A statistical learning approach to subspace identification of dynamical systems

Among the different approaches to identification of linear dynamical systems, subspace identification has become increasingly popular in the last decade. The reasons are the algorithmic simplicity thanks to the absence of non-convex optimization problems, the numerical stabil- ity and the statistical properties. Interestingly, concerning the statistical side, research in subspace identification has been concentrated on proving properties related to asymptotic unbiasedness. In this extended abstract we motivate how the use of an appropriate regularization can be helpful in the small sample case. Furthermore, this regularization allows one to use the kernel trick to identify systems where the input term in the state and output equations is a nonlinear function of the input variables.