|Identification Of Hybrid Systems Using Stable Spline Kernels|
All the approaches for identification of hybrid systems ap- peared 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 typ- ically tested only on quite simple systems, e.g. with ARX subsystems of order " or at most 2. This is a significant limi- tation for real applications. Here, we propose a new regular- ized 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 pro- cesses, embedding information on submodels predictor sta- bility. Using the Bayesian interpretation of regularization, the problem of classifying and distributing the data to the subsys- tems is cast as marginal likelihood optimization. An approx- imated optimization is performed by a Markov chain Monte Carlo scheme. Then, the stable spline algorithm is used to re- construct each subsystem. Numerical experiments show that HSS can identify complex (high-order) piecewise affine sys- tems, without having exact information on ARX subsystems order.