Model description:
The following time series is modeled using RBF networks
$$y(t)=\left(0.8-0.5e^{-y^{2}(t-1)}\right)y(t-1)-\left(0.3+0.9e^{-y^{2}(t-1)}\right)y(t-2)+0.1\sin(\pi y(t-1))+\xi(t),$$
where $\xi(t)$ is a zero-mean Gaussian white noise sequence with variance 0.01.
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Publication details:
| Title | Two-Stage Mixed Discrete–Continuous Identification of Radial Basis Function (RBF) Neural Models for Nonlinear Systems |
| Publication Type | Journal Article |
| Year of Publication | 2008 |
| Authors | Li, Kang, Peng Jian-Xun, and Bai E.-W. |
| Journal | IEEE Transactions on Circuits and Systems I: Regular Papers |
| Volume | 56 |
| Start Page | 630 |
| Issue | 3 |
| Pagination | 630-643 |
| Date Published | 08/2008 |
| ISSN | 1549-8328 |
| Accession Number | 10543358 |
| Keywords | computational complexity, integer programming, Nonlinear dynamical systems, radial basis function networks |
| Abstract | The identification of nonlinear dynamic systems using radial basis function (RBF) neural models is studied in this paper. Given a model selection criterion, the main objective is to effectively and efficiently build a parsimonious compact neural model that generalizes well over unseen data. This is achieved by simultaneous model structure selection and optimization of the parameters over the continuous parameter space. It is a mixed-integer hard problem, and a unified analytic framework is proposed to enable an effective and efficient two-stage mixed discrete-continuous identification procedure. This novel framework combines the advantages of an iterative discrete two-stage subset selection technique for model structure determination and the calculus-based continuous optimization of the model parameters. Computational complexity analysis and simulation studies confirm the efficacy of the proposed algorithm. |
| DOI | 10.1109/TCSI.2008.2002545 |