Optimal Piecewise Affine Approximations of Nonlinear Functions Obtained from Measurements

The paper describes a two-stage procedure for obtaining piecewise affine approximations of static nonlinearities obtained from measured data. In the first step we search for a suitable function which fits the data while minimizing the fitting error. Subsequently we show how to approximate, in an optimal fashion, the nonlinear fitting function by a piecewise affine function of pre-specified complexity. We illustrate that approximation of arbitrary nonlinear functions boils down to a series of one-dimensional approximations, rendering the procedure efficient from a computational point of view.