Ensuring monotonic gain characteristics in estimated models by fuzzy model structures

We consider the situation where a non-linear physical system is identi ed from input-output data. In case no speci c physical structural knowledge about the system is available, parameterized grey-box models cannot be used. Identi cation in black box type of model structures is then the only alternative, and general approaches like neural nets, neuro-fuzzy models, etc., have to be applied. However, certain non-structural knowledge 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 main question is then how to utilize and maintain such information in an otherwise black-box framework. In this paper we show how this can be done, by applying a speci c fuzzy model structure, with strict parametric constraints. The usefulness of the approach is illustrated by experiments on real-world