H/sub infinity / optimal control as a weighted Wiener-Hopf problem

It is shown that H/sub infinity / optimization is equivalent to weighted H/sub 2/ optimization in the sense that the solution of the latter problem also solves the former. The weighting rational matrix that achieves this equivalence is explicitly computed in terms of a state-space realization. The authors do not suggest transforming H/sub infinity / optimization problems to H/sub 2/ optimization problems as a computational approach. Rather, their results reveal an interesting connection between H/sub infinity / and H/sub 2/ optimization problems which is expected to offer additional insight. For example, H/sub 2/ optimal controllers are known to have an optimal observer-full state feedback structure. The result obtained shows that the minimum entropy solution of H/sub infinity / optimal control problems can be obtained as an H/sub 2/ optimal solution. Therefore, it can be expected that the corresponding H/sub infinity / optimal controller has an optimal observer-full state feedback structure.<
>