On the optimality of open-loop LQG measurement scheduling

This note revisits the problem of optimally controlling a Linear-Quadratic-Gaussian (LQG) plant and its measurement subsystem. The standard treatment of this problem uses dynamic programming to establish that LQG regulation and open-loop measurement scheduling are optimal. Here it is shown that these results can be obtained more directly using a straightforward conditioning argument that highlights the dependence of the results on the data independence, for open-loop schedules, of the LQG cost.