On the set of obtainable reference trajectories using minimum variance control

In this paper it is investigated what will be the set of reference trajectories that can be tracked when Minimum Variance control is used. A necessary condition on the dynamic evaluation of a reference trajectory is deduced. For the case of a time-invariant system all the trackable reference trajectories are characterized exactly. The effect of limiting the control possibilities on the ability to track a certain reference trajectory is also discussed. The analyzed system is assumed to be linear, finite dimensional and discrete-time. The derived results are interpreted for economic systems.