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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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    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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