Skip to main content
SpringerLink
Log in

Aitken-based Acceleration Estimation Algorithms for a Nonlinear Model with Exponential Terms by Using the Decomposition

  • Regular Papers
  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper studies some parameter estimation algorithms for a class of nonlinear models with exponential terms, i.e., the radial basis function-based state-dependent autoregressive (RBF-AR) models. An Aitken-based multi-innovation stochastic gradient algorithm is presented for the RBF-AR models based on the Aitken method. Inspired by the decomposition-coordination principle of large systems, an Aitken-based hierarchical multi-innovation stochastic gradient algorithm is proposed by combining the decomposition technique with the Aitken method. The effectiveness of the proposed algorithms are validated through two simulation examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Kathari and A. K. Tangirala, “Scalar correlation functions for model structure selection in high-dimensional time-series modelling,” ISA Transactions, vol. 100, pp. 275–288, May 2020.

    Article  Google Scholar 

  2. T. Hasegawa, K. Kojima, Y. Kawai, and M. Nagasaki, “Time-series filtering for replicated observations via a kernel approximate bayesian computation,” IEEE Transactions on Signal Processing, vol. 66, no. 23, pp. 6148–6161, December 2018.

    Article  MathSciNet  MATH  Google Scholar 

  3. Z. Y. Shi, T. Tamura, and T. Ozaki, “Nonlinear time series modelling with the radial basis function-based state-dependent autoregressive model,” International Journal of Systems Science, vol. 30, no. 7, pp. 717–727, July 1999.

    Article  MATH  Google Scholar 

  4. G. Y. Chen, M. Gan, and G. L. Chen, “Generalized exponential autoregressive models for nonlinear time series: Stationarity, estimation and applications,” Information Sciences, vol. 438, pp. 46–57, April 2018.

    Article  MathSciNet  MATH  Google Scholar 

  5. M. A. Ghazal and A. Elhassanein, “Dynamics of EXPAR models for high frequency data,” International Journal of Applied Mathematics and Statistics, vol. 14, no. M09, pp. 88–96, 2009.

    MathSciNet  Google Scholar 

  6. M. Gan, C. L. P. Chen, H. X. Li, and L. Chen, “Gradient radial basis function based varying-coefficient autoregressive model for nonlinear and nonstationary time series,” IEEE Signal Processing Letters, vol. 22, no. 7, pp. 809–812, July 2015.

    Article  Google Scholar 

  7. F. Zhou, H. Peng, Y. M. Qin, Z. Y. Zeng, and X. Y. Tian, “A RBF-ARX model-based robust MPC for tracking control without steady state knowledge,” Journal of Process Control, vol. 51. pp. 42–54, March 2017.

    Article  Google Scholar 

  8. F. Zhou, H. Peng, X. Y. Zeng, and X. Y. Tian, “RBF-ARX model-based two-stage scheduling RPC for dynamic systems with bounded disturbance,” Neural Computing & Applications, vol. 31, no. 8, pp. 4185–4200, August 2019.

    Article  Google Scholar 

  9. Y. M. Fan and X. M. Liu, “Two-stage auxiliary model gradient-based iterative algorithm for the input nonlinear controlled autoregressive system with variable-gain non-linearity,” International Journal of Robust and Nonlinear Control, vol. 30, no. 14, pp. 5492–5509, September 2020.

    Article  MathSciNet  MATH  Google Scholar 

  10. Y. Gu, Q. Zhu, and H. Nouri, “Bias compensation-based parameter and state estimation for a class of time-delay nonlinear state-space models,” IET Control Theory and Applications, vol. 14, no. 15, pp. 2176–2185, October 2020.

    Article  Google Scholar 

  11. H. Peng, T. Ozaki, V. Haggan-Ozaki, and Y. Toyoda, “A parameter optimization method for radial basis function type models,” IEEE Transactions on Neural Networks, vol. 14, no. 2, pp. 432–438, March 2003.

    Article  MATH  Google Scholar 

  12. X. Y. Zeng, H. Peng, and F. Zhou, “A regularized SNPOM for stable parameter estimation of RBF-AR(X) model,” IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no. 4, pp. 779–791, April 2018.

    Article  Google Scholar 

  13. G. Y. Chen, M. Gan, C. L. P. Chen, and H. X. Li, “A regularized variable projection algorithm for separable nonlinear least-squares problems,” IEEE Transactions on Automatic Control, vol. 64, no. 2, pp. 526–537, February 2019.

    MathSciNet  MATH  Google Scholar 

  14. M. Gan, G. Y. Chen, L. Chen, and C. L. P. Chen, “Term selection for a class of separable nonlinear models,” IEEE Transactions on Neural Networks and Learning Systems, vol. 31, no. 2, pp. 445–451, February 2020.

    Article  MathSciNet  Google Scholar 

  15. Y. Ji, C. Zhang, Z. Kang, and T. Yu, “Parameter estimation for block-oriented nonlinear systems using the key term separation,” International Journal of Robust and Nonlinear Control, vol. 30, no. 9, pp. 3727–3752, June 2020.

    Article  MathSciNet  MATH  Google Scholar 

  16. Y. H. Zhou, F. Ding, Y. Ji, and T. Hayat, “Recursive methods for estimating the radial basis function-based state-dependent autoregressive model,” International Journal of Robust and Nonlinear Control, vol. 30, no. 6, pp. 2475–2492, April 2020.

    Article  MathSciNet  MATH  Google Scholar 

  17. M. H. Li and X. M. Liu, “Maximum likelihood least squares based iterative estimation for a class of bilinear systems using the data filtering technique,” International Journal of Control Automation and Systems, vol. 18, no. 6, pp. 1581–1592, June 2020.

    Article  Google Scholar 

  18. M. H. Li and X. M. Liu, “Maximum likelihood hierarchical least squares-based iterative identification for dualrate stochastic systems,” International Journal of Adaptive Control and Signal Processing, vol. 35, no. 2, pp. 240–261, February 2021.

    Article  MathSciNet  Google Scholar 

  19. R. Haelterman and D. Van Eester, “Accelerating the convergence of a tokamak modeling code with Aitken’s method,” Computer Physics Communications, vol. 196, pp. 70–79, November 2015.

    Article  Google Scholar 

  20. J. Chen, Y. J. Liu, and Q. M. Zhu, “Bias compensation recursive algorithm for dual-rate rational models,” IET Control Theory and Applications, vol. 12, no. 16, pp. 2184–2193, November 2018.

    Article  MathSciNet  Google Scholar 

  21. I. Pavaloiu and E. Catinas, “On a robust Aitken-Newton method based on the Hermite polynomial,” Applied Mathematics and Computation, vol. 287, pp. 224–231, September 2016.

    Article  MathSciNet  MATH  Google Scholar 

  22. C. Q. Guo, L. J. Wang, and F. Deng, “The auxiliary model based hierarchical estimation algorithms for bilinear stochastic systems with colored noises,” International Journal of Control Automation and Systems, vol. 18, no. 3, pp. 650–660, March 2020.

    Article  Google Scholar 

  23. L. J. Wang, Y. Ji, L. J. Wan, and N. Bu, “Hierarchical recursive generalized extended least squares estimation algorithms for a class of nonlinear stochastic systems with colored noise,” Journal of the Franklin Institute, vol. 356, no. 16, pp. 10102–10122, November 2019.

    Article  MathSciNet  MATH  Google Scholar 

  24. Y. Ji, X. K. Jiang, and L. J. Wan, “Hierarchical least squares parameter estimation algorithm for two-input Hammerstein finite impulse response systems,” Journal of the Franklin Institute, vol. 357, pp. 5019–5032, May 2020.

    Article  MathSciNet  MATH  Google Scholar 

  25. M. B. Priestley, “State-dependent models: A general approach to non-linear time series analysis,” Journal of Time Series Analysis, vol. 1, no. 1, pp. 47–71, 1980.

    Article  MathSciNet  MATH  Google Scholar 

  26. L. V. Truong, S. D. Huang, V. T. Yen, and P. V. Cuong, “Adaptive trajectory neural network tracking control for industrial robot manipulators with deadzone robust compensator,” International Journal of Control Automation and Systems, vol. 18, no. 9, pp. 2423–2434, September 2020.

    Article  Google Scholar 

  27. S. Konishi and G. Kitagawa, Information Criteria and Statistical Modeling, Springer, Berlin, 2008.

    Book  MATH  Google Scholar 

  28. M. Karimi, “Order selection criteria for vector autoregressive models,” Signal Processing, vol. 91, no. 4, pp. 955–969, April 2011.

    Article  MATH  Google Scholar 

  29. R. B. Feng, C. S. Leung, and A. G. Constantinides, “LCA based RBF training algorithm for the concurrent fault situation,” Neurocomputing, vol. 191, pp. 341–351, May 2016.

    Article  Google Scholar 

  30. L. J. Wang, Y. Ji, H. L. Yang, and L. Xu, “Decomposition-based multiinnovation gradient identification algorithms for a special bilinear system based on its input-output representation,” International Journal of Robust and Nonlinear Control, vol. 30, no. 9, pp. 3607–3623, June 2020.

    Article  MathSciNet  MATH  Google Scholar 

  31. Y. Ji and Z. Kang, “Three-stage forgetting factor stochastic gradient parameter estimation methods for a class of nonlinear systems,” International Journal of Robust and Nonlinear Control, vol. 31, no. 3, pp. 871–987, February 2021.

    Article  MathSciNet  Google Scholar 

  32. Y. Ji, Z. Kang, and C. Zhang, “Two-stage gradient-based recursive estimation for nonlinear models by using the data filtering,” International Journal of Control, Automation and Systems, vol. 19, no. 8, pp. 2706–2715, August 2021.

    Article  Google Scholar 

  33. M. Li and X. Liu, “Iterative parameter estimation methods for dual-rate sampled-data bilinear systems by means of the data filtering technique,” IET Control Theory and Applications, vol. 15, no. 9, pp. 1230–1245, June 2021.

    Article  Google Scholar 

  34. X. Liu and Y. Fan, “Maximum likelihood extended gradient-based estimation algorithms for the input nonlinear controlled autoregressive moving average system with variable-gain nonlinearity,” International Journal of Robust and Nonlinear Control, vol. 31, no. 9, pp. 4017–4036, June 2021.

    Article  Google Scholar 

  35. S. Y. Liu, Y. L. Zhang, L. Xu, A. Alsaedi, and T. Hayat, “Extended gradient-based iterative algorithm for bilinear state-space systems with moving average noises by using the filtering technique,” International Journal of Control Automation and Systems, vol. 19, no. 4, pp. 1597–1606, 2021.

    Article  Google Scholar 

  36. H. Ma, X. Zhang, Q. Y. Liu, F. Ding, X. B. Jin, A. Alsaedi, and T. Hayat, “Partiallly-coupled gradient-based iterative algorithms for multivariable output-error-like systems with autoregressive moving average noises,” IET Control Theory and Applications, vol. 14, no. 17, pp. 2613–2627, November 2020.

    Article  Google Scholar 

  37. L. Zhang, S. Y. Tang, and L. L. Lv, “An finite iterative algorithm for sloving periodic Sylvester bimatrix equations,” Journal of the Franklin Institute, vol. 357, no. 15, pp. 10757–10772, October 2020.

    Article  MathSciNet  MATH  Google Scholar 

  38. T. Han and W. X. Zheng, “Bipartite output consensus for heterogeneous multi-agent systems via output regulation approach,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 68, no. 1, pp. 281–285, January 2021.

    Article  Google Scholar 

  39. L. Xu and G.L. Song, “A recursive parameter estimation algorithm for modeling signals with multi-frequencies,” Circuits Systems and Signal Processing, vol. 39, no. 8, pp. 4198–4224, August 2020.

    Article  MATH  Google Scholar 

  40. G. Wang, T. Zhang, Y. Dai, J. Lin, and L. Chen, “A serial-parallel self-attention network joint with multi-scale dilated convolution,” IEEE Access, vol. 9, no. 5, pp. 71909–71919, 2021.

    Google Scholar 

  41. L. Xu, “The damping iterative parameter identification method for dynamical systems based on the sine signal measurement,” Signal Processing, vol. 120, pp. 660–667, March 2016.

    Article  Google Scholar 

  42. L. Xu, W. Xiong, A. Alsaedi, and T. Hayat, “Hierarchical parameter estimation for the frequency response based on the dynamical window data,” International Journal of Control, Automation and Systems, vol. 16, no. 4, pp. 1756–1764, August 2018.

    Article  Google Scholar 

  43. L. Xu, “Hierarchical Newton and least squares iterative estimation algorithm for dynamic systems by transfer functions based on the impulse responses,” International Journal of Systems Science, vol. 50, no. 1, pp. 141–151, 2019.

    Article  MathSciNet  Google Scholar 

  44. Y. H. Zhou and F. Ding, “Modeling nonlinear processes using the radial basis function-based state-dependent autoregressive models,” IEEE Signal Processing Letters, vol. 27, pp. 1600–1604, September 2020.

    Article  Google Scholar 

  45. F. Ding, L. Xu, and Q. M. Zhu, “Performance analysis of the generalised projection identification for time-varying systems,” IET Control Theory and Applications, vol. 10, no. 18, pp. 2506–2514, December 2016.

    Article  MathSciNet  Google Scholar 

  46. F. Ding, G. Liu, and X. Liu, “Parameter estimation with scarce measurements,” Automatica, vol. 47, no. 8, pp. 1646–1655, August 2011.

    Article  MathSciNet  MATH  Google Scholar 

  47. L. Xu, “The parameter estimation algorithms based on the dynamical response measurement data,” Advances in Mechanical Engineering, vol. 9, no. 11, November 2017. DOI: https://doi.org/10.1177/1687814017730003

    Google Scholar 

  48. Y. M. Zhou, S. J. Mei, J. J. Feng, D. W. Sun, F. Mei, J. X. Xu, and X. A. Cao, “Effects of PEDOT:PSS:GO composite hole transport layer on the luminescence of perovskite light-emitting diodes,” RSC Advances, vol. 10, no. 44, pp. 26381–26387, 2020.

    Article  Google Scholar 

  49. X. K. Wan, Z. Y. Jin, H. B. Wu, J. J. Liu, B. R. Zhu, and H. G. Xie, “Heartbeat classification algorithm based on one-dimensional convolution neural network,” Journal of Mechanics in Medicine and Biology, vol. 20, no. 7, Article Number: 2050046, September 2020.

    Google Scholar 

  50. X. K. Wan, J. J. Liu, Z. Y. Jin, B. R. Zhu, and M. R. Zhang, “Ventricular repolarization instability quantified by instantaneous frequency of ECG ST intervals,” Technology and Health Care, vol. 29, no. 1, pp. 73–83, 2021.

    Article  Google Scholar 

  51. Y. Zhang, Z. Yan, C. C. Zhou, T. Z. Wu, and Y. Y. Wang, “Capacity allocation of HESS in micro-grid based on ABC algorithm,” International Journal of Low-Carbon Technologies, vol. 15, no. 4, pp. 496–505, November 2020.

    Article  Google Scholar 

  52. M. H. Wu, H. H. Yue, J. Wang, Y. Huang, M. Liu, Y. Jiang, C. Ke, and C. Zeng, “Object detection based on RGC mask R-CNN,” IET Image Processing, vol. 14, no. 8, pp. 1502–1508, June 2020.

    Article  Google Scholar 

  53. Z. Y. Zhao, X. Y. Wang, P. Yao, and Y. T. Bai, “A health performance evaluation method of multirotors under wind turbulence,” Nonlinear Dynamics, vol. 102, no. 3, pp. 1701–1715, October 2020.

    Article  Google Scholar 

  54. X. M. Zhang, Z. Y. Zhao, Z. Y. Wang, and X. Y. Wang, “Fault detection and identification method for quadcopter based on airframe vibration signals,” Sensors, vol. 21, no. 2, pp. 581, January 2021.

    Article  Google Scholar 

  55. X. L. Zhao, Z. Y. Lin, B. Fu, and S. L. Gong, “Research on frequency control method for micro-grid with a hybrid approach of FFR-OPPT and pitch angle of wind turbine,” International Journal of Electrical Power & Energy Systems, vol. 127, Article Number: 106670, January 2021.

  56. Y. Cao, J. K. Wen, and L. C. Ma, “Tracking and collision avoidance of virtual coupling train control system,” Alexandria Engineering Journal, vol. 60, no. 2, pp. 2115–2125, April 2021.

    Article  Google Scholar 

  57. S. Su, X. K. Wang, Y. Cao, and J. T. Yin, “An energy-efficient train operation approach by integrating the metro timetabling and eco-driving,” IEEE Transactions on Intelligent Transportation Systems, vol. 21, no. 10, pp. 4252–4268, October 2020.

    Article  Google Scholar 

  58. S. Su, T. Tang, J. Xun, F. Cao, and Y. H. Wang, “Design of running grades for energy-efficient train regulation: A case study for Beijing Yizhuang line,” IEEE Intelligent Transportation Systems Magazine, vol. 13, no. 2, pp. 189–200, 2021.

    Article  Google Scholar 

  59. Y. Cao, Z. Wang, F. Liu, P. Li, and G. Xie, “Bio-inspired speed curve optimization and sliding mode tracking control for subway trains,” IEEE Transactions on Vehicular Technology, vol. 68, no. 7, pp. 6331–6342, July 2019.

    Article  Google Scholar 

  60. Y. Cao, Y. K. Sun, G. Xie, and T. Wen, “Fault diagnosis of train plug door based on a hybrid criterion for IMFs selection and fractional wavelet package energy entropy,” IEEE Transactions on Vehicular Technology, vol. 68, no. 8, pp. 7544–7551, August 2019.

    Article  Google Scholar 

  61. D. C. Chen, X. X. Zhang, J. Tang, Z. L. Cui, and H. Cui, “Pristine and Cu decorated hexagonal InN monolayer, a promising candidate to detect and scavenge SF6 decompositions based on first-principle study,” Journal of Hazardous Materials, vol. 363, pp. 346–357, February 2019.

    Article  Google Scholar 

  62. H. Cui, D. C. Chen, Y. Zhang, and X. X. Zhang, “Dissolved gas analysis in transformer oil using Pd catalyst decorated MoSe2 monolayer: A first-principles theory,” Sustainable Materials and Technologies, vol. 20, no. e00094, July 2019.

    Google Scholar 

  63. H. Cui, T. Liu, Y. Zhang, and X. X. Zhang, “Ru-InN monolayer as a gas scavenger to guard the operation status of SF6 insulation devices: A first-principles theory,” IEEE Sensors Journal, vol. 19, no. 13, pp. 5249–5255, July 2019.

    Article  Google Scholar 

  64. H. Cui, X. X. Zhang, D. C. Chen, and J. Tang, “Adsorption mechanism of SF6 decomposed species on pyridinelike PtN3 embedded CNT: A DFT study,” Applied Surface Science, vol. 447, pp. 594–598, July 2018.

    Article  Google Scholar 

  65. H. Cui, X. X. Zhang, Y. Li, D. C. Chen, and Y. Zhang, “First-principles insight into Ni-doped InN monolayer as a noxious gases scavenger,” Applied Surface Science, vol. 494, pp. 859–866, June 2019.

    Article  Google Scholar 

  66. H. Cui, X. X. Zhang, G. Z. Zhang, and J. Tang, “Pd-doped MoS2 monolayer: A promising candidate for DGA in transformer oil based on DFT method,” Applied Surface Science, vol. 470, pp. 1035–1042, March 2019.

    Article  Google Scholar 

  67. H. Cui, G. Z. Zhang, X. X. Zhang, and J. Tang, “Rh-doped MoSe2 as a toxic gas scavenger: A first-principles study,” Nanoscale Advances, vol. 1, no. 2, pp. 772–780, February 2019.

    Article  Google Scholar 

  68. X. X. Zhang, Y. G. Gui, H. Y. Xiao, and Y. Zhang, “Analysis of adsorption properties of typical partial discharge gases on Ni-SWCNTs using density functional theory,” Applied Surface Science, vol. 379, pp. 47–54, August 2016.

    Article  Google Scholar 

  69. X. X. Zhang, L. Yu, Y. G. Gui, and W. H. Hu, “First-principles study of SF6 decomposed gas adsorbed on Audecorated graphene,” Applied Surface Science, vol. 367, pp. 259–269, March 2016.

    Article  Google Scholar 

  70. X. X. Zhang, L. Yu, X. Q. Wu, and W. H. Hu, “Experimental sensing and density functional theory study of H2S and SOF2 adsorption on Au-modified graphene,” Advanced Science, vol. 2, no. 11, Article Number: 1500101, November 2015.

    Google Scholar 

  71. S. S. Tian, X. X. Zhang, S. Xiao, J. Zhang, Q. Chen, and Y. Li, “Application of C6F12O/CO2 mixture in 10 kV medium-voltage switchgear,” IET Science Measurement and Technology, vol. 13, no. 9, pp. 1225–1230, November 2019.

    Article  Google Scholar 

  72. X. X. Zhang, Y. Zhang, Y. Huang, Y. Li, H. T. Cheng, and S. Xiao, “Detection of decomposition products of C4F7N-CO2 gas mixture based on infrared spectroscopy,” Vibrational Spectroscopy, vol. 110, Article Number: 103114, September 2020.

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, China

    Yihong Zhou & Feng Ding

  2. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Ahmed Alsaedi & Tasawar Hayat

Authors
  1. Yihong Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Feng Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ahmed Alsaedi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tasawar Hayat
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Feng Ding.

Additional information

Recommended by Associate Editor Nikey Kaisare under the direction of Editor Jay H. Lee.

This work was supported by the National Natural Science Foundation of China (No. 61873111) and the 111 Project (B12018), the Qing Lan Project of Jiangsu Province, the “333” Project of Jiangsu Province (No. BRA2018328) and the Jiangsu Overseas Visiting Scholar Program for University Prominent Young & Middle-Aged Teachers and Presidents.

Yihong Zhou was born in Suzhou, Jiangsu Province, China in 1995. She received her B.Sc. degree from Jiangsu Normal University, Xuzhou, China in 2018, and now is a Ph.D. student in the School of Internet of Things Engineering, Jiangnan University, Wuxi, China. Her interests include system modeling, system identification and adaptive control.

Feng Ding received his B.Sc. degree from the Hubei University of Technology (Wuhan, China) in 1984, and his M.Sc. and Ph.D. degrees both from the Tsinghua University, in 1991 and 1994, respectively. He has been a professor in the School of Internet of Things Engineering at the Jiangnan University (Wuxi, China) since 2004. His current research interests include model identification and adaptive control. He authored five books on System Identification.

Ahmed Alsaedi obtained his Ph.D. degree from Swansea University (UK) in 2002. He has a broad experience of research in applied mathematics. His fields of interest include dynamical systems, nonlinear analysis involving ordinary differential equations, fractional differential equations, boundary value problems, mathematical modeling, biomathematics, Newtonian and Non-Newtonian fluid mechanics. He served as the chairman of the mathematics department at KAU and presently he is serving as director of the research program at KAU. Under his great leadership, this program is running quite successfully and it has attracted a large number of highly rated researchers and distinguished professors from all over the world. He is also the head of NAAM international research group at KAU.

Tasawar Hayat was born in Khanewal, Punjab, Distinguished National Professor and Chairperson of Mathematics Department at Quaid-I-Azam University is renowned worldwide for his seminal, diversified and fundamental contributions in models relevant to physiological systems, control engineering. He has a honor of being fellow of Pakistan Academy of Sciences, Third World Academy of Sciences (TWAS) and Islamic World Academy of Sciences in the Mathematical Sciences.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhou, Y., Ding, F., Alsaedi, A. et al. Aitken-based Acceleration Estimation Algorithms for a Nonlinear Model with Exponential Terms by Using the Decomposition. Int. J. Control Autom. Syst. 19, 3720–3730 (2021). https://doi.org/10.1007/s12555-020-0688-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-020-0688-y

Keywords

Search

Navigation