Model-free subspace-based LQG-design

When only input/output data of an unknown system are available, the classical way to design a linear quadratic Gaussian controller for that system mainly consists of three separate parts. First a system identification step is performed to find the system parameters. With these parameters a Kalman filter is designed to find an estimate of the state of the system. Finally, this state is then used in an LQ-controller. In the literature these three steps are hardly ever considered as one joint problem. Based on techniques from the field of sub-space system identification the present paper gives a new, much more direct method to calculate a finite-horizon LQG-controller. The three steps of the LQG-controller design, i.e. system identification, Kalman filter and LQ-control design are replaced by a QR- and a SV-decomposition. The equivalence between the new subspace-based approach and the classical approach is proven