On the set of obtainable reference trajectories using minimum variance control

In this paper we show that a reference trajectory that can be tracked by means of minimum variance control has to satisfy the condition that it is generated according to the structural parameters of the system. For time-invariant systems necessary and sufficient conditions are derived about the dynamic evaluation of such a reference trajectory. When only limited control possibilities are available to regulate the system we show that these limitations. if they are modelled via the cost criterium. show up directly in the dynamic evaluation of these trajectories. In case the applied control may only vary within the limits of predescribed values, application of optimal control results in a bang-bang control. The analysis of the closed-loop system becomes then more complicated. As a special case the discrete time target path controllability problem is solved. The performed mathematical analysis is kept simple (due to the choice of the cost criteria), and the obtained results are illustrated by means of a simulation study. The analyzed system is assumed to be linear, finite dimensional and discrete-time.