Identification of Piecewise Affine Systems Using Sum-of-Norms Regularization

Systems today often consist of logic switches working besides continuous physical systems. The demand for novel hybrid system identification algorithms is therefore of growing interest and essential for the development of control algorithms for this type of systems. An important type of hybrid systems is piecewise affine systems. The identification of piecewise affine systems is here tackled by overparametrizing and assigning a regressor-parameter to each of the observations. The regressor parameters are forced to be the same if that not causes a major increase in the fit term. The formulation takes the shape of a least-squares problem with sum-of-norms regularization over regressor parameter differences, a generalization of l1-regularization. The regularization constant is used to trade off fit and the number of partitions of the model.CADIC