Kernel Methods for Linear Discrete-Time Equations

This paper discusses several problems in dynamical systems and control, where methods from learning theory are used in the state space of linear systems. This is in contrast to previous approaches in the frequency domain [19, 6]. We refer to [6] for a general survey on applications of machine learning to system identification. Basically, learning theory allows to deal with problems when only data from a given system are given. Reproducing Kernel Hilbert Spaces (RKHS) allow to work in a very large dimensional space in order to simplify the underlying problem.