This paper broadens the classical optimal control approach to the optimal regulation of a non-measurable, but parametrized uncertainty. A locally optimal feedback strategy (LOFS) is derived by minimizing a measure of the performance index sensitivity with respect to the uncertainty parameter vector. In the state feedback case the LOFS can be characterized by an extension of the well-known Matrix-Riccati equation. Conditions for stability and finiteness of the resulting linear feedback law are derived for the stationary LQ case with uncertain parameters. Different numerical algorithms also covering the output feedback case are presented. Examples demonstrate the superior performance of the proposed feedback for problems with a significant parametric uncertainty.