Piecewise affine systems identification: a learning theoretical approach

In this paper we study the problem of the identification of a hybrid model for a nonlinear system, based on input-output data measurements. We consider in particular the identification of piecewise affine models of nonlinear single-input/single-output systems through the prediction error minimization approach. The objective of this work is to analyze the performance of the identified model as the number of data used in the identification procedure grows to infinity. We consider a stochastic setting where the input and output signals are strictly stationary stochastic processes. Under suitable ergodicity assumptions, we show that the identified model is asymptotically optimal. The adopted approach is based on recent developments in statistical learning theory, and appears promising for studying the finite-sample properties of the identified model.