  Hybrid system identification is a key tool to achieve reliable models of
Cyber-Physical Systems from data. PieceWise Affine models guarantees universal
approximation, local linearity and equivalence to other classes of hybrid
system. Still, PWA identification is a challenging problem, requiring the
concurrent solution of regression and classification tasks. In this work, we
focus on the identification of PieceWise Auto Regressive with eXogenous input
models with arbitrary regions (NPWARX), thus not restricted to polyhedral
domains, and characterized by discontinuous maps. To this end, we propose a
method based on a probabilistic mixture model, where the discrete state is
represented through a multinomial distribution conditioned by the input
regressors. The architecture is conceived following the Mixture of Expert
concept, developed within the machine learning field. To achieve nonlinear
partitioning, we parametrize the discriminant function using a neural network.
Then, the parameters of both the ARX submodels and the classifier are
concurrently estimated by maximizing the likelihood of the overall model using
Expectation Maximization. The proposed method is demonstrated on a nonlinear
piece-wise problem with discontinuous maps.
