Highly efficient maximum-likelihood identification methods for bilinear systems with colored noises
Abstract
This paper mainly discussed the highly efficient iterative identification methods for bilinear systems with autoregressive moving average noise. Firstly, the input-output representation of the bilinear systems is derived through eliminating the unknown state variables in the model. Then based on the maximum-likelihood principle, a maximum-likelihood gradient-based iterative (ML-GI) algorithm is proposed to identify the parameters of the bilinear systems with colored noises. For improving the computational efficiency, the original identification model is divided into three sub-identification models with smaller dimensions and fewer parameters, and a hierarchical maximum-likelihood gradient-based iterative (H-ML-GI) algorithm is derived by using the hierarchical identification principle. A gradient-based iterative (GI) algorithm is given for comparison. Finally, the algorithms are verified by a simulation example and a practical continuous stirred tank reactor (CSTR) example. The results show that the proposed algorithms are effective for identifying bilinear systems with colored noises and the H-ML-GI algorithm has a higher computational efficiency and a faster convergence rate than the ML-GI algorithm and the GI algorithm.
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References
1. Raković SV, Dai L, Xia Y. Homothetic tube model predictive control for nonlinear systems. IEEE Trans Automat Contr 2023; 68(8): 4554–4569.
2. Xu L. Separable Newton recursive estimation method through system responses based on dynamically discrete measurements with increasing data length. Int J Control Autom Syst 2022; 20(2): 432–443.
3. Xu L. Parameter estimation for nonlinear functions related to system responses. Int J Control Autom Syst 2023; 21(6): 1780–1792.
4. Pan J, Liu Y, Shu J. Gradient-based parameter estimation for a nonlinear exponential autoregressive time-series model by using the multi-innovation. Int J Control Autom Syst 2023; 21(1): 140–150.
5. Pan J, Liu S, Shu J, et al. Hierarchical recursive least squares estimation algorithm for second-order Volterra nonlinear systems. Int J Control Autom Syst 2022; 20(12): 3940–3950.
6. Pan J, Zhang H, Guo H, et al. Multivariable CAR-like system identification with multi-innovation gradient and least squares algorithms. Int J Control Autom Syst 2023; 21(5): 1455–1464.
7. Wang Y, Ding F. Filtering-based iterative identification for multivariable systems. IET Control Theory Appl 2016; 10(8): 894–902.
8. Ding F, Xu L, Zhang X, et al. Filtered auxiliary model recursive generalized extended parameter estimation methods for Box–Jenkins systems by means of the filtering identification idea. Int J Robust Nonlinear Control 2023; 33(10): 5510–5535.
9. Ji Y, Jiang A. Filtering-based accelerated estimation approach for generalized time-varying systems with disturbances and colored noises. IEEE Trans Circuits Syst II Express Briefs 2023; 70(1): 206–210.
10. Lee KW, Singh SN. Composite adaptive control of submarine and parameter identification by integral regressor excitation. Proc IMechE, Part I: J Systems and Control Engineering 2024; 238(5): 907–928.
11. Li W, Krstic M. Prescribed-time output-feedback control of stochastic nonlinear systems. IEEE Trans Automat Contr 2023; 68(3): 1431–1446.
12. Marzougui S, Bedoui S, Abderrahim K. On the combined estimation of the parameters and the states of fractional-order systems. Proc IMechE, Part I: J Systems and Control Engineering 2023; 237(10): 1853–1866.
13. Ding F, Liu X, Liu M. The recursive least squares identification algorithm for a class of Wiener nonlinear systems. J Franklin Inst 2016; 353(7): 1518–1526.
14. Gupta S, Padhee S, Pekar L. Recursive least squares identification of heat exchanger system using block-structured models. Proc IMechE, Part I: J Systems and Control Engineering 2022; 236(4): 870–879.
15. Hafezi Z, Arefi MM. Recursive generalized extended least squares and RML algorithms for identification of bilinear systems with ARMA noise. ISA Trans 2019; 88: 50–61.
16. Liu S, Zhang X, Xu L, et al. Expectation–maximization algorithm for bilinear systems by using the Rauch–Tung–Striebel smoother. Automatica 2022; 142: 110365.
17. Favoreel W, De Moor B, Van Overschee P. Subspace identification of bilinear systems subject to white inputs. IEEE Trans Automat Contr 1999; 44(6): 1157–1165.
18. Dai H, Sinha NK. Robust recursive least-squares method with modified weights for bilinear system identification. IEE Proc Control Theory Appl 1989; 136(3): 122–126.
19. Wu X. Data filtering based multi-innovation gradient identification for bilinear systems with colored noise. Int J Adapt Control Signal Process 2023; 37(7): 1940–1960.
20. Gu Y, Dai W, Zhu Q, et al. Hierarchical multi-innovation stochastic gradient identification algorithm for estimating a bilinear state-space model with moving average noise. J Comput Appl Math 2023; 420: 114794.
21. Liu S, Wang Y, Ding F, et al. Joint iterative state and parameter estimation for bilinear systems with autoregressive noises via the data filtering. ISA Trans 2024; 147: 337–349.
22. Fnaiech F, Ljung L. Recursive identification of bilinear systems. Int J Control 1987; 45(2): 453–470.
23. An S, He Y, Wang L. Maximum likelihood based multi-innovation stochastic gradient identification algorithms for bilinear stochastic systems with ARMA noise. Int J Adapt Control Signal Process 2023; 37(10): 2690–2705.
24. Kawaria N, Patidar R, George NV. Parameter estimation of MIMO bilinear systems using a Levy shuffled frog leaping algorithm. Soft Comput 2017; 21(14): 3849–3858.
25. Li M, Liu X. Maximum likelihood hierarchical least squares-based iterative identification for dual-rate stochastic systems. Int J Adapt Control Signal Process 2021; 35(2): 240–261.
26. Li M, Liu X. Iterative identification methods for a class of bilinear systems by using the particle filtering technique. Int J Adapt Control Signal Process 2021; 35(10): 2056–2074.
27. Alfonsi A, Kebaier A, Rey C. Maximum likelihood estimation for Wishart processes. Stoch Process Appl 2016; 126(11): 3243–3282.
28. Li S, Ji Y. Maximum likelihood interval-varying recursive least squares identification for output-error autoregressive systems with scarce measurements. J Franklin Inst 2023; 360(11): 7230–7246.
29. Gibson S, Wills A, Ninness B. Maximum-likelihood parameter estimation of bilinear systems. IEEE Trans Automat Contr 2005; 50(10): 1581–1596.
30. Wang X, Ma J, Xiong W. Expectation-maximization algorithm for bilinear state-space models with time-varying delays under non-Gaussian noise. Int J Adapt Control Signal Process 2023; 37(10): 2706–2724.
31. Li M, Liu X. 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.
32. Ding F. Least squares parameter estimation and multi-innovation least squares methods for linear fitting problems from noisy data. J Comput Appl Math 2023; 426: 115107.
33. Wang L, An S, He Y, et al. The filtering based maximum likelihood recursive least squares parameter estimation algorithms for a class of nonlinear stochastic systems with colored noise. Int J Control Autom Syst 2023; 21(1): 151–160.
34. Liu X, Fan Y. Maximum likelihood extended gradient-based estimation algorithms for the input nonlinear controlled autoregressive moving average system with variable-gain nonlinearity. Int J Robust Nonlinear Control 2021; 31(9): 4017–4036.
35. Ma H, Pan J, Ding F, et al. 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.
36. Pan 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.
37. Ding F, Lv L, Pan J, et al. Two-stage gradient-based iterative estimation methods for controlled autoregressive systems using the measurement data. Int J Control Autom Syst 2020; 18(4): 886–896.
38. Young PC. Refined instrumental variable estimation: maximum likelihood optimization of a unified Box–Jenkins model. Automatica 2015; 52: 35–46.
39. Ding F, Xu L, Zhang X, et al. Hierarchical gradient- and least-squares-based iterative estimation algorithms for input-nonlinear output-error systems from measurement information by using the over-parameterization. Int J Robust Nonlinear Control 2024; 34(2): 1120–1147.
40. Ding F, Xu L, Zhang X, et al. Recursive identification methods for general stochastic systems with colored noises by using the hierarchical identification principle and the filtering identification idea. Annu Rev Control 2024; 57: 100942.
41. Liu J, Ji Y. Auxiliary model-based recursive least squares algorithm for two-input single-output Hammerstein output-error moving average systems by using the hierarchical identification principle. Int J Robust Nonlinear Control 2022; 32(13): 7575–7593.
42. Wang J, Ji Y, Zhang X, et al. Two-stage gradient-based iterative algorithms for the fractional-order nonlinear systems by using the hierarchical identification principle. Int J Adapt Control Signal Process 2022; 36(7): 1778–1796.
43. Li M, Liu X, Ding F. 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. Int J Adapt Control Signal Process 2019; 33(7): 1189–1211.
44. Liu H, Wang J, Ji Y. Maximum likelihood recursive generalized extended least squares estimation methods for a bilinear-parameter systems with ARMA noise based on the over-parameterization model. Int J Control Autom Syst 2022; 20(8): 2606–2615.
45. Ji 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.
46. Bai Y, Yan B, Zhou C, et al. State of art on state estimation: Kalman filter driven by machine learning. Annu Rev Control 2023; 56: 100909.
47. Bernard P, Andrieu V, Astolfi D. Observer design for continuous-time dynamical systems. Annu Rev Control 2022; 53: 224–248.
48. Hou J, Chen F, Li P, et al. Gray-box parsimonious subspace identification of Hammerstein-type systems. IEEE Trans Ind Electron 2021; 68(10): 9941–9951.
49. Ding F, Shao X, Xu L, et al. Filtered generalized iterative parameter identification for equation-error autoregressive models based on the filtering identification idea. Int J Adapt Control Signal Process 2024; 38(4): 1363–1385.
50. Li M, Liu X. Particle filtering-based iterative identification methods for a class of nonlinear systems with interval-varying measurements. Int J Control Autom Syst 2022; 20(7): 2239–2248.
51. Xing H, Ding F, Pan F, et al. Hierarchical recursive least squares parameter estimation methods for multiple-input multiple-output systems by using the auxiliary models. Int J Adapt Control Signal Process 2023; 37(11): 2983–3007.
52. Fan Y, Liu X. Two-stage auxiliary model gradient-based iterative algorithm for the input nonlinear controlled autoregressive system with variable-gain nonlinearity. Int J Robust Nonlinear Control 2020; 30(14): 5492–5509.
53. Dong D, Petersen IR. Quantum estimation, control and learning: opportunities and challenges. Annu Rev Control 2022; 54: 243–251.
54. Gehlhar R, Tucker M, Young AJ, et al. A review of current state-of-the-art control methods for lower-limb powered prostheses. Annu Rev Control 2023; 55: 142–164.
55. Koga S, Krstic M. State estimation of the Stefan PDE: a tutorial on design and applications to polar ice and batteries. Annu Rev Control 2022; 53: 199–223.
56. Nurdin HI, Guţá M. Parameter estimation and system identification for continuously-observed quantum systems. Annu Rev Control 2022; 54: 295–304.
57. Petersen IR, Dong D. Special section on estimation and control of quantum systems. Annu Rev Control 2022; 54: 241–242.
58. Saviolo A, Loianno G. Learning quadrotor dynamics for precise, safe, and agile flight control. Annu Rev Control 2023; 55: 45–60.
59. Zhang XM, Han QL, Ge X, et al. Sampled-data control systems with non-uniform sampling: a survey of methods and trends. Annu Rev Control 2023; 55: 70–91.
60. Yang D, Ding F. Multi-innovation gradient-based iterative identification methods for feedback nonlinear systems by using the decomposition technique. Int J Robust Nonlinear Control 2023; 33(13): 7755–7773.
61. Yang D, Liu Y, Ding F, et al. Hierarchical gradient-based iterative parameter estimation algorithms for a nonlinear feedback system based on the hierarchical identification principle. Circuits Syst Signal Process 2024; 43: 124–151.
62. Liu H, Wang J, Meng X. Hierarchical maximum likelihood generalized extended stochastic gradient algorithms for bilinear-in-parameter systems. Optim Control Appl Methods 2022; 43(2): 402–417.
63. Ji Y, Kang Z, Zhang X, et al. Model recovery for multi-input signal-output nonlinear systems based on the compressed sensing recovery theory. J Franklin Inst 2022; 359(5): 2317–2339.
64. Fan Y, Liu X. Auxiliary model-based multi-innovation recursive identification algorithms for an input nonlinear controlled autoregressive moving average system with variable-gain nonlinearity. Int J Adapt Control Signal Process 2022; 36(3): 521–540.
65. Ji Y, Kang Z, Liu X. The data filtering based multiple-stage Levenberg–Marquardt algorithm for Hammerstein nonlinear systems. Int J Robust Nonlinear Control 2021; 31(15): 7007–7025.
66. Chen J, Zhu Q, Liu Y. Modified Kalman filtering based multi-step-length gradient iterative algorithm for ARX models with random missing outputs. Automatica 2020; 118: 109034.
67. Zhang T, Zhao S, Luan X, et al. Bayesian inference for state-space models with student-t mixture distributions. IEEE Trans Cybern 2023; 53(7): 4435–4445.
68. Zhao S, Shmaliy YS, Ahn CK, et al. An improved iterative FIR state estimator and its applications. IEEE Trans Ind Inform 2020; 16(2): 1003–1012.
69. Zhao S, Shmaliy YS, Liu F. Batch optimal FIR smoothing: increasing state informativity in nonwhite measurement noise environments. IEEE Trans Ind Inform 2023; 19(5): 6993–7001.
70. Zhao S, Li K, Ahn CK, et al. Tuning-free Bayesian estimation algorithms for faulty sensor signals in state-space. IEEE Trans Ind Electron 2023; 70(1): 921–929.
71. Zhao S, Huang B, Zhao C. Online probabilistic estimation of sensor faulty signal in industrial processes and its applications. IEEE Trans Ind Electron 2021; 68(9): 8853–8862.
72. Xiong J, Pan J, Chen G, et al. Sliding mode dual-channel disturbance rejection attitude control for a quadrotor. IEEE Trans Ind Electron 2022; 69(10): 10489–10499.
73. Pan J, Chen Q, Xiong J, et al. A novel quadruple-boost nine-level switched-capacitor inverter. J Electr Eng Technol 2023; 18(1): 467–480.
74. Pan J, Shao B, Xiong J, et al. Attitude control of quadrotor UAVs based on adaptive sliding mode. Int J Control Autom Syst 2023; 21(8): 2698–2707.
75. Xu L, Xu H, Ding F. Adaptive multi-innovation gradient identification algorithms for a controlled autoregressive autoregressive moving average model. Circuits Syst Signal Process 2024; 43: 3718–3747.
76. Zhao S, Shmaliy YS, Ahn CK, et al. Self-tuning unbiased finite impulse response filtering algorithm for processes with unknown measurement noise covariance. IEEE Trans Control Syst Technol 2021; 29(3): 1372–1379.
77. Zhao S, Huang B. Trial-and-error or avoiding a guess? Initialization of the Kalman filter. Automatica 2020; 121: 109184.
78. Xu L, Ding F. Separable synthesis gradient estimation methods and convergence analysis for multivariable systems. J Comput Appl Math 2023; 427: 115104.
79. Ding F, Ma H, Pan J, et al. Hierarchical gradient- and least squares-based iterative algorithms for input nonlinear output-error systems using the key term separation. J Franklin Inst 2021; 358(9): 5113–5135.
80. Xu L, Ding F. Decomposition and composition modeling algorithms for control systems with colored noises. Int J Adapt Control Signal Process 2024; 38(1): 255–278.
81. Bi Y, Ji Y. Parameter estimation of fractional-order Hammerstein state space system based on the extended Kalman filter. Int J Adapt Control Signal Process 2023; 37(7): 1827–1846.
82. Sun S, Xu L, Ding F, et al. Filtered multi-innovation-based iterative identification methods for multivariate equation-error ARMA systems. Int J Adapt Control Signal Process 2023; 37(3): 836–855.
83. Sun S, Wang X, Ding F. Hierarchical iterative identification algorithms for a nonlinear system with dead-zone and saturation nonlinearity based on the auxiliary model. Int J Adapt Control Signal Process 2023; 37(7): 1866–1892.
84. Zhao S, Shmaliy YS, Ahn CK, et al. Probabilistic monitoring of correlated sensors for nonlinear processes in state space. IEEE Trans Ind Electron 2020; 67(3): 2294–2303.
85. Zhang X, Ding F. Hierarchical parameter and state estimation for bilinear systems. Int J Syst Sci 2020; 51(2): 275–290.
86. Chen J, Pu Y, Guo L, et al. Second-order optimization methods for time-delay autoregressive eXogenous models: nature gradient descent method and its two modified methods. Int J Adapt Control Signal Process 2023; 37(1): 211–223.
87. Wei C, Zhang X, Xu L, et al. Overall recursive least squares and overall stochastic gradient algorithms and their convergence for feedback nonlinear controlled autoregressive systems. Int J Robust Nonlinear Control 2022; 32(9): 5534–5554.
88. Jin Y. A coupled recursive least squares algorithm for multivariable systems and its computational amount analysis by using the coupling identification concept. Int J Adapt Control Signal Process. 2024; 38(2):513–533.
89. Wang Y, Yang L. An efficient recursive identification algorithm for multilinear systems based on tensor decomposition. Int J Robust Nonlinear Control 2021; 31(16): 7920–7936.
90. Li J, Ding F, Hayat T. A novel nonlinear optimization method for fitting a noisy Gaussian activation function. Int J Adapt Control Signal Process 2022; 36(3): 690–707.
91. Ji Y, Liu J, Liu H. An identification algorithm of generalized time-varying systems based on the Taylor series expansion and applied to a pH process. J Process Control 2023; 128: 103007.
92. Miao G, Ding F, Liu Q, et al. Iterative parameter identification algorithms for transformed dynamic rational fraction input–output systems. J Comput Appl Math 2023; 434: 115297.
93. Cao Y, Sun Y, 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 Vehicular Technol 2019; 68(8): 7544–7551.
94. Zhou Y, Ling KV, Ding F, et al. Online network-based identification and its application in satellite attitude control systems. IEEE Trans Aerosp Electron Syst 2023; 59(3): 2530–2543.
95. Cao Y, Ma L, Xiao S, et al. Standard analysis for transfer delay in CTCS-3. Chin J Electron 2017; 26(5): 1057–1063.
96. Sun Y, Cao Y, Li P. Contactless fault diagnosis for railway point machines based on multi-scale fractional wavelet packet energy entropy and synchronous optimization strategy. IEEE Trans Vehicular Technol 2022; 71(6): 5906–5914.
97. Zhao S, Wang J, Shmaliy YS, et al. Discrete time q-lag maximum likelihood FIR smoothing and iterative recursive algorithm. IEEE Trans Signal Process 2021; 69: 6342–6354.
98. Zhao S, Shmaliy YS, Andrade-Lucio JA, et al. Multipass optimal FIR filtering for processes with unknown initial states and temporary mismatches. IEEE Trans Ind Inform 2021; 17(8): 5360–5368.
99. Liu Q, Chen F. Model transformation based distributed stochastic gradient algorithm for multivariate output-error systems. Int J Syst Sci 2023; 54(7): 1484–1502.
100. Zhou Y, Ding F. A novel recursive multivariate nonlinear time-series modeling method by using the coupling identification concept. Appl Math Model 2024; 127: 571–587.
101. Wang DQ, Liu HB. Highly efficient identification methods for dual-rate Hammerstein systems. IEEE Trans Control Syst Technol 2015; 23(5): 1952–1960.
102. Xing H, Ding F, Zhang X, et al. Highly-efficient filtered hierarchical identification algorithms for multiple-input multiple-output systems with colored noises. Syst Control Lett 2024; 186: 105762.
103. Wan X, Liao T, Gong W, et al. A precise respiratory and heart rate detection method for millimeter-wave radar. J Mech Med Biol 2024.
104. Xu J, Mei X, Chen Y, et al. An effective premature ventricular contraction detection algorithm based on adaptive template matching and characteristic recognition. Signal Image Video Process 2024; 18(3): 2811–2818.
105. Wan X, Liu Y, Mei X, et al. A novel atrial fibrillation automatic detection algorithm based on ensemble learning and multi-feature discrimination. Med Biol Eng Comput 2024; 62: 1809–1820.
106. Cao Y, Wen J, Hobiny A, et al. Parameter-varying artificial potential field control of virtual coupling system with nonlinear dynamics. Fractals 2022; 30(02): 2240099.
107. Cao Y, Wen J, Ma L. Tracking and collision avoidance of virtual coupling train control system. Alex Eng J 2021; 60(2): 2115–2125.
108. Su S, Wang X, Cao Y, et al. An energy-efficient train operation approach by integrating the metro timetabling and eco-driving. IEEE Trans Intell Transp Syst 2020; 21(10): 4252–4268.
109. Cao Y, An Y, Su S, et al. A statistical study of railway safety in China and Japan 1990–2020. Accid Anal Prev 2022; 175: 106764.
110. Cao Y, Yang Y, Ma L, et al. Research on virtual coupled train control method based on GPC & VAPF. Chin J Electron 2022; 31(5): 897–905.
111. Wang X, Su S, Cao Y, et al. Robust control for dynamic train regulation in fully automatic operation system under uncertain wireless transmissions. IEEE Trans Intell Transp Syst 2022; 23(11): 20721–20734.
112. Cao Y, Zhang Z, Cheng F, et al. Trajectory optimization for high-speed trains via a mixed integer linear programming approach. IEEE Trans Intell Transp Syst 2022; 23(10): 17666–17676.
113. Cao Y, Sun Y, 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; 23(8): 12074–12083.
114. Cao Y, Wang ZC, Liu F, et al. Bio-inspired speed curve optimization and sliding mode tracking control for subway trains. IEEE Trans Vehicular Technol 2019; 68(7): 6331–6342.
115. Xu L, Ding F, Zhang X, et al. Novel parameter estimation method for the systems with colored noises by using the filtering identification idea. Syst Control Lett 2024; 186: 105774.
116. Liao L, Yang D, Li X, et al. Fault diagnosis of lithium-ion batteries based on wavelet packet decomposition and Manhattan average distance. Int J Green Energy 2024; 1–15.
117. Shu J, Wang S, Yu S, et al. CFSA-Net: efficient large-scale point cloud semantic segmentation based on cross-fusion self-attention. Comput Mat Contin 2023; 77(3): 2677–2697.
118. Ma H, Ding F, Wang Y. A novel multi-innovation gradient support vector machine regression method. ISA Trans 2022; 130: 343–359.
119. Wang Y, Ding F, Wu M. Recursive parameter estimation algorithm for multivariate output-error systems. J Franklin Inst 2018; 355(12): 5163–5181.
120. Cao Y, Ji Y, Sun Y, et al. The fault diagnosis of a switch machine based on deep random forest fusion. IEEE Intell Transp Syst Mag 2023; 15(1): 437–452.
121. Cui T, Ding F, Hayat T. Moving data window-based partially-coupled estimation approach for modeling a dynamical system involving unmeasurable states. ISA Trans 2022; 128: 437–452.
122. Liao L, Hu X, Chen H, et al. Quantitative diagnosis of micro-short circuit for lithium-ion batteries considering aging based on incremental capacity curve. J Energy Storage 2024; 79: 110240
123. Liao L, Hu X, Li H, et al. Design of an improved modular multilevel converter reconfigurable equalization scheme based on difference of voltage variation. J Electrochem Energy Convers Storage 2024; 21(3): 031010.
124. Hu C, Ji Y, Ma C. Joint two-stage multi-innovation recursive least squares parameter and fractional-order estimation algorithm for the fractional-order input nonlinear output-error autoregressive model. Int J Adapt Control Signal Process 2023; 37(7): 1650–1670.
125. Hu C, Liu H, Ji Y. Parameter and order estimation algorithms and convergence analysis for lithium-ion batteries. Int J Robust Nonlinear Control 2023; 33(18): 11411–11433.
126. Ji 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): 971–987.
127. Xu L, Ding F, Lu X, et al. Hierarchical multi-innovation generalised extended stochastic gradient methods for multivariable equation-error autoregressive moving average systems. IET Control Theory Appl 2020; 14(10): 1276–1286.
128. Xu L, Ding F, Yang E. Separable recursive gradient algorithm for dynamical systems based on the impulse response signals. Int J Control Autom Syst 2020; 18(12): 3167–3177.
129. Wang X, Ding F. Modified particle filtering-based robust estimation for a networked control system corrupted by impulsive noise. Int J Robust Nonlinear Control 2022; 32(2): 830–850.
130. Liu S, Ding F, Xu L, et al. Hierarchical principle-based iterative parameter estimation algorithm for dual-frequency signals. Circuits Syst Signal Process 2019; 38(7): 3251–3268.
131. Hou J. Parsimonious model based consistent subspace identification of Hammerstein systems under periodic disturbances. Int J Control Autom Syst 2024; 22(1): 61–71.
132. Wan L, Ding F. Decomposition- and gradient-based iterative identification algorithms for multivariable systems using the multi-innovation theory. Circuits Syst Signal Process 2019; 38(7): 2971–2991.
133. Chang Y, Zhou F, Yan H, et al. Noise and interference suppression control method of DC-DC buck converters based on cascaded filter LADRC. Int J Control Autom Syst 2024; 22: 1526–1536.
134. Hou J, Liu J, Chen F, et al. Robust lithium-ion state-of-charge and battery parameters joint estimation based on an enhanced adaptive unscented Kalman filter. Energy 2023; 271(15): 126998.
135. Hou J, Wang H, Su H, et al. A bias-correction modeling method of Hammerstein–Wiener systems with polynomial nonlinearities using noisy measurements. Mech Syst Signal Process 2024; 213: 111329.
136. Liu LJ. Decomposition-based maximum likelihood gradient iterative algorithm for multivariate systems with colored noise. Int J Robust Nonlinear Control. 2024; 34(11):7265–72843.
137. Liu LJ, Xia HF, Ma JX, Li F. Auxiliary model-based maximum likelihood gradient iterative identification for feedback nonlinear systems. Optim Control Appl Methods. 2024; 45.
138. Xu N, Ding F, Xu L. Convergence analysis of a synchronous gradient estimation scheme for time-varying parameter systems. J Comput Appl Math. 2024; 443: 115724.
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