On the data based time varying LQG controllers via Cholesky factorisations

The linear quadratic Gaussian control (LQG) problem is considered for input output linear systems corrupted with noise. In a computer based environment it is reasonable to assume that the model is obtained from practical experiments and hence only is partially known. For that reason, it may be preferable to derive the optimal control law from the basis of a finite number of data. In the paper it is shown how Cholesky factorisations of the noise spectrum and of the weightings in the performance index gives the resulting LQG-controller as a direct output control law. Modifications of the performance index in order to reduce the complexity of the controller is proposed. Both the off-line and the on-line LQG problems are considered. In addition comparisons are made to generalised predictive control (GPC) and to the state space Kalman filter based control law.