A frequency criterion for the existence of an optimal control for Ito   equations
  The following optimization problem is considered. For a linear vector Ito equation. it is required to find an optimal deterministic control vector which minimizes a quadratic the functional. A necessary and sufficient condition for the existence of a optimal control are formulated in the form of frequency inequalities. It is shown that an optimal control can be found by solving a certain linear-quadratic deterministic optimization problem. 
Nikolai Dokuchaev
math.OC