Piecewise smooth system identification in reproducing kernel Hilbert space

The paper extends the recent approach of Ohlsson and Ljung for piecewise affine system identification to the nonlinear case while taking a clustering point of view. In this approach, the problem is cast as the minimization of a convex cost function implementing a trade-off between the fit to the data and a sparsity prior on the number of pieces. Here, we consider the nonlinear case of piecewise smooth system identification without prior knowledge on the type of nonlinearities involved. This is tackled by simultaneously learning a collection of local models from a reproducing kernel Hilbert space via the minimization of a convex functional, for which we prove a representer theorem that provides the explicit form of the solution. An example of application to piecewise smooth system identification shows that both the mode and the nonlinear local models can be accurately estimated.