially Interconnected Systems , 2020, Mathematics.

[44]  Ling Xu,et al.  A Recursive Parameter Estimation Algorithm for Modeling Signals with Multi-frequencies , 2020, Circuits Syst. Signal Process..

[45]  Bart De Schutter,et al.  Optimizing the performance of the feedback controller for state‐based switching bilinear systems , 2020, Optimal Control Applications and Methods.

[46]  Meihang Li,et al.  Maximum likelihood hierarchical least squares‐based iterative identification for dual‐rate stochastic systems , 2020, International Journal of Adaptive Control and Signal Processing.

[47]  Feng Ding,et al.  Modeling Nonlinear Processes Using the Radial Basis Function-Based State-Dependent Autoregressive Models , 2020, IEEE Signal Processing Letters.

[48]  Ling Xu,et al.  Separable multi‐innovation stochastic gradient estimation algorithm for the nonlinear dynamic responses of systems , 2020, International Journal of Adaptive Control and Signal Processing.

[49]  Yu Zhang,et al.  Capacity allocation of HESS in micro-grid based on ABC algorithm , 2020, International Journal of Low-Carbon Technologies.

[50]  Ximei Liu,et al.  Two‐stage auxiliary model gradient‐based iterative algorithm for the input nonlinear controlled autoregressive system with variable‐gain nonlinearity , 2020, International Journal of Robust and Nonlinear Control.

[51]  Jinfeng Liu,et al.  Robust economic model predictive control of nonlinear networked control systems with communication delays , 2020, International Journal of Adaptive Control and Signal Processing.

[52]  Ahmed Alsaedi,et al.  Data filtering based maximum likelihood gradient estimation algorithms for a multivariate equation-error system with ARMA noise , 2020, J. Frankl. Inst..

[53]  Yan Ji,et al.  Hierarchical least squares parameter estimation algorithm for two-input Hammerstein finite impulse response systems , 2020, J. Frankl. Inst..

[54]  Tao Yu,et al.  Parameter estimation for block‐oriented nonlinear systems using the key term separation , 2020, International Journal of Robust and Nonlinear Control.

[55]  Huizhong Yang,et al.  Robust point‐to‐point iterative learning control with trial‐varying initial conditions , 2020, IET Control Theory & Applications.

[56]  Yi Shen,et al.  Reachable set estimation for uncertain nonlinear systems with time delay , 2020, Optimal Control Applications and Methods.

[57]  Xiaoyi Wang,et al.  A health performance evaluation method of multirotors under wind turbulence , 2020, Nonlinear Dynamics.

[58]  Qinyao Liu,et al.  Recursive coupled projection algorithms for multivariable output-error-like systems with coloured noises , 2020, IET Signal Process..

[59]  Xiao Zhang,et al.  Adaptive parameter estimation for a general dynamical system with unknown states , 2020, International Journal of Robust and Nonlinear Control.

[60]  Qinyao Liu,et al.  Recursive identification of bilinear time-delay systems through the redundant rule , 2020, J. Frankl. Inst..

[61]  Hassan Nouri,et al.  Bias compensation‐based parameter and state estimation for a class of time‐delay non‐linear state‐space models , 2020, IET Control Theory & Applications.

[62]  Zhen Kang,et al.  Three‐stage forgetting factor stochastic gradient parameter estimation methods for a class of nonlinear systems , 2020, International Journal of Robust and Nonlinear Control.

[63]  Jing Chen,et al.  Stochastic average gradient algorithm for multirate FIR models with varying time delays using self‐organizing maps , 2020 .

[64]  Shuai Su,et al.  An Energy-Efficient Train Operation Approach by Integrating the Metro Timetabling and Eco-Driving , 2020, IEEE Transactions on Intelligent Transportation Systems.

[65]  T. Hayat,et al.  Partially‐coupled gradient‐based iterative algorithms for multivariable output‐error‐like systems with autoregressive moving average noises , 2020, IET Control Theory & Applications.

[66]  F. Ding,et al.  Auxiliary model multiinnovation stochastic gradient parameter estimation methods for nonlinear sandwich systems , 2020, International Journal of Robust and Nonlinear Control.

[67]  F. Ding,et al.  Recursive parameter estimation and its convergence for bilinear systems , 2020, IET Control Theory & Applications.

[68]  Vladimir Stojanovic,et al.  Robust identification for fault detection in the presence of non-Gaussian noises: application to hydraulic servo drives , 2020 .

[69]  Ling Xu,et al.  Separable Recursive Gradient Algorithm for Dynamical Systems Based on the Impulse Response Signals , 2020 .

[70]  Xiao Zhang,et al.  Hierarchical parameter and state estimation for bilinear systems , 2020, Int. J. Syst. Sci..

[71]  Feng Ding,et al.  Hierarchical recursive signal modeling for multifrequency signals based on discrete measured data , 2021, International Journal of Adaptive Control and Signal Processing.

[72]  Feng Ding,et al.  Hierarchical Estimation Approach for RBF-AR Models With Regression Weights Based on the Increasing Data Length , 2021, IEEE Transactions on Circuits and Systems II: Express Briefs.

[73]  Yan Ji,et al.  The data filtering based multiple‐stage Levenberg–Marquardt algorithm for Hammerstein nonlinear systems , 2021, International Journal of Robust and Nonlinear Control.

[74]  Zheng Liu,et al.  Knowledge-Data-Driven Model Predictive Control for a Class of Nonlinear Systems , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[75]  Min Gan,et al.  A novel reduced-order algorithm for rational models based on Arnoldi process and Krylov subspace , 2021, Autom..

[76]  Wang Gaihua,et al.  A Serial-Parallel Self-Attention Network Joint With Multi-Scale Dilated Convolution , 2021, IEEE Access.

[77]  Xiaoyi Wang,et al.  Multi-stream hybrid architecture based on cross-level fusion strategy for fine-grained crop species recognition in precision agriculture , 2021, Comput. Electron. Agric..

[78]  Weihai Zhang,et al.  Finite‐time adaptive control for nonlinear systems with uncertain parameters based on the command filters , 2021, International Journal of Adaptive Control and Signal Processing.

[79]  Tiezhou Wu,et al.  Lithium-ion battery state of health estimation using the incremental capacity and wavelet neural networks with genetic algorithm , 2021, Journal of Energy Storage.

[80]  Feng Ding,et al.  Decomposition strategy-based hierarchical least mean square algorithm for control systems from the impulse responses , 2021, Int. J. Syst. Sci..

[81]  Honggui Han,et al.  Cooperative Fuzzy-Neural Control for Wastewater Treatment Process , 2021, IEEE Transactions on Industrial Informatics.

[82]  Shuai Su,et al.  Design of Running Grades for Energy-Efficient Train Regulation: A Case Study for Beijing Yizhuang Line , 2019, IEEE Intelligent Transportation Systems Magazine.

[83]  Yan Ji,et al.  Iterative parameter and order identification for fractional‐order nonlinear finite impulse response systems using the key term separation , 2021, International Journal of Adaptive Control and Signal Processing.

[84]  Ximei Liu,et al.  Maximum likelihood extended gradient‐based estimation algorithms for the input nonlinear controlled autoregressive moving average system with variable‐gain nonlinearity , 2021, International Journal of Robust and Nonlinear Control.

[85]  Yan Ji,et al.  Two-stage Gradient-based Recursive Estimation for Nonlinear Models by Using the Data Filtering , 2021, International Journal of Control, Automation and Systems.

[86]  Peiyi Zhu,et al.  State filtering and parameter estimation for two‐input two‐output systems with time delay , 2021, IET Control Theory & Applications.

[87]  Junfei Qiao,et al.  Intelligent Optimal Control System With Flexible Objective Functions and Its Applications in Wastewater Treatment Process , 2021, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[88]  Song Wang,et al.  DP-LinkNet: A convolutional network for historical document image binarization , 2021, KSII Trans. Internet Inf. Syst..

[89]  Wei Xiong,et al.  An enhanced binarization framework for degraded historical document images , 2021, EURASIP J. Image Video Process..

[90]  Lianchuan Ma,et al.  Tracking and collision avoidance of virtual coupling train control system , 2021, Future Gener. Comput. Syst..

[91]  Tingli Su,et al.  Deep-Learning Forecasting Method for Electric Power Load via Attention-Based Encoder-Decoder with Bayesian Optimization , 2021, Energies.

[92]  Fei Liu,et al.  Adaptive optimization algorithm for nonlinear Markov jump systems with partial unknown dynamics , 2021, International Journal of Robust and Nonlinear Control.

[93]  Huirui Zhou,et al.  Optimal Sizing of Isolated Microgrid Containing Photovoltaic/Photothermal/Wind/Diesel/Battery , 2021, International Journal of Photoenergy.

[94]  Meihang Li,et al.  Iterative identification methods for a class of bilinear systems by using the particle filtering technique , 2021, International Journal of Adaptive Control and Signal Processing.

[95]  Yongkui Sun,et al.  A Sound-Based Fault Diagnosis Method for Railway Point Machines Based on Two-Stage Feature Selection Strategy and Ensemble Classifier , 2022, IEEE Transactions on Intelligent Transportation Systems.

[96]  Lianchuan Ma,et al.  Tracking and collision avoidance of virtual coupling train control system , 2021, Future Gener. Comput. Syst..

[97]  Meihang Li,et al.  Iterative parameter estimation methods for dual‐rate sampled‐data bilinear systems by means of the data filtering technique , 2021, IET Control Theory & Applications.

[98]  Ping Ma,et al.  Filtering‐based recursive least squares estimation approaches for multivariate equation‐error systems by using the multiinnovation theory , 2021, International Journal of Adaptive Control and Signal Processing.

[99]  Feng Ding,et al.  Partially-coupled nonlinear parameter optimization algorithm for a class of multivariate hybrid models , 2022, Appl. Math. Comput..