Optimal control in the presence of state uncertainty

The problem of optimal control given full state knowledge has been solved many years ago and is very well documented. Nonetheless, in most control settings it is virtually impossible to know the exact state value. To deal with this fact, two concepts were introduced: certainty equivalence and separation principle. In this paper, it is presented a novel necessary condition for certainty equivalence to hold, without such condition, in the presence of state uncertainty current optimal controllers lead to suboptimal control. Furthermore, it is also presented a novel controller that remains optimal even when the necessary condition in question is violated. takes into account the effect of the sate estimation error in the control. It is proven that the the new controller is never outperformed by classical approaches.