A stable spline convex approach to hybrid systems identification

In this paper we propose a new regularized technique for identification of piecewise affine systems which combines the ℓ1 loss and the recently introduced stable spline kernel. This latter is used to define a quadratic penalty which embeds information on the stability of each isolated subsystem. Our procedure determines sequentially the complexity of each affine subsystem, and then its impulse response, estimating from data couples of hyperparameters. The algorithm involves a series of operations which promote intra-submodel regularization hence favoring subsystems detection and reconstruction. Numerical experiments involving high-order piecewise affine systems show the effectiveness of the new approach.