Predictive LQ control with constraints

Rossiter et al. (1996) has developed necessary and sufficient conditions for stable input and output predictions. The work by Scokaert et al. (1996) has shown how to force a predictive controller onto the LQ optimal control law in the constraint free case, whereas a more recent algorithm presented by Kouvaritakis et al. (1996) achieved this via a different means. Here the latter algorithm is presented in a new way using perturbations on an L₂ optimal solution to illustrate the connections between it and the earlier work of Rossiter et al. and Scokaert et al. Furthermore, examples are given to contrast the performance of the three algorithms