Abstract
In this paper, a new class of parametric non-linear functions, named Parabolic Approximating Functions (PAFs), is presented. Depending on the point of view, PAFs can be regarded as a class of quadratic splines, or a class of Takagi-Sugeno models: their main feature is the way they are parametrized, which makes extremely easy the imposition of constraints on their first and second derivative. In particular, this class of functions can be extremely useful in the realm of system identification and data-based control system design, thanks to the ease by which such a basic constraint as function invertibility - otherwise typically hard to be handled rigorously - can in fact be efficiently dealt with.
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