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Volume 9 Issue 3
Mar.  2022

IEEE/CAA Journal of Automatica Sinica

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Kun Zhu, Chengpu Yu, and Yiming Wan, "Recursive Least Squares Identification With Variable-Direction Forgetting via Oblique Projection Decomposition," IEEE/CAA J. Autom. Sinica, vol. 9, no. 3, pp. 547-555, Mar. 2022. doi: 10.1109/JAS.2021.1004362
Citation: Kun Zhu, Chengpu Yu, and Yiming Wan, "Recursive Least Squares Identification With Variable-Direction Forgetting via Oblique Projection Decomposition," IEEE/CAA J. Autom. Sinica, vol. 9, no. 3, pp. 547-555, Mar. 2022. doi: 10.1109/JAS.2021.1004362

Recursive Least Squares Identification With Variable-Direction Forgetting via Oblique Projection Decomposition

doi: 10.1109/JAS.2021.1004362
Funds:  This work was supported by the National Natural Science Foundation of China (61803163, 61991414, 61873301)
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  • In this paper, a new recursive least squares (RLS) identification algorithm with variable-direction forgetting (VDF) is proposed for multi-output systems. The objective is to enhance parameter estimation performance under non-persistent excitation. The proposed algorithm performs oblique projection decomposition of the information matrix, such that forgetting is applied only to directions where new information is received. Theoretical proofs show that even without persistent excitation, the information matrix remains lower and upper bounded, and the estimation error variance converges to be within a finite bound. Moreover, detailed analysis is made to compare with a recently reported VDF algorithm that exploits eigenvalue decomposition (VDF-ED). It is revealed that under non-persistent excitation, part of the forgotten subspace in the VDF-ED algorithm could discount old information without receiving new data, which could produce a more ill-conditioned information matrix than our proposed algorithm. Numerical simulation results demonstrate the efficacy and advantage of our proposed algorithm over this recent VDF-ED algorithm.

     

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  • [1]
    L. Ljung, “Perspectives on system identification,” Annual Reviews in Control, vol. 34, no. 1, pp. 1–12, 2010. doi: 10.1016/j.arcontrol.2009.12.001
    [2]
    M. S. Mahmoud and M. O. Oyedeji, “Adaptive and predictive control strategies for wind turbine systems: A survey,” IEEE/CAA Journal of Automatica Sinica, vol. 6, no. 2, pp. 364–378, 2019. doi: 10.1109/JAS.2019.1911375
    [3]
    T. Soderstrom and L. Ljung, Theory and Practice of Recursive Identification. Cambridge, USA: The MIT Press, 1987.
    [4]
    B. Q. Mu and H. F. Chen, “Recursive identification of multi-input multioutput errors-in-variables Hammerstein systems,” IEEE Trans. Automatic Control, vol. 60, no. 3, pp. 843–849, 2014.
    [5]
    P. Zhou, P. Dai, H. Song, and T. Chai, “Data-driven recursive subspace identification based online modelling for prediction and control of molten iron quality in blast furnace ironmaking,” IET Control Theory and Applications, vol. 11, no. 4, pp. 2343–2351, 2017.
    [6]
    X. Wang and F. Ding, “Convergence of the recursive identification algorithms for multivariate pseudo-linear regressive systems,” Int. Journal of Adaptive Control and Signal Processing, vol. 30, no. 6, pp. 824–842, 2015.
    [7]
    Y. Wang, F. Ding, and M. Wu, “Recursive parameter estimation algorithm for multivariate output-error systems,” Journal of the Franklin Institute, vol. 355, no. 12, pp. 5163–5181, 2018. doi: 10.1016/j.jfranklin.2018.04.013
    [8]
    K. Bekiroglu, S. Srinivasan, E. Png, R. Su, and C. Lagoa, “Recursive approximation of complex behaviours with IoT-data imperfections,” IEEE/CAA Journal of Automatica Sinica, vol. 7, no. 3, pp. 656–667, 2020. doi: 10.1109/JAS.2020.1003126
    [9]
    J. Lou, L. Jia, R. Tao, and Y. Wang, “Distributed incremental biascompensated RLS estimation over multi-agent networks,” Science China Information Sciences, vol. 60, no. 3, Article No. 032204, 2017. doi: 10.1007/s11432-016-0284-2
    [10]
    C. Yu, J. Chen, S. Li, and M. Verhaegen, “Identification of affinely parameterized state–space models with unknown inputs,” Automatica, vol. 122, Article No. 109271, 2020. doi: 10.1016/j.automatica.2020.109271
    [11]
    M. Dai, Y. He, and X. Yang, “Continuous-time system identification with nuclear norm minimization and GPMF-based subspace method,” IEEE/CAA Journal of Automatica Sinica, vol. 3, no. 2, pp. 184–191, 2016. doi: 10.1109/JAS.2016.7451106
    [12]
    R. M. Johnstone, C. R. Johnson, R. R. Bitmead, and B. D. O. Anderson, “Exponential convergence of recursive least squares with exponential forgetting factor,” Systems and Control Letters, vol. 2, no. 2, pp. 77–82, 1982. doi: 10.1016/S0167-6911(82)80014-5
    [13]
    S. Bruggemann and R. R. Bitmead, “Exponential convergence of recursive least squares with forgetting factor for multiple-output systems,” Automatica, vol. 124, Article No. 109389, 2021. doi: 10.1016/j.automatica.2020.109389
    [14]
    D. Bertin, S. Bittanti, and P. Bolzern, “Tracking of nonstationary systems by means of different prediction error direction forgetting techniques,” in Proc. IFAC Workshop on Adaptive Systems in Control and Signal Processing, Pergamon, Turkey, 1987, pp. 185–190.
    [15]
    C. Paleologu, J. Benesty, and S. Ciochina, “A robust variable forgetting factor recursive least-squares algorithm for system identification,” IEEE Signal Processing Letters, vol. 15, pp. 597–600, 2008. doi: 10.1109/LSP.2008.2001559
    [16]
    S. Leung and C. F. So, “Gradient-based variable forgetting factor RLS algorithm in time-varying environments,” IEEE Trans. Signal Processing, vol. 53, no. 8, pp. 3141–3150, 2005. doi: 10.1109/TSP.2005.851110
    [17]
    J. Dokoupil, A. Voda, and P. Vaclavek, “Regularized extended estimation with stabilized exponential forgetting,” IEEE Trans. Automatic Control, vol. 62, no. 12, pp. 6513–6520, 2017. doi: 10.1109/TAC.2017.2656379
    [18]
    A. L. Bruce, A. Goel, and D. S. Bernstein, “Convergence and consistency of recursive least squares with variable-rate forgetting,” Automatica, vol. 119, Article No. 109052, 2020. doi: 10.1016/j.automatica.2020.109052
    [19]
    J. E. Parkum, N. Poulsen, and J. Holst, “Recursive forgetting algorithms,” Int. Journal of Control, vol. 55, no. 1, pp. 109–128, 1992. doi: 10.1080/00207179208934228
    [20]
    S. Bittanti, P. Bolzern, and M. Campi, “Convergence and exponential convergence of identification algorithms with directional forgetting factor,” Automatica, vol. 26, no. 5, pp. 929–932, 1990. doi: 10.1016/0005-1098(90)90012-7
    [21]
    L. Cao and H. Schwartz, “A directional forgetting algorithm based on the decomposition of the information matrix,” Automatica, vol. 36, no. 11, pp. 1725–1731, 2000. doi: 10.1016/S0005-1098(00)00093-5
    [22]
    S. A. U. Islam and D. S. Bernstein, “Recursive least squares for realtime implementation [Lecture Notes],” IEEE Control Systems, vol. 39, no. 3, pp. 82–85, 2019. doi: 10.1109/MCS.2019.2900788
    [23]
    A. Goel, A. L. Bruce, and D. S. Bernstein, “Recursive least squares with variable-direction forgetting: Compensating for the loss of persistency [Lecture Notes],” IEEE Control Systems, vol. 40, no. 4, pp. 80–102, 2020.
    [24]
    A. L. Bruce, A. Goel, and D. S. Bernstein, “Recursive least squares with matrix forgetting,” in Proc. American Control Conf., Denver, CO, USA, 2020, pp. 1406–1410.
    [25]
    F. Ding, P. X. Liu, and G. Liu, “Multiinnovation least-squares identification for system modeling,” IEEE Trans. Systems,Man,and Cybernetics,Part B (Cybernetics), vol. 40, no. 3, pp. 767–778, 2009.
    [26]
    H. V. Henderson and S. R. Searle, “The vec-permutation matrix, the vec operator and kronecker products: A review,” Linear and Multilinear Algebra, vol. 9, no. 4, pp. 271–288, 1981. doi: 10.1080/03081088108817379
    [27]
    P. C. Hansen, “Oblique projections and standard-form transformations for discrete inverse problems,” Numerical Linear Algebra with Applications, vol. 20, no. 2, pp. 250–258, 2013. doi: 10.1002/nla.802
    [28]
    C. D. Meyer, Matrix Analysis and Applied Linear Algebra. Philadelphia, USA: SIAM, 2000.

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    Highlights

    • A VDF algorithm is proposed for identifying MO systems under non-persistent excitation
    • The VDF strategy relies on oblique projection decomposition of the information matrix
    • Boundedness of the information matrix is proved under non-persistent excitation
    • Convergence of estimation error variance is proved under non-persistent excitation
    • Detailed analysis is made to compare with a VDF algorithm via eigenvalue decomposition

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