Recovering piecewise affine maps by sparse optimization

Piecewise Affine maps (PWA) constitute an attractive modeling abstraction for nonlinear dynamic systems. An important feature of PWA model structures is that they carry the quite natural intuition according to which the operating space of a complex physical system can be decomposed into an appropriate number of pieces on which the system can be viewed as being affine. The paper presents a new method for the recovery of piecewise affine systems from observed samples of data. This problem is usually addressed through data clustering procedures which, unfortunately, are rarely guaranteed to be optimal. The ambition of this work is to overcome the need of resorting to a systematic clustering. To this end, some ideas of sparse optimization are used in combination with the local linearity property of PWA maps.