Abstract
The proposed chapter aims at presenting a unified framework of prediction-error based identification of LPV systems using freshly developed theoretical results. Recently, these methods have got a considerable attention as they have certain advantages in terms of computational complexity, optimality in the stochastic sense and available theoretical tools to analyze estimation errors like bias, variance, etc., and the understanding of consistency and convergence. Beside the introduction of the theoretical tools and the prediction-error framework itself,the scope of the chapter includes a detailed investigation of the LPV extension of the classical model structures like ARX, ARMAX, Box–Jenkins, OE, FIR, and series expansion models, like orthonormal basis functions based structures, together with their available estimation approaches including linear regression, nonlinear optimization, and iterative IV methods. Questions of model structure selection and experimental design are also investigated. In this way, the chapter provides a detailed overview about the state-of-the-art of LPV prediction-error identification giving the reader an easy guide to find the right tools of his LPV identification problems.
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Notes
- 1.
- 2.
\(h : {\mathbb{R}}^{n} \rightarrow\mathbb{R}\) is a real meromorphic function if \(h = f/g\) with f, g analytic and g≠0.
- 3.
The notation \(\bar{\mathbb{E}}\{x\} {=\lim }_{N\rightarrow \infty }\frac{1} {N}{\sum\nolimits }_{k=1}^{N}\mathbb{E}\{x(k)\}\) is adopted from the prediction-error framework of [16].
- 4.
It is more natural to use dynamic dependence in the parametrization of the coefficients in (2.34), but for the sake of simplicity we use only static dependence here.
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Tóth, R., Heuberger, P.S.C., Van den Hof, P.M.J. (2012). Prediction-Error Identification of LPV Systems: Present and Beyond. In: Mohammadpour, J., Scherer, C. (eds) Control of Linear Parameter Varying Systems with Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1833-7_2
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