RESEARCH ARTICLE
Auxiliary model-based multi-innovation recursive identification algorithms for an input nonlinear controlled autoregressive moving average system with variable-gain nonlinearity
Yamin Fan,
Ximei Liu,
Corresponding Author
Yamin Fan
College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao, 266061 P. R. China
Correspondence Ximei Liu and Yamin Fan, College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao, 266061, P. R. China.
Emails: [email protected]; [email protected]
Search for more papers by this authorCorresponding Author
Ximei Liu
College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao, 266061 P. R. China
Correspondence Ximei Liu and Yamin Fan, College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao, 266061, P. R. China.
Emails: [email protected]; [email protected]
Search for more papers by this authorYamin Fan,
Ximei Liu,
Corresponding Author
Yamin Fan
College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao, 266061 P. R. China
Correspondence Ximei Liu and Yamin Fan, College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao, 266061, P. R. China.
Emails: [email protected]; [email protected]
Search for more papers by this authorCorresponding Author
Ximei Liu
College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao, 266061 P. R. China
Correspondence Ximei Liu and Yamin Fan, College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao, 266061, P. R. China.
Emails: [email protected]; [email protected]
Search for more papers by this authorFunding information: National Natural Science Foundation of China, 61472195
Summary
For the parameter estimation problem of an input nonlinear controlled autoregressive moving average system with variable-gain nonlinearity, this article gives an analytical form of the variable-gain nonlinearity by introducing an appropriate switching function and derives an auxiliary model-based extended stochastic gradient algorithm with a forgetting factor and an auxiliary model-based recursive extended least-squares algorithm. For the sake of improving the parameter estimation accuracy, an auxiliary model-based multi-innovation extended stochastic gradient algorithm with a forgetting factor and an auxiliary model-based multi-innovation recursive extended least-squares algorithm are presented by utilizing the multi-innovation identification theory. The simulation results confirm the effectiveness of the proposed algorithms and show that the auxiliary model-based multi-innovation recursive identification algorithms have higher identification accuracy compared with the other two algorithms.
Open Research
DATA AVAILABILITY STATEMENT
All data generated or analyzed during this study are included in this article.
REFERENCES
- 1Xu L, Xiong WL, Alsaedi A, Hayat T. Hierarchical parameter estimation for the frequency response based on the dynamical window data. Int J Control Autom Syst. 2018; 16(4): 1756-1764.
- 2Ding F, Liu G, Liu XP. Parameter estimation with scarce measurements. Automatica. 2011; 47(8): 1646-1655.
- 3Ding F, Liu YJ, Bao B. Gradient based and least squares based iterative estimation algorithms for multi-input multi-output systems. Proc Inst Mech Eng I J Syst Control Eng. 2012; 226(1): 43-55.
- 4Xu L, Song GL. A recursive parameter estimation algorithm for modeling signals with multi-frequencies. Circuits Syst Signal Process. 2020; 39(8): 4198-4224.
- 5Ding F. Combined state and least squares parameter estimation algorithms for dynamic systems. Appl Math Model. 2014; 38(1): 403-412.
- 6Li MH, Liu XM. Maximum likelihood least squares based iterative estimation for a class of bilinear systems using the data filtering technique. Int J Control Autom Syst. 2020; 18(6): 1581-1592.
- 7Rahmani MR, Farrokhi M. Robust identification of MISO neuro-fractional-order Hammerstein systems. Int J Robust Nonlinear Control. 2019; 29: 2137-2148.
- 8Li JH, Zheng WX, Gu J, Liang H. Parameter estimation algorithms for Hammerstein output error systems using Levenberg-Marquardt optimization method with varying interval measurements. J Frankl Inst. 2017; 354(1): 316-331.
- 9Vörös J. Modeling and parameter identification of systems with multisegment piecewise-linear characteristics. IEEE Trans Automat Contr. 2002; 47(1): 184-188.
- 10Vörös J. Parameter identification of Wiener systems with multisegment piecewise-linear nonlinearities. Syst Control Lett. 2007; 56(2): 99-105.
- 11Liu Y, Bai EW. Iterative identification of Hammerstein systems with piecewise-linear nonlinearities. Automatica. 2006; 43(2): 346-354.
- 12Zhang J, Yu F, Chin K. Recursive identification of Hammerstein systems with dead-zone nonlinearity in the presence of bounded noise. Int J Syst Sci. 2017; 48(11): 2394-2404.
- 13Levanony L, Berman N. Recursive nonlinear system identification by a stochastic gradient algorithm: stability, performance, and model nonlinearity considerations. IEEE Trans Signal Process. 2004; 52(9): 2540-2550.
- 14Pan J, Jiang X, Wan XK, Ding W. A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems. Int J Control Autom Syst. 2017; 15(3): 1189-1197.
- 15Ding F. System Identification - Multi-Innovation Identification Theory and Methods. Science Press; 2016.
- 16Xu L. Parameter estimation algorithms for dynamical response signals based on the multi-innovation theory and the hierarchical principle. IET Signal Process. 2017; 11(2): 228-237.
- 17Gu Y, Chou Y, Liu J, et al. Moving horizon estimation for multirate systems with time-varying time-delays. J Frankl Inst. 2019; 356(4): 2325-2345.
- 18Xu L, Alsaedi A, Hayat T. A multi-innovation state and parameter estimation algorithm for a state space system with d-step state-delay. Signal Process. 2017; 140: 97-103.
- 19Xu L. Parameter estimation for control systems based on impulse responses. Int J Control Autom Syst. 2017; 15(6): 2471-2479.
- 20Xu L. Recursive least squares and multi-innovation stochastic gradient parameter estimation methods for signal modeling. Circuits Syst Signal Process. 2017; 36(4): 1735-1753.
- 21Wan HY, Luan XL, Karimi HR, Liu F. Dynamic self-triggered controller codesign for Markov jump systems. IEEE Trans Automat Contr. 2021; 66(3): 1353-1360.
- 22Pan J, Ma H, Zhang X, et al. Recursive coupled projection algorithms for multivariable output-error-like systems with coloured noises. IET Signal Process. 2020; 14(7): 455-466.
- 23Ma H, Pan J, Ding W. Partially-coupled least squares based iterative parameter estimation for multi-variable output-error-like autoregressive moving average systems. IET Control Theory Appl. 2019; 13(18): 3040-3051.
- 24Pan J, Li W, Zhang HP. Control algorithms of magnetic suspension systems based on the improved double exponential reaching law of sliding mode control. Int J Control Autom Syst. 2018; 16(6): 2878-2887.
- 25Ma H, Zhang X, Liu QY, et al. Partially-coupled gradient-based iterative algorithms for multivariable output-error-like systems with autoregressive moving average noises. IET Control Theory Appl. 2020; 14(17): 2613-2627.
- 26Wang DQ, Zhang S, Gan M, Qiu JL. A novel EM identification method for Hammerstein systems with missing output data. IEEE Trans Ind Inf. 2020; 16(4): 2500-2508.
- 27Vörös J. Iterative algorithm for parameter identification of Hammerstein systems with two-segment nonlinearities. IEEE Trans Automat Contr. 1999; 44(11): 2145-2149.
- 28Ji Y, Kang Z, Zhang C. Two-stage gradient-based recursive estimation for nonlinear models by using the data filtering. Int J Control Autom Syst. 2021; 19(8): 2706-2715.
- 29Liu YJ. An efficient hierarchical identification method for general dual-rate sampled-data systems. Automatica. 2014; 50(3): 962-970.
- 30Ji Y, Kang Z, Liu XM. The data filtering based multiple-stage Levenberg-Marquardt algorithm for Hammerstein nonlinear systems. Int J Robust Nonlinear Control. 2021; 31(15): 7007-7025.
- 31Wang YJ. Novel data filtering based parameter identification for multiple-input multiple-output systems using the auxiliary model. Automatica. 2016; 71: 308-313.
- 32Li MH, Liu XM. Iterative identification methods for a class of bilinear systems by using the particle filtering technique. Int J Adapt Control Signal Process. 2021; 35(11): 2056-2074.
- 33Zhou YH, Zhang X. Partially-coupled nonlinear parameter optimization algorithm for a class of multivariate hybrid models. Appl Math Comput. 2022; 414:126663.
- 34Zhou YH. Modeling nonlinear processes using the radial basis function-based state-dependent autoregressive models. IEEE Signal Process Lett. 2020; 27: 1600-1604.
- 35Ding J. Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data. IEEE Trans Automat Contr. 2022; 56(11): 2677-2683.
- 36 Zhou YH. Hierarchical estimation approach for RBF-AR models with regression weights based on the increasing data length. IEEE Trans Circuits Syst-II Exp Briefs. 2021. https://doi.org/10.1109/TCSII.2021.3076112
- 37Xu L. Hierarchical Newton and least squares iterative estimation algorithm for dynamic systems by transfer functions based on the impulse responses. Int J Syst Sci. 2019; 50(1): 141-151.
- 38Ji Y, Kang Z. Three-stage forgetting factor stochastic gradient parameter estimation methods for a class of nonlinear systems. Int J Robust Nonlinear Control. 2021; 31(3): 871-987.
- 39Ding F, Qiu L, Chen T. Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems. Automatica. 2009; 45(2): 324-332.
- 40Zhang X, Yang EF. Highly computationally efficient state filter based on the delta operator. Int J Adapt Control Signal Process. 2019; 33(6): 875-889.
- 41Zhang X, Yang EF. State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors. Int J Adapt Control Signal Process. 2019; 33(7): 1157-1173.
- 42Zhang X, Yang EF. State filtering-based least squares parameter estimation for bilinear systems using the hierarchical identification principle. IET Control Theory Appl. 2018; 12(12): 1704-1713.
- 43Zhang X, Hayat T. Combined state and parameter estimation for a bilinear state space system with moving average noise. J Frankl Inst. 2018; 355(6): 3079-3103.
- 44Zhang X, Hayat T. Recursive parameter identification of the dynamical models for bilinear state space systems. Nonlinear Dyn. 2017; 89(4): 2415-2429.
- 45Xu L, Hayat T. Hierarchical recursive signal modeling for multi-frequency signals based on discrete measured data. Int J Adapt Control Signal Process. 2021; 35(5): 676-693.
- 46Xu L. Separable recursive gradient algorithm for dynamical systems based on the impulse response signals. Int J Control Autom Syst. 2020; 18(12): 3167-3177.
- 47Ji Y, Jiang XK, Wan LJ. Hierarchical least squares parameter estimation algorithm for two-input Hammerstein finite impulse response systems. J Frankl Inst. 2020; 357(8): 5019-5032.
- 48Wang LJ, Ji Y, Wan LJ, et al. Hierarchical recursive generalized extended least squares estimation algorithms for a class of nonlinear stochastic systems with colored noise. J Frankl Inst. 2019; 356(16): 10102-10122.
- 49Ding F. Coupled-least-squares identification for multivariable systems. IET Control Theory Appl. 2013; 7(1): 68-79.
- 50Ding F, Liu XG, Chu J. Gradient-based and least-squares-based iterative algorithms for Hammerstein systems using the hierarchical identification principle. IET Control Theory Appl. 2013; 7(2): 176-184.
- 51Ji Y, Zhang C, Kang Z, et al. Parameter estimation for block-oriented nonlinear systems using the key term separation. Int J Robust Nonlinear Control. 2020; 30(9): 3727-3752.
- 52Xu L, Yang EF. Auxiliary model multiinnovation stochastic gradient parameter estimation methods for nonlinear sandwich systems. Int J Robust Nonlinear Control. 2021; 31(1): 148-165.
- 53Wang LJ, Guo J, Xu C, et al. Hybrid model predictive control strategy of supercapacitor energy storage system based on double active bridge. Energies. 2019; 12(11): 2134.
- 54Li XY, Wang HL, Wu BY, et al. A stable and efficient technique for linear boundary value problems by applying kernel functions. Appl Numer Math. 2022; 172: 206-214.
- 55Zhang X, Hayat T. A hierarchical approach for joint parameter and state estimation of a bilinear system with autoregressive noise. Mathematics. 2019; 7(4):356.
- 56Han HG, Liu HX, Li JM, et al. Cooperative fuzzy-neural control for wastewater treatment process. IEEE Trans Ind Inf. 2021; 17(9): 5971-5981.
- 57Han HG, Liu Z, Liu HX, et al. Knowledge-data-driven model predictive control for a class of nonlinear systems. IEEE Trans Syst Man Cyber-Syst. 2021; 51(7): 4492-4504.
- 58Han HG, Zhang L, Liu HX, et al. Intelligent optimal control system with flexible objective functions and its applications in wastewater treatment process. IEEE Trans Syst Man Cybern-Syst. 2021; 51(6): 3464-3476.
- 59Bu N, Pang JX, Deng M. Robust fault tolerant tracking control for the multi-joint manipulator based on operator theory. J Frankl Inst. 2020; 357(5): 2696-2714.
- 60Ding F, Chen T. Combined parameter and output estimation of dual-rate systems using an auxiliary model. Automatica. 2004; 40(10): 1739-1748.
- 61Ding F, Chen T. Parameter estimation of dual-rate stochastic systems by using an output error method. IEEE Trans Automat Contr. 2005; 50(9): 1436-1441.
- 62Ding F, Liu G, Liu XP. Partially coupled stochastic gradient identification methods for non-uniformly sampled systems. IEEE Trans Automat Contr. 2010; 55(8): 1976-1981.
- 63Ma P, Wang L. Filtering-based recursive least squares estimation approaches for multivariate equation-error systems by using the multiinnovation theory. Int J Adapt Control Signal Process. 2021; 35(9): 1898-1915.
- 64Ding JL, Zhang WH. Finite-time adaptive control for nonlinear systems with uncertain parameters based on the command filters. Int J Adapt Control Signal Process. 2021; 35(9): 1754-1767.
- 65Chen J, Zhu QM, Liu YJ. Modified Kalman filtering based multi-step-length gradient iterative algorithm for ARX models with random missing outputs. Automatica. 2020; 118:109034.
- 66Xu L, Zhu Q. Decomposition strategy-based hierarchical least mean square algorithm for control systems from the impulse responses. Int J Syst Sci. 2021; 52(9): 1806-1821.
- 67Chen J, Huang B, Gan M, et al. A novel reduced-order algorithm for rational models based on Arnoldi process and Krylov subspace. Automatica. 2021; 129:109663.
- 68Mao YW, Liu S, Liu JF. Robust economic model predictive control of nonlinear networked control systems with communication delays. Int J Adapt Control Signal Process. 2020; 34(5): 614-637.
- 69Chen J, Shen QY, Ma JX, et al. Stochastic average gradient algorithm for multirate FIR models with varying time delays using self-organizing maps. Int J Adapt Control Signal Process. 2020; 34(7): 955-970.
- 70Ding F, Liu XP, Liu G. Identification methods for Hammerstein nonlinear systems. Digit Signal Process. 2011; 21(2): 215-238.
- 71Ding F. Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling. Appl Math Model. 2013; 37(4): 1694-1704.
- 72Xiong W, Jia X, Yang D, et al. DP-LinkNet: a convolutional network for historical document image binarization. KSII Trans Internet Inf Syst. 2021; 15(5): 1778-1797.
- 73Xiong W, Zhou L, Yue L, et al. An enhanced binarization framework for degraded historical document images. EURASIP J Image Video Process. 2021; 2021:13.
- 74Chang C, Wang QY, Jiang JC, et al. Lithium-ion battery state of health estimation using the incremental capacity and wavelet neural networks with genetic algorithm. J Energy Storage. 2021; 38:102570.
- 75Kang Z, Ji Y, Liu XM, et al. Hierarchical recursive least squares algorithms for Hammerstein nonlinear autoregressive output-error systems. Int J Adapt Control Signal Process. 2021; 35(11): 2276-2295.
- 76Zhao G, Gao TH, Wang YD, et al. Optimal sizing of isolated microgrid containing photovoltaic/photothermal/wind/diesel/battery. Int J Photoenergy. 2021; 2021: 5566597.
- 77Kong JL, Wang HX, Wang XY, et al. Multi-stream hybrid architecture based on cross-level fusion strategy for fine-grained crop species recognition in precision agriculture. Comput Electron Agr. 2021; 185:106134.
- 78Zheng YY, Kong JL, Jin XB, et al. CropDeep: the crop vision dataset for deep-learning-based classification and detection in precision agriculture. Sensors. 2019; 19(5):1058.
- 79Zhang X. Adaptive parameter estimation for a general dynamical system with unknown states. Int J Robust Nonlinear Control. 2020; 30(4): 1351-1372.
- 80Zhang X. Recursive parameter estimation methods and convergence analysis for a special class of nonlinear systems. Int J Robust Nonlinear Control. 2020; 30(4): 1373-1393.
- 81Wang JW, Ji Y, Zhang C. Iterative parameter and order identification for fractional-order nonlinear finite impulse response systems using the key term separation. Int J Adapt Control Signal Process. 2021; 35(8): 1562-1577.
- 82Zhang X. Recursive parameter estimation and its convergence for bilinear systems. IET Control Theory Appl. 2020; 14(5): 677-688.
- 83Zhang X. Hierarchical parameter and state estimation for bilinear systems. Int J Syst Sci. 2020; 51(2): 275-290.
- 84Zhang X, Hayat T. Recursive identification of bilinear time-delay systems through the redundant rule. J Frankl Inst. 2020; 357(1): 726-747.
- 85Zhao ZY, Wang XY, Yao P, et al. A health performance evaluation method of multirotors under wind turbulence. Nonlinear Dyn. 2020; 102(3): 1701-1715.
- 86 Cao Y, Sun YK, Xie G, et al. A sound-based fault diagnosis method for railway point machines based on two-stage feature selection strategy and ensemble classifier. IEEE Trans Intell Transp Syst. 2022. doi:10.1109/TITS.2021.3109632
- 87Cao Y, Ma LC, Xiao S, et al. Standard analysis for transfer delay in CTCS-3. Chin J Electron. 2017; 26(5): 1057-1063.
- 88Cao Y, Wen JK, Ma LC. Tracking and collision avoidance of virtual coupling train control system. Alex Eng J. 2021; 60(2): 2115-2125.
- 89Cao Y, Wen JK, Ma LC. Tracking and collision avoidance of virtual coupling train control system. Futur Gener Comput Syst. 2021; 120: 76-90.
- 90Su S, Wang XK, Cao Y, Yin JT. An energy-efficient train operation approach by integrating the metro timetabling and eco-driving. IEEE Trans Intell Transp Syst. 2020; 21(10): 4252-4268.
- 91Su S, Tang T, Xun J, et al. Design of running grades for energy-efficient train regulation: a case study for Beijing Yizhuang line. IEEE Intell Transp Syst Mag. 2021; 13(2): 189-200.
- 92Cao Y, Wang Z, Liu F, et al. Bio-inspired speed curve optimization and sliding mode tracking control for subway trains. IEEE Trans Veh Technol. 2019; 68(7): 6331-6342.
- 93Cao Y, Sun YK, Xie G, et al. Fault diagnosis of train plug door based on a hybrid criterion for IMFs selection and fractional wavelet package energy entropy. IEEE Trans Veh Technol. 2019; 68(8): 7544-7551.
- 94Wang XG, Zhao M, Zhou Y, et al. Design and analysis for multi-disc coreless axial-flux permanent-magnet synchronous machine. IEEE Transn Appl Superconductivity. 2021; 31(8): 5203804.
- 95Wang XG, Wan ZW, Tang L, et al. Electromagnetic performance analysis of an axial flux hybrid excitation motor for HEV drives. IEEE Trans Appl Superconductivity. 2021; 31(8): 5205605.
