Consistent identification of Hammerstein systems using an ersatz nonlinearity

We develop a method for identifying SISO Ham merstein systems with an unknown static nonlinearity, linear dynamics, white input noise and colored output noise. We use least squares with a μ-Markov model to estimate the Markov parameters of the linear time-invariant dynamical system. Since the input...

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Bibliographic Details
Main Authors: Ali, Asad A., D'Amato, A. M., Holzel, M. S., Kukreja, S. L., Bernstein, Dennis S.
Format: Conference Proceeding
Language:English
Subjects:
Computational modeling
Least squares approximation
Linear systems
Markov processes
Noise
Noise measurement
Numerical models
Online Access:Request full text
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Description
Summary:We develop a method for identifying SISO Ham merstein systems with an unknown static nonlinearity, linear dynamics, white input noise and colored output noise. We use least squares with a μ-Markov model to estimate the Markov parameters of the linear time-invariant dynamical system. Since the input to the linear system is not available, we use a substitute (ersatz) nonlinearity to transform the input for use in the regressor matrix. We prove that the Markov parameters of the system can be estimated consistently up to a constant scalar as the amount of data increases. This method is demonstrated with several numerical examples.
ISSN:0743-1619
2378-5861
DOI:10.1109/ACC.2011.5990956