Ensuring Certain Physical Properties in Black BoxModels

We consider the situation where a nonlinear physical system is identiied from input-output data. In case no speciic physical structural knowledge about the system is available, parameterized grey box models cannot be used. Identiication in black-box-type of model structures is then the only alternative, and general approaches like neural networks, wavelet models, neuro-fuzzy models, etc., have to be applied. However, certain non-structural knowledge about the system is sometimes available. It could be known, e.g., that the step response is monotonic, or that the steady-state gain curve is monotonic. The question is then how to utilize and maintain such knowledge in a black box framework. In this paper we show how to incorporate this type of prior information in an otherwise black box environment, by applying a speciic fuzzy model structure, with strict parametric constraints. The usefulness of the approach is illustrated by experiments on real-world data.