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This work targets the identification of a class of models for hybriddynamical systems characterized by nonlinear autoregressive exogenous (NARX)components, with finite-dimensional polynomial expansions, and by a Markovianswitching mechanism. The estimation of the model parameters is performed undera probabilistic framework via Expectation Maximization, including submodelcoefficients, hidden state values and transition probabilities. Discrete modeclassification and NARX regression tasks are disentangled within theiterations. Soft-labels are assigned to latent states on the trajectories byaveraging over the state posteriors and updated using the parametrizationobtained from the previous maximization phase. Then, NARXs parameters arerepeatedly fitted by solving weighted regression subproblems through a cyclicalcoordinate descent approach with coordinate-wise minimization. Moreover, weinvestigate a two stage selection scheme, based on a l1-norm bridge estimationfollowed by hard-thresholding, to achieve parsimonious models through selectionof the polynomial expansion. The proposed approach is demonstrated on a SMNARXproblem composed by three nonlinear sub-models with specific regressors.

Estimation of Switched Markov Polynomial NARX models