  This work targets the identification of a class of models for hybrid
dynamical systems characterized by nonlinear autoregressive exogenous (NARX)
components, with finite-dimensional polynomial expansions, and by a Markovian
switching mechanism. The estimation of the model parameters is performed under
a probabilistic framework via Expectation Maximization, including submodel
coefficients, hidden state values and transition probabilities. Discrete mode
classification and NARX regression tasks are disentangled within the
iterations. Soft-labels are assigned to latent states on the trajectories by
averaging over the state posteriors and updated using the parametrization
obtained from the previous maximization phase. Then, NARXs parameters are
repeatedly fitted by solving weighted regression subproblems through a cyclical
coordinate descent approach with coordinate-wise minimization. Moreover, we
investigate a two stage selection scheme, based on a l1-norm bridge estimation
followed by hard-thresholding, to achieve parsimonious models through selection
of the polynomial expansion. The proposed approach is demonstrated on a SMNARX
problem composed by three nonlinear sub-models with specific regressors.
