Non-parametric orthogonal series identification of Hammerstein systems
- 1 December 1989
- journal article
- research article
- Published by Taylor & Francis Ltd in International Journal of Systems Science
- Vol. 20 (12), 2355-2367
- https://doi.org/10.1080/00207728908910318
Abstract
The non-linearity in a discrete system governed by the Hammerstein functional is identified. The system is driven by a random while input signal and the output is disturbed by a random white noise. No parametric a priori information concerning the non-linearity is available and non-parametric algorithms are proposed. The algorithms are derived from the trigonometric as well as Hermite orthogonal series. It is shown that the algorithms converge to the unknown characteristic in a pointwise manner and that the mean integrated square error converges to zero as the number of observations tends to infinity. The rate of convergence is examined. A numerical example is also given.Keywords
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