Optimal observer solution for predictive and LQG optimal control

Considers the formulation of linear quadratic Gaussian (LQG) feedback optimal control and optimal generalised predictive control (GPC). It has previously been shown that GPC design can be improved if the future output predictions are based on a Kalman filter state estimate, in a similar fashion to LQG design. Optimality conditions on the Kalman filter can then be investigated and a suitable state-space formulation is considered. An incremental CARMA model of the process under control is employed in a reconstructible canonical form in order to simplify the Kalman filter representation