Journal article
Testing if a nonlinear system is additive or not
Automatica (Oxford), Vol.104, pp.134-140
06/2019
DOI: 10.1016/j.automatica.2019.02.053
Abstract
Additive nonlinear systems are one of the most widely used nonlinear and non-parametric models to describe nonlinear behaviors. A number of analysis and identification techniques have been developed in the literature for such systems. To apply, however, one has to make sure that the system is additive or can be approximated well by an additive system. This is a nontrivial problem and has eluded researchers for a long time. To the best of our knowledge, only scatter results are reported in the literature. The difficulties lie in the fact that the function and its structure are unknown so estimating its derivatives under an unknown multidimensional density function could be subject to the curse of dimensionality. In this paper, we present two methods to check if a system is additive. The first one estimates the squared derivative average via the Fourier transform. The other one directly estimates the squared derivative average in a reproducing kernel Hilbert space (RKHS) setting. For both methods, convergence results are established and practical numerical algorithms are developed.
Details
- Title: Subtitle
- Testing if a nonlinear system is additive or not
- Creators
- Changming Cheng - University of IowaEr-wei Bai - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Automatica (Oxford), Vol.104, pp.134-140
- Publisher
- Elsevier Ltd
- DOI
- 10.1016/j.automatica.2019.02.053
- ISSN
- 0005-1098
- eISSN
- 1873-2836
- Grant note
- CNS-1239509 / National Science Foundation, United States (http://dx.doi.org/10.13039/100000001) 15005188 / China Postdoctoral Science Foundation (http://dx.doi.org/10.13039/501100002858) 11632011; 11702171; 51121063 / National Natural Science Foundation of China (http://dx.doi.org/10.13039/501100001809)
- Language
- English
- Date published
- 06/2019
- Academic Unit
- Electrical and Computer Engineering
- Record Identifier
- 9984197520502771
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