From linear to nonlinear identification: One step at a time

We propose a model structure based on High Level Canonical Piecewise Linear (HL CPWL) functions and a corresponding Nonlinear Output Error (NOE) identification algorithm. We explore the approximation capabilities of this novel structure together with its generalization and stability properties. Starting from a linear Output Error (OE) approximation, this model family yields an identification algorithm such that the order of the model can be easily increased during the identification process, retaining the previously achieved approximation. The parameters of the HL CPWL functions are learned using a simple algorithm that guarantees BIBO stability of the model. Applying our method is very straightforward and constitutes a principled approach for transitioning from linear to nonlinear model structures. Furthermore, it offers the possibility of an efficient hardware implementation in VLSI. A few examples are provided in this article in order to demonstrate the potential of our approach.