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We propose two optimization-based heuristics for structure selection andidentification of PieceWise Affine (PWA) models with exogenous inputs. Thefirst method determines the number of affine sub-models assuming known modelorder of the sub-models, while the second approach estimates the model orderfor a given number of affine sub-models. Both approaches rely on the use ofregularization-based shrinking strategies, that are exploited within acoordinate-descent algorithm. This allows us to estimate the structure of thePWA models along with its model parameters. Starting from an over-parameterizedmodel, the key idea is to alternate between an identification step andstructure refinement, based on the sparse estimates of the model parameters.The performance of the presented strategies is assessed over two benchmarkexamples.

Shrinkage Strategies for Structure Selection and Identification of Piecewise Affine Models