Regularisierungsverfahren für die Identifikation mittels lokal-affiner Modelle (Regularization Techniques for Identification Using Local-Affine Models)

Untersucht werden Regularisierungsverfahren für die Identifikation nichtlinearer dynamischer Systeme mittels lokal-affiner Modelle. Die implizite Regularisierung durch lokale Parameterschätzung in Gleichungsfehler-Anordnung wird einer expliziten Regularisierung nach Tikhonov mit globaler Parameterschätzung in Ausgangsfehler-Anordnung gegenübergestellt. Nach Beschreibung von exakter und approximativer Tikhonov-Regularisierung zweiter Ordnung wird ein neuartiger global-lokaler Regularisierungsoperator speziell für lokal-affine Modelle hergeleitet, der die lokale Interpretierbarkeit der Teilmodelle garantiert. Regularization techniques for the identification of nonlinear dynamic systems using local-affine models are investigated. The implicit regularization by local parameter estimation in equation error structure is compared with the explicit regularization according to Tikhonov with global parameter estimation in output error structure. After the specification of exact and approximative Tikhonov regularization of second order, a novel global-local regularization operator is derived specifically for local-affine models which ensures the local interpretability of the submodels.

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