Universal approximations of discrete-time control systems over finite time

We present an algorithm for obtaining approximate internal descriptions for a discrete-time control system, given a finite number of external experiments (input-output data). The system is required only to be causal, with a continuous input-output map. The experiments should be done in a prescribed way, with bounded inputs acting over a finite period of time. The approximation will be valid over the ranges of inputs and time covered by the experiments. The algorithm can be considered as an exact partial realization procedure for state-affine systems. An ε-stable computer program will be sketched.