Piecewise affine (PWA) regression is a supervised learning method which aims at
estimating, from a set of training data, a PWA map approximating the relationship between a
set of explanatory variables (commonly called regressors) and continuous-valued outputs. In
this paper, we describe a recursive and numerically efficient PWA regression algorithm, and
discuss its application to the identification of multi-input multi-output PWA dynamical models
in autoregressive form and to the identification of linear parameter-varying models.

This article presents a two‐stage algorithm for piecewise affine (PWA) regression. In the first
stage, a moving horizon strategy is employed to simultaneously estimate the model
parameters and to classify the training data by solving a small‐size mixed‐integer quadratic
programming problem. In the second stage, linear multicategory separation methods are
used to partition the regressor space. The framework of PWA regression is adapted to the
identification of PWA AutoRegressive with eXogenous input (PWARX) models as well as …