http://iet.metastore.ingenta.com
1887

Maximum likelihood gradient-based iterative estimation for multivariable systems

Maximum likelihood gradient-based iterative estimation for multivariable systems

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

This study concerns the parameter identification issues for a class of multivariable systems with moving average noise. The main contributions are to transform a multivariable system into several subsystems for reducing the computational complexity by means of the decomposition technique and to deal with the coloured noise for improving the estimation accuracy by using the maximum likelihood principle and the iterative estimation theory. As the maximum likelihood gradient-based iterative algorithm makes sufficient use of all the observed data at each iteration, the parameter estimation accuracy can be enhanced. The numerical simulation results demonstrate that the proposed algorithm has faster convergence rates and better tracking performance than the compared multivariable extended stochastic gradient algorithm.

References

    1. 1)
      • 1. Na, J., Huang, Y., Wu, X., et al: ‘Active adaptive estimation and control for vehicle suspensions with prescribed performance’, IEEE Trans. Control Syst. Technol., 2018, 26, (6), pp. 20632077.
    2. 2)
      • 2. Ding, J., Chen, J.Z., Lin, J.X., et al: ‘Particle filtering based parameter estimation for systems with output-error type model structures’, J. Franklin Inst., 2019, 356, https://doi.org/10.1016/j.jfranklin.2019.04.027.
    3. 3)
      • 3. Gan, M., Chen, C.L.P., Chen, G.Y., et al: ‘On some separated algorithms for separable nonlinear squares problems’, IEEE Trans. Cybern., 2018, 48, (10), pp. 28662870.
    4. 4)
      • 4. Zhang, X., Ding, F., Alsaadi, F.E., et al: ‘Recursive parameter identification of the dynamical models for bilinear state space systems’, Nonlinear Dyn., 2017, 89, (4), pp. 24152429.
    5. 5)
      • 5. Zhang, X., Xu, L., et al: ‘Combined state and parameter estimation for a bilinear state space system with moving average noise’, J. Franklin Inst., 2018, 355, (6), pp. 30793103.
    6. 6)
      • 6. Gan, M., Li, H.X., Peng, H.: ‘A variable projection approach for efficient estimation of RBF-ARX model’, IEEE Trans. Cybern., 2015, 45, (3), pp. 462471.
    7. 7)
      • 7. Li, J.H., Zheng, W.X., Gu, J.P., et al: ‘A recursive identification algorithm for Wiener nonlinear systems with linear state-space subsystem’, Circuits Syst. Signal Process., 2018, 37, (6), pp. 23742393.
    8. 8)
      • 8. Zhou, Z.P., Liu, X.F.: ‘State and fault estimation of sandwich systems with hysteresis’, Int. J. Robust Nonlinear Control, 2018, 28, (13), pp. 39743986.
    9. 9)
      • 9. Chen, G.Y., Gan, M., Ding, F., et al: ‘Modified Gram-Schmidt method-based variable projection algorithm for separable nonlinear models’, IEEE Trans. Neural Netw. Learn. Syst., 2018, doi: 10.1109/TNNLS.2018.2884909.
    10. 10)
      • 10. Xu, L.: ‘The parameter estimation algorithms based on the dynamical response measurement data’, Adv. Mech. Eng., 2017, 9, (11), pp. 112, doi: 10.1177/1687814017730003.
    11. 11)
      • 11. Xu, L., Ding, F.: ‘Parameter estimation for control systems based on impulse responses’, Int. J. Control Autom. Syst., 2017, 15, (6), pp. 24712479.
    12. 12)
      • 12. Ding, F., Liu, X.P., Liu, G.: ‘Gradient based and least-squares based iterative identification methods for OE and OEMA systems’, Digit. Signal Process., 2010, 20, (3), pp. 664677.
    13. 13)
      • 13. Ding, F., Liu, X.G., Chu, J.: ‘Gradient-based and least-squares-based iterative algorithms for Hammerstein systems using the hierarchical identification principle’, IET Control Theory Applic., 2013, 7, (2), pp. 176184.
    14. 14)
      • 14. Liu, L.J., Wang, Y., Wang, C., et al: ‘Maximum likelihood recursive least squares estimation for multivariate equation-error ARMA systems’, J. Franklin Inst., 2018, 355, (15), pp. 76097625.
    15. 15)
      • 15. Pan, J., Jiang, X., Wan, X.K., et al: ‘A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems’, Int. J. Control Autom. Syst., 2017, 15, (3), pp. 11891197.
    16. 16)
      • 16. Liu, Q.Y., Ding, F., Xu, L., et al: ‘Partially coupled gradient estimation algorithm for multivariable equation-error autoregressive moving average systems using the data filtering technique’, IET Control Theory Appl., 2019, 13, (5), pp. 642650.
    17. 17)
      • 17. Ma, J.X., Xiong, W.L., Chen, J., et al: ‘Hierarchical identification for multivariate Hammerstein systems by using the modified Kalman filter’, IET Control Theory Applic., 2017, 11, (6), pp. 857869.
    18. 18)
      • 18. Chen, J., Huang, B., et al: ‘Variational Bayesian approach for ARX systems with missing observations and varying time-delays’, Automatica, 2018, 94, pp. 194204.
    19. 19)
      • 19. Liu, Q.Y., Ding, F.: ‘Auxiliary model-based recursive generalized least squares algorithm for multivariate output-error autoregressive systems using the data filtering’, Circuits Syst. Signal Process., 2019, 38, (2), pp. 590610.
    20. 20)
      • 20. Pan, J., Ma, H., Jiang, X., et al: ‘Adaptive gradient-based iterative algorithm for multivariate controlled autoregressive moving average systems using the data filtering technique’, Complexity, 2018, 2018, pp. 111, Article ID 9598307. https://doi.org/10.1155/2018/9598307.
    21. 21)
      • 21. Ding, J.L.: ‘The hierarchical iterative identification algorithm for multi-input-output-error systems with autoregressive noise’, Complexity, 2017, 2017, pp. 111, Article ID 5292894. https://doi.org/10.1155/2017/5292894.
    22. 22)
      • 22. Wang, Y.J., Ding, F., Wu, M.H.: ‘Recursive parameter estimation algorithm for multivariate output-error systems’, J. Franklin Inst., 2018, 355, (12), pp. 51635181.
    23. 23)
      • 23. Yu, C.P., Verhaegen, M.: ‘Blind multivariable ARMA subspace identification’, Automatica, 2016, 66, pp. 314.
    24. 24)
      • 24. Zhang, X., Ding, F., et al: ‘State filtering-based least squares parameter estimation for bilinear systems using the hierarchical identification principle’, IET Control Theory Applic., 2018, 12, (12), pp. 17041713.
    25. 25)
      • 25. Chen, G.Y., Gan, M., Chen, C.L.P., et al: ‘A regularized variable projection algorithm for separable nonlinear least squares problems’, IEEE Trans. Autom. Control, 2019, 64, (2), pp. 526537.
    26. 26)
      • 26. Wang, Y.J., Ding, F.: ‘A filtering based multi-innovation gradient estimation algorithm and performance analysis for nonlinear dynamical systems’, IMA J. Appl. Math., 2017, 82, (6), pp. 11711191.
    27. 27)
      • 27. Li, M.H., Liu, X.M.: ‘Auxiliary model based least squares iterative algorithms for parameter estimation of bilinear systems using interval-varying measurements’, IEEE Access, 2018, 6, pp. 2151821529.
    28. 28)
      • 28. Li, M.H., Liu, X.M.: ‘The least squares based iterative algorithms for parameter estimation of a bilinear system with autoregressive noise using the data filtering technique’, Signal Process., 2018, 147, pp. 2334.
    29. 29)
      • 29. Ding, F., Xu, L., Alsaadi, F.E., et al: ‘Iterative parameter identification for pseudo-linear systems with ARMA noise using the filtering technique’, IET Control Theory Applic., 2018, 12, (7), pp. 892899.
    30. 30)
      • 30. Xu, L., Ding, F.: ‘Iterative parameter estimation for signal models based on measured data’, Circuits Syst. Signal Process., 2018, 37, (7), pp. 30463069.
    31. 31)
      • 31. Cao, Y., Lu, H., Wen, T.: ‘A safety computer system based on multi-sensor data processing’, Sensors, 2019, 19, (4), Article Number: 88. https://doi.org/10.3390/s19040818.
    32. 32)
      • 32. Fu, B., Ouyang, C.X., Li, C.S., et al: ‘An improved mixed integer linear programming approach based on symmetry diminishing for unit commitment of hybrid power system’, Energies, 2019, 12, (5), Article Number: 833. doi: 10.3390/en12050833.
    33. 33)
      • 33. Cao, Y., Ma, L.C., Xiao, S., et al: ‘Standard analysis for transfer delay in CTCS-3’, Chin. J. Electron., 2017, 26, (5), pp. 10571063.
    34. 34)
      • 34. Cao, Y., Wen, Y., Meng, X., et al: ‘Performance evaluation with improved receiver design for asynchronous coordinated multipoint transmissions’, Chin. J. Electron., 2016, 25, (2), pp. 372378.
    35. 35)
      • 35. Young, P.C.: ‘Refined instrumental variable estimation: maximum likelihood optimization of a unified Box-Jenkins model’, Automatica, 2015, 52, pp. 3546.
    36. 36)
      • 36. Chen, F.Y., Ding, F., Xu, L., et al: ‘Data filtering based maximum likelihood extended gradient method for multivariable systems with autoregressive moving average noise’, J. Franklin Inst., 2018, 355, (7), pp. 33813398.
    37. 37)
      • 37. Chen, F.W., Agüero, J.C., Gilson, M., et al: ‘EM-based identification of continuous-time ARMA models from irregularly sampled data’, Automatica, 2017, 77, pp. 293301.
    38. 38)
      • 38. Xu, L., Ding, F., Zhu, Q.M.: ‘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), pp. 141151.
    39. 39)
      • 39. Xu, L., Xiong, W.L., Alsaedi, A., et al: ‘Hierarchical parameter estimation for the frequency response based on the dynamical window data’, Int. J. Control Autom. Syst., 2018, 16, (4), pp. 17561764.
    40. 40)
      • 40. Xia, H.F., Ji, Y., Xu, L., et al: ‘Maximum likelihood-based recursive least-squares algorithm for multivariable systems with colored noises using the decomposition technique’, Circuits Syst. Signal Process., 2019, 38, (3), pp. 9861004.
    41. 41)
      • 41. Zhang, X., Ding, F., Xu, L., et al: ‘A hierarchical approach for joint parameter and state estimation of a bilinear system with autoregressive noise’, Mathematics, 2019, 7, (4), pp. 117. https://doi.org/10.3390/math7040356.
    42. 42)
      • 42. Ding, F.: ‘Two-stage least squares based iterative estimation algorithm for CARARMA system modeling’, Appl. Math. Model., 2013, 37, (7), pp. 47984808.
    43. 43)
      • 43. Ding, F., Chen, H.B., Xu, L., et al: ‘A hierarchical least squares identification algorithm for Hammerstein nonlinear systems using the key term separation’, J. Franklin Inst., 2018, 355, (8), pp. 37373752.
    44. 44)
      • 44. Ding, F.: ‘Decomposition based fast least squares algorithm for output error systems’, Signal Process., 2013, 93, (5), pp. 12351242.
    45. 45)
      • 45. Liu, Y.J., Wang, D.Q., Ding, F.: ‘Least squares based iterative algorithms for identifying Box-Jenkins models with finite measurement data’, Digit. Signal Process., 2010, 20, (5), pp. 14581467.
    46. 46)
      • 46. Yang, F., Zhang, P., Li, X.X.: ‘The truncation method for the Cauchy problem of the inhomogeneous Helmholtz equation’, Appl. Anal., 2019, 98, (5), pp. 9911004.
    47. 47)
      • 47. Tian, X.P., Niu, H.M.: ‘A bi-objective model with sequential search algorithm for optimizing network-wide train timetables’, Comput. Ind. Eng., 2019, 127, pp. 12591272.
    48. 48)
      • 48. Ma, F.Y., Yin, Y.K., Li, M.: ‘Start-up process modelling of sediment microbial fuel cells based on data driven’, Math. Probl. Eng., 2019, https://doi.org/10.1155/2019/7403732.
    49. 49)
      • 49. Wang, Y., Si, Y., Huang, B., et al: ‘Survey on the theoretical research and engineering applications of multivariate statistics process monitoring algorithms: 2008-2017’, Canadian J. Chem. Eng., 2018, 96, (10), pp. 20732085.
    50. 50)
      • 50. Li, N., Guo, S., Wang, Y.: ‘Weighted preliminary-summation-based principal component analysis for non-Gaussian processes’, Control Eng. Pract., 2019, 87, pp. 122132.
    51. 51)
      • 51. Wang, Y.J., Ding, F., Xu, L.: ‘Some new results of designing an IIR filter with colored noise for signal processing’, Digit. Signal Process., 2018, 72, pp. 4458.
    52. 52)
      • 52. Pan, J., Li, W., Zhang, H.P.: ‘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), pp. 28782887.
    53. 53)
      • 53. Sun, Z.Y., Zhang, D., Meng, Q., et al: ‘Feedback stabilization of time-delay nonlinear systems with continuous time-varying output function’, Int. J. Syst. Sci., 2019, 50, (2), pp. 244255.
    54. 54)
      • 54. Zhan, X.S., Cheng, L.L., Wu, J., et al: ‘Optimal modified performance of MIMO networked control systems with multi-parameter constraints’, ISA Trans., 2019, 84, (1), pp. 111117.
    55. 55)
      • 55. Wu, T.Z., Shi, X., Liao, L., et al: ‘A capacity configuration control strategy to alleviate power fluctuation of hybrid energy storage system based on improved particle swarm optimization’, Energies, 2019, 12, (4), Article Number: 642. doi: 10.3390/en12040642.
    56. 56)
      • 56. Wu, M.H., Li, X., Liu, C., et al: ‘Robust global motion estimation for video security based on improved k-means clustering’, J. Ambient Intell. Humanized Comput., 2019, 10, (2), pp. 439448.
    57. 57)
      • 57. Wan, X.K., Wu, H., Qiao, F., et al: ‘Electrocardiogram baseline wander suppression based on the combination of morphological and wavelet transformation based filtering’, Comput. Math. Methods Med., 2019, https://doi.org/10.1155/2019/7196156.
    58. 58)
      • 58. Feng, L., Li, Q.X., Li, Y.F.: ‘Imaging with 3-D aperture synthesis radiometers’, IEEE Trans. Geosci. Remote Sens., 2019, 57, (4), pp. 23952406.
    59. 59)
      • 59. Shi, W.X., Liu, N., Zhou, Y.M., et al: ‘Effects of postannealing on the characteristics and reliability of polyfluorene organic light-emitting diodes’, IEEE Trans. Electron Devices, 2019, 66, (2), pp. 10571062.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2018.6240
Loading

Related content

content/journals/10.1049/iet-cta.2018.6240
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address