Dynamic Algorithm for Lqgpcpredictive

In this paper the optimal control law is derived for a multi-variable state space Linear Quadratic Gaussian Predictive Controller (LQGPC). A dynamic performance index is utilized resulting in an optimal steady state controller. Knowledge of future reference values is incorporated into the controller design and the solution is derived using the method of Lagrange multipliers. It is shown how the well-known GPC controller can be obtained as a special case of the LQGPC controller design. The important advantage of using the LQGPC framework for designing predictive controllers, e.g. GPC, is that LQGPC enables a systematic restriction of the design parameters to yield a stable closed loop system. The system model considered in this paper can be further extended to also include direct feed-through and knowledge about future external inputs.