Optimal controllers not satisfying the separation theorem

The paper deals with the problem of finding an optimal feedback control for stochastic continuous-time system with incomplete information. In the case of linear-quadratic-Gaussian assumptions, a standard solution is given by the separation theorem via two separate problems of estimation and control. Other controllers of the same structure (dynamic unit + feedback) that minimize a quadratic functional but do not satisfy the separation principle are considered. For all such (equivalent) controllers, the quadratic functional has the same value.