Identification of hybrid systems using stable spline kernels

Abstract

All the approaches for identification of hybrid systems appeared in the literature assume known the model complexity. Widely used models are e.g. piecewise ARX with a priori fixed orders. In addition, the developed algorithms are typically tested only on quite simple systems, e.g. with ARX subsystems of order 1 or at most 2. This is a significant limitation for real applications. Here, we propose a new regularized technique for identification of piecewise affine systems, which we dub the hybrid stable spline algorithm (HSS). HSS exploits the recently introduced stable spline kernel to model the submodels impulse responses as zero-mean Gaussian processes, embedding information on submodels predictor stability. Using the Bayesian interpretation of regularization, the problem of classifying and distributing the data to the subsystems is cast as marginal likelihood optimization. An approximated optimization is performed by a Markov chain Monte Carlo scheme. Then, the stable spline algorithm is used to reconstruct each subsystem. Numerical experiments show that HSS can identify high-order piecewise affine systems, without having exact information on ARX subsystems order.