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C. Hametner, C. Mayr, M. Kozek, S. Jakubek:
"Stability analysis of data-driven local model networks";
Mathematical and Computer Modelling of Dynamical Systems, 20 (2014), 3; 224 - 247.

This article discusses stability analysis of data-driven dynamic local model networks. In contrast to traditional fuzzy modelling, the structure and complexity of such model architectures is not unique when only observed input- and output data are available for their parametrization. The present article complements the well-known trade-off between accuracy and complexity by the notion of stability. For this purpose, existing Lyapunov stability criteria for local model networks are extended by a decay rate which represents a scalar and quantitative stability measure. It allows to compare models with different degrees of complexity also in view of their stability. For some of the commonly available Lyapunov stability criteria, the individual local model transitions are crucial. Therefore, in this article, an approach is introduced to determine the actually occurring
model transitions by means of the identification data. The methods presented in the article are illustrated and discussed by means of a simulation example. It is shown how
model complexity and the related approximation quality can have an adverse impact on the stability and how the outcome of different Lyapunov criteria is affected by the proper determination of local model transitions.

local model networks, Lyapunov method, stability analysis, system identification

http://dx.doi.org/10.1080/13873954.2013.821494

Project Head Stefan Jakubek:
Christian Doppler Labor für Modellbasierte Kalibriermethoden