By Grzegorz Mzyk
This ebook considers an issue of block-oriented nonlinear dynamic process id within the presence of random disturbances. This category of structures comprises a number of interconnections of linear dynamic blocks and static nonlinear components, e.g., Hammerstein method, Wiener approach, Wiener-Hammerstein ("sandwich") approach and additive NARMAX structures with suggestions. Interconnecting signs aren't obtainable for size. The mixed parametric-nonparametric algorithms, proposed within the e-book, should be chosen dependently at the earlier wisdom of the process and indications. such a lot of them are in line with the decomposition of the complicated procedure id activity into easier neighborhood sub-problems through the use of non-parametric (kernel or orthogonal) regression estimation. within the parametric degree, the generalized least squares or the instrumental variables process is often utilized to deal with correlated excitations. restrict houses of the algorithms were proven analytically and illustrated in uncomplicated experiments.
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Extra info for Combined Parametric-Nonparametric Identification of Block-Oriented Systems (Lecture Notes in Control and Information Sciences, Volume 454)
Respectively. 4 NARMAX System We also consider in this book a special case of NARMAX systems, consisting of two branches of Hammerstein structures, from which one plays the role of nonlinear feedback (see Fig. 10). 50) i=0 where η() is nonlinear static characteristic in feedback. The system is assumed to be stable as a whole. 50) when the characteristic η() is linear. zk uk wk w' k Fig. 5 Interconnected MIMO System Finally, we introduce the system with arbitrary structure of connections (Fig.
E. , s} (cf. 12)). , wt−s,M )T , and YN is a noisy output vector. In Stage 1 we assume that M − s > N ≥ s + 1 = dim γ. 14) is independent of estimating parameter vector c of the static subsystem. 4. Recalling that the ’input’ data are contaminated by the additive (estimation) errors, wt−r,M = wt−r + ςt−r,M , we note that recovering of γ from the data ΘN,M , YN is in fact the errors-in-variables estimation problem. This is unlike the aforementioned  where input data are accurate and only output measurements are corrupted by the noise (white).
Moreover, for each part of the system, the method is immune to possible errors in prior knowledge of companion subsystem. These advantages are achieved at the expense of a bit slower than the best possible convergence rate of the obtained parameter estimates, which is a consequence of the leading role of nonparametric regression estimation in the scheme and slower convergence of nonparametric methods. 2 Infinite Memory Hammerstein System In this section the two-stage approach is generalized for the Hammerstein systems with the IIR dynamics (see  and ).