Gradient estimation algorithms for the parameter identification of bilinear systems using the auxiliary model

Abstract For the bilinear system with white noise, the difficulty of identification is that there exists the product term of the state and input in the system. To overcome this difficulty, we derive the input–output representation of a class of special bilinear systems by using the transformation, and present a stochastic gradient (SG) algorithm and a gradient-based iterative algorithm for estimating the parameters of the systems in the case of the known input–output data by means of the auxiliary model. The proposed gradient-based iterative algorithm can generate more accurate parameter estimates than the auxiliary model based SG algorithm. The performance of the proposed algorithms are tested by two numerical examples.

[1]  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.

[2]  F. Ma,et al.  Start-Up Process Modelling of Sediment Microbial Fuel Cells Based on Data Driven , 2019, Mathematical Problems in Engineering.

[3]  Jing Chen,et al.  Hierarchical identification for multivariate Hammerstein systems by using the modified Kalman filter , 2017 .

[4]  Donghai Li,et al.  On disturbance rejection in magnetic levitation , 2019, Control Engineering Practice.

[5]  Feng Ding,et al.  Maximum Likelihood Recursive Identification for the Multivariate Equation-Error Autoregressive Moving Average Systems Using the Data Filtering , 2019, IEEE Access.

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

[7]  Wen-Qin Wang,et al.  Adaptive weight matrix design and parameter estimation via sparse modeling for MIMO radar , 2017, Signal Process..

[8]  C. Yin,et al.  The Perturbed Compound Poisson Risk Process with Investment and Debit Interest , 2010 .

[9]  Dandan Meng.  Recursive Least Squares and Multi-innovation Gradient Estimation Algorithms for Bilinear Stochastic Systems , 2017, Circuits Syst. Signal Process..

[10]  Song Xiao,et al.  Experimental Study on Compatibility of Eco-Friendly Insulating Medium C5F10O/CO2 Gas Mixture With Copper and Aluminum , 2019, IEEE Access.

[11]  Feng Ding,et al.  Decomposition based least squares iterative identification algorithm for multivariate pseudo-linear ARMA systems using the data filtering , 2017, J. Frankl. Inst..

[12]  Jie Ding,et al.  Particle filtering based parameter estimation for systems with output-error type model structures , 2019, J. Frankl. Inst..

[13]  Feng Ding,et al.  Gradient-Based Iterative Parameter Estimation Algorithms for Dynamical Systems from Observation Data , 2019, Mathematics.

[14]  Graham C. Goodwin,et al.  Adaptive filtering prediction and control , 1984 .

[15]  W. Shi,et al.  Effects of Postannealing on the Characteristics and Reliability of Polyfluorene Organic Light-Emitting Diodes , 2019, IEEE Transactions on Electron Devices.

[16]  Jian Pan,et al.  Recursive Algorithms for Multivariable Output-Error-Like ARMA Systems , 2019, Mathematics.

[17]  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.

[18]  C. Yin,et al.  Optimality of the threshold dividend strategy for the compound Poisson model , 2011 .

[19]  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.

[20]  C. Yin,et al.  ON THE OPTIMAL DIVIDEND PROBLEM FOR A SPECTRALLY POSITIVE LÉVY PROCESS , 2013, ASTIN Bulletin.

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

[22]  C. Yin,et al.  Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs , 2014, 1409.0407.

[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]  Bo Fu,et al.  Research on the Predictive Optimal PID Plus Second Order Derivative Method for AGC of Power System with High Penetration of Photovoltaic and Wind Power , 2019, Journal of Electrical Engineering & Technology.

[25]  Bo Fu,et al.  An Improved Mixed Integer Linear Programming Approach Based on Symmetry Diminishing for Unit Commitment of Hybrid Power System , 2019, Energies.

[26]  Bo Fu,et al.  Research on Automatic Generation Control with Wind Power Participation Based on Predictive Optimal 2-Degree-of-Freedom PID Strategy for Multi-area Interconnected Power System , 2018, Energies.

[27]  Yuehong Su,et al.  A Capacity Configuration Control Strategy to Alleviate Power Fluctuation of Hybrid Energy Storage System Based on Improved Particle Swarm Optimization , 2019, Energies.

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

[29]  Bo Fu,et al.  Reliability analysis of hybrid multi-carrier energy systems based on entropy-based Markov model , 2016 .

[30]  Wan Xiangkui,et al.  A T-wave alternans assessment method based on least squares curve fitting technique , 2016 .

[31]  Xiangkui Wan,et al.  Two-stage Gradient-based Iterative Estimation Methods for Controlled Autoregressive Systems Using the Measurement Data , 2020, International Journal of Control, Automation and Systems.

[32]  C. Yin,et al.  An extension of Paulsen–Gjessing’s risk model with stochastic return on investments , 2013, 1302.6757.

[33]  C. Yin,et al.  Optimal dividends problem with a terminal value for spectrally positive Levy processes , 2013, 1302.6011.

[34]  N. Sinha,et al.  Robust recursive least-squares method with modified weights for bilinear system identification , 1989 .

[35]  Jie Ding,et al.  Particle filtering‐based recursive identification for controlled auto‐regressive systems with quantised output , 2019, IET Control Theory & Applications.

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

[37]  Jian-Xin Xu,et al.  Iterative learning control design for linear discrete-time systems with multiple high-order internal models , 2015, Autom..

[38]  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.

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

[40]  Nan Zhao,et al.  Android-based mobile educational platform for speech signal processing , 2017 .

[41]  Nan Zhao,et al.  Joint Optimization of Cooperative Spectrum Sensing and Resource Allocation in Multi-channel Cognitive Radio Sensor Networks , 2016, Circuits Syst. Signal Process..

[42]  Feng Ding,et al.  Hierarchical Principle-Based Iterative Parameter Estimation Algorithm for Dual-Frequency Signals , 2019, Circuits Syst. Signal Process..

[43]  Song Xiao,et al.  AC Breakdown and Decomposition Characteristics of Environmental Friendly Gas C5F10O/Air and C5F10O/N2 , 2019, IEEE Access.

[44]  Yuan Tian,et al.  Dissolved Gas Analysis in Transformer Oil Using Pt-Doped WSe2 Monolayer Based on First Principles Method , 2019, IEEE Access.

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

[46]  Feng Ding,et al.  Filtering-Based Multistage Recursive Identification Algorithm for an Input Nonlinear Output-Error Autoregressive System by Using the Key Term Separation Technique , 2017, Circuits Syst. Signal Process..

[47]  Xiaoxing Zhang,et al.  A First-Principles Study of the SF6 Decomposed Products Adsorbed Over Defective WS2 Monolayer as Promising Gas Sensing Device , 2019, IEEE Transactions on Device and Materials Reliability.

[48]  Hui Liu,et al.  Novel Method for Identifying Fault Location of Mixed Lines , 2018, Energies.

[49]  Youqing Wang,et al.  Weighted preliminary-summation-based principal component analysis for non-Gaussian processes , 2019, Control Engineering Practice.

[50]  Tingli Su,et al.  Integrated Predictor Based on Decomposition Mechanism for PM2.5 Long-Term Prediction , 2019, Applied Sciences.

[51]  C. Yin,et al.  Exact joint laws associated with spectrally negative Lévy processes and applications to insurance risk theory , 2011, 1101.0445.

[52]  Feng Ding,et al.  New gradient based identification methods for multivariate pseudo-linear systems using the multi-innovation and the data filtering , 2017, J. Frankl. Inst..

[53]  Yiyang Pei,et al.  Dynamic Contract Incentive Mechanism for Cooperative Wireless Networks , 2018, IEEE Transactions on Vehicular Technology.

[54]  Ting Cui,et al.  Joint Multi-innovation Recursive Extended Least Squares Parameter and State Estimation for a Class of State-space Systems , 2020 .

[55]  Qiao Zhu,et al.  A Low-Cost Lateral Active Suspension System of the High-Speed Train for Ride Quality Based on the Resonant Control Method , 2018, IEEE Transactions on Industrial Electronics.