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Least squares algorithm for an input nonlinear system with a dynamic subspace state space model

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Abstract

For a Hammerstein input nonlinear system with a subspace state space linear element, this paper transforms the system into a bilinear identification model by using the property of the shift operator to the state space model and presents a recursive and an iterative least squares algorithms to generate parameter estimates and state estimates by using the hierarchical identification principle and by replacing the unknown state variables with their estimates. The proposed approaches are computationally more efficient than the over-parameterization model based least squares method.

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Acknowledgements

This research was supported by the Shandong Provincial Natural Science Foundation (ZR2010FM024), the Shandong Province Higher Educational Science and Technology Program (J10LG12), the Basic Research Project of Qingdao Municipal Science and Technology Program (12-1-4-2-(3)-jch), the National Natural Science Foundation of China (61104001).

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Authors and Affiliations

  1. College of Automation Engineering, Qingdao University, Qingdao, 266071, P.R. China

    Dongqing Wang

  2. College of Automation & Electronic Engineering, Qingdao University of Science & Technology, Qingdao, 266061, P.R. China

    Feng Ding & Liu Ximei

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  1. Dongqing Wang
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  2. Feng Ding
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  3. Liu Ximei
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Correspondence to Dongqing Wang.

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Wang, D., Ding, F. & Ximei, L. Least squares algorithm for an input nonlinear system with a dynamic subspace state space model. Nonlinear Dyn 75, 49–61 (2014). https://doi.org/10.1007/s11071-013-1048-8

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