Generalized LQG design by filter and controller model selection

Abstract

This paper investigates a generalization of the conventional approach to LQG control design. First we investigate removing the assumption that the Kalman filter as the observer is necessarily based on the same model as the best plant model. The controller gain matrix design is performed as usual, based on the optimal solution to the deterministic design for the best model of the red-world plant. For the next case, we also remove this controller design restriction to investigate robustness to uncertainties in the plant model. The filter and controller gain matrices are both determined by models possibly other than the plant model. We relate the plant model to the filter and controller design models by a position correlation (mean square error on output) measure in order to determine optimal performance.