Nonlinear Dynamics

, Volume 75, Issue 1–2, pp 49–61 | Cite as

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

Original Paper


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.


Hammerstein model State space models Hierarchical identification principle Least squares 



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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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.College of Automation EngineeringQingdao UniversityQingdaoP.R. China
  2. 2.College of Automation & Electronic EngineeringQingdao University of Science & TechnologyQingdaoP.R. China

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