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Recursive Least Squares Algorithm for Nonlinear Dual-rate Systems Using Missing-Output Estimation Model

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Abstract

In this paper, a recursive least squares algorithm is proposed for a class of nonlinear dual-rate systems. By using the missing-output estimation model, the unavailable outputs can be estimated. Then, the unknown parameters can be estimated from all the inputs and outputs. Compared with the polynomial transformation technique and the lifting technique, the unknown parameters can be estimated directly by using the missing-output estimation model, without increasing the number of parameters. The convergence analysis and the simulation results indicate that the proposed method is effective.

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References

  1. F.Y. Chen, F. Ding, J.H. Li, Maximum likelihood gradient-based iterative estimation algorithm for a class of input nonlinear controlled autoregressive ARMA systems. Nonlinear Dyn. 79(2), 927–936 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Chen, Several gradient parameter estimation algorithms for dual-rate sampled systems. J. Franklin Inst. 351(1), 543–554 (2014)

    Article  MATH  Google Scholar 

  3. J. Chen, Y.X. Ni, Parameter identification methods for an additive nonlinear system. Circuits Syst. Signal Process. 33(10), 3053–3064 (2014)

    Article  MATH  Google Scholar 

  4. F. Ding, T. Chen, Combined parameter and output estimation of dual-rate systems using an auxiliary model. Automatica 40(10), 1739–1748 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  5. F. Ding, X.M. Liu, Y. Gu, An auxiliary model based least squares algorithm for a dual-rate state space system with time-delay using the data filtering. J. Franklin Inst. 353(2), 398–408 (2016)

    Article  MathSciNet  Google Scholar 

  6. F. Ding, X.M. Liu, M.M. Liu, The recursive least squares identification algorithm for a class of Wiener nonlinear systems. J. Franklin Inst. 353(7), 1518–1526 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  7. F. Ding, X.M. Liu, X.Y. Ma, Kalman state filtering based least squares iterative parameter estimation for observer canonical state space systems using decomposition. J. Comput. Appl. Math. 301, 135–143 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  8. F. Ding, X.P. Liu, H.Z. Yang, Parameter identification and intersample output estimation for dual-rate systems. IEEE Trans. Syst. Man Cybern. A Syst. Hum. 38(4), 966–975 (2008)

    Article  Google Scholar 

  9. F. Ding, X.H. Wang, Q.J. Chen, Y.S. Xiao, Recursive least squares parameter estimation for a class of output nonlinear systems based on the model decomposition. Circuits Syst. Signal Process. (2016). doi:10.1007/s00034-015-0190-6

    MathSciNet  MATH  Google Scholar 

  10. J. Ding, J.X. Lin, Modified subspace identification for periodically non-uniformly sampled systems by using the lifting technique. Circuits Syst. Signal Process. 33(5), 1439–1449 (2014)

    Article  Google Scholar 

  11. G.C. Goodwin, K.S. Sin, Adaptive Filtering, Prediction and Control (Prentice-Hall, Englewood Cliff, 1984)

    MATH  Google Scholar 

  12. H. Li, Y. Shi, W. Yan, On neighbor information utilization in distributed receding horizon control for consensus-seeking. IEEE Trans. Cybern. (2016). doi:10.1109/TCYB.2015.2459719

    Google Scholar 

  13. H. Li, Y. Shi, W. Yan, Distributed receding horizon control of constrained nonlinear vehicle formations with guaranteed \(\gamma \)-gain stability. Automatica 68, 148–154 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  14. H. Li, P. Xie, W. Yan, Receding horizon formation tracking control of constrained Underactuated autonomous underwater vehicles. IEEE Trans. Ind. Electron. (2016). doi:10.1109/TIE.2016.2589921

    Google Scholar 

  15. H. Li, W. Yan, Model predictive stabilization of constrained underactuated autonomous underwater vehicles with guaranteed feasibility and stability. IEEE/ASME Trans. Mechatron. (2016). doi:10.1109/TMECH.2016.2587288

    Google Scholar 

  16. Y. Liu, E.W. Bai, Iterative identification of Hammerstein systems. Automatica 43(2), 346–354 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  17. Y.W. Mao, F. Ding, Adaptive filtering parameter estimation algorithms for Hammerstein nonlinear systems. Signal Process. 128, 417–425 (2016)

    Article  Google Scholar 

  18. Y.W. Mao, F. Ding, Multi-innovation stochastic gradient identification for Hammerstein controlled autoregressive autoregressive systems based on the filtering technique. Nonlinear Dyn. 79(3), 1745–1755 (2015)

    Article  MATH  Google Scholar 

  19. G. Mercère, L. Bako, Parameterization and identification of multivariable state-space systems: a canonical approach. Automatica 47(8), 1547–1555 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  20. J. Pan, X.H. Yang, H.F. Cai, B.X. Mu, Image noise smoothing using a modified Kalman filter. Neurocomputing 173, 1625–1629 (2016)

    Article  Google Scholar 

  21. R. Piza, J. Salt, A. Sala, A. Cuenca, Hierarchical triple-maglev dual-rate control over a profibus-DP network. IEEE Trans. Control Syst. Technol. 22(1), 1–12 (2014)

    Article  Google Scholar 

  22. M. Schoukens, A. Marconato, R. Pintelon, G. Vandersteen, Y. Rolain, Parametric identification of parallel Wiener–Hammerstein systems. Automatica 51, 111–122 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  23. Y. Shi, H. Fang, M. Yan, Kalman filter based adaptive control for networked systems with unknown parameters and randomly missing outputs. Int. J. Robust Nonlinear Control. 19(18), 1976–1992 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  24. M. Srinivasarao, S.C. Patwardhan, R.D. Gudi, Nonlinear predictive control of irregularly sampled multirate systems using blackbox observers. J. Process Control 17(1), 17–35 (2007)

    Article  MATH  Google Scholar 

  25. J. Vörös, Modeling and identification of systems with backlash. Automatica 46(2), 369–374 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  26. C. Wang, T. Tang, Several gradient-based iterative estimation algorithms for a class of nonlinear systems using the filtering technique. Nonlinear Dyn. 77(3), 769–780 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  27. C. Wang, T. Tang, Recursive least squares estimation algorithm applied to a class of linear-in-parameters output error moving average systems. Appl. Math. Lett. 29, 36–41 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  28. C. Wang, L. Zhu, Parameter identification of a class of nonlinear systems based on the multi-innovation identification theory. J. Franklin Inst. 352(10), 4624–4637 (2015)

    Article  MathSciNet  Google Scholar 

  29. D.Q. Wang, Hierarchical parameter estimation for a class of MIMO Hammerstein systems based on the reframed models. Appl. Math. Lett. 57, 13–19 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  30. D.Q. Wang, F. Ding, Parameter estimation algorithms for multivariable Hammerstein CARMA systems. Inf. Sci. 355, 237–248 (2016)

    Article  MathSciNet  Google Scholar 

  31. D.Q. Wang, W. Zhang, Improved least squares identification algorithm for multivariable Hammerstein systems. J. Franklin Inst. 352(11), 5292–5307 (2015)

    Article  MathSciNet  Google Scholar 

  32. T.Z. Wang, J. Qi, H. Xu, L. Liu, D.J. Gao, Fault diagnosis method based on FFT-RPCA-SVM for cascaded-multilevel inverter. ISA Trans. 60, 156–163 (2016)

    Article  Google Scholar 

  33. T.Z. Wang, H. Wu, M.Q. Ni, An adaptive confidence limit for periodic non-steady conditions fault detection. Mech. Syst. Signal Process. 72–73, 328–345 (2016)

    Article  Google Scholar 

  34. X.H. Wang, F. Ding, Convergence of the recursive identification algorithms for multivariate pseudo-linear regressive systems. Int. J. Adapt. Control Signal Process. 30(6), 824–842 (2016)

    Article  MathSciNet  Google Scholar 

  35. X.H. Wang, F. Ding, Convergence of the auxiliary model based multi-innovation generalized extended stochastic gradient algorithm for Box–Jenkins systems. Nonlinear Dyn. 82(1–2), 269–280 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  36. X.H. Wang, F. Ding, Recursive parameter and state estimation for an input nonlinear state space system using the hierarchical identification principle. Signal Process. 117, 208–218 (2015)

    Article  Google Scholar 

  37. Y.J. Wang, F. Ding, Novel data filtering based parameter identification for multiple-input multiple-output systems using the auxiliary model. Automatica 71, 308–313 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  38. Y.J. Wang, F. Ding, The auxiliary model based hierarchical gradient algorithms and convergence analysis using the filtering technique. Signal Process. 128, 212–221 (2016)

    Article  Google Scholar 

  39. Y.J. Wang, F. Ding, The filtering based iterative identification for multivariable systems. IET Control Theory Appl. 10(8), 894–902 (2016)

    Article  MathSciNet  Google Scholar 

  40. L. Xu, The damping iterative parameter identification method for dynamical systems based on the sine signal measurement. Signal Process. 120, 660–667 (2016)

    Article  Google Scholar 

  41. L. Xu, A proportional differential control method for a time-delay system using the Taylor expansion approximation. Appl. Math. Comput. 236, 391–399 (2014)

    MathSciNet  MATH  Google Scholar 

  42. L. Xu, Application of the Newton iteration algorithm to the parameter estimation for dynamical systems. J. Comput. Appl. Math. 288, 33–43 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  43. L. Xu, L. Chen, W.L. Xiong, Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration. Nonlinear Dyn. 79(3), 2155–2163 (2015)

    Article  MathSciNet  Google Scholar 

  44. B. Yu, Y. Shi, H. Huang, \(l_2-l_\infty \) filtering for multirate systems using lifted models. Circuits Syst. Signal Process. 27(5), 699–711 (2008)

    Article  MATH  Google Scholar 

  45. H. Zayyani, Continuous mixed \(p\)-norm adaptive algorithm for system identification. IEEE Signal Process. Lett. 21(9), 1108–1110 (2014)

    Article  Google Scholar 

  46. H. Zhang, Y. Shi, J. Wang, On energy-to-peak filtering for nonuniformly sampled nonlinear systems: a Markovian jump system approach. IEEE Trans. Fuzzy Syst. 22(1), 212–222 (2014)

    Article  Google Scholar 

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Correspondence to Jing Chen.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 61403165, 61374126), the Natural Science Foundation of Jiangsu Province (No. BK20131109) and the Post Doctoral Foundation of Jiangsu Province (No. 1501015A).

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Chen, J., Liu, Y. & Wang, X. Recursive Least Squares Algorithm for Nonlinear Dual-rate Systems Using Missing-Output Estimation Model. Circuits Syst Signal Process 36, 1406–1425 (2017). https://doi.org/10.1007/s00034-016-0368-6

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