Shrinkage Strategies for Structure Selection and Identification of\n Piecewise Affine Models

We propose two optimization-based heuristics for structure selection and\nidentification of PieceWise Affine (PWA) models with exogenous inputs. The\nfirst method determines the number of affine sub-models assuming known model\norder of the sub-models, while the second approach estimates the model order\nfor a given number of affine sub-models. Both approaches rely on the use of\nregularization-based shrinking strategies, that are exploited within a\ncoordinate-descent algorithm. This allows us to estimate the structure of the\nPWA models along with its model parameters. Starting from an over-parameterized\nmodel, the key idea is to alternate between an identification step and\nstructure refinement, based on the sparse estimates of the model parameters.\nThe performance of the presented strategies is assessed over two benchmark\nexamples.\n