The state feedback optimization of first-order affine nonlinear singular control systems is formulated as a time-invariant parameter optimization problem. Degrees of freedom (DF) is applied to the differential balance equations with initial control or its time derivatives and switching times as parameters, and uncovered that the state feedback optimization problem has -2 DF, clarifying admissible singular control structures. Using these two novel concepts, we considered end-point optimization problems in fed-batch fermentation problem to illustrate the state feedback optimization of the feed flow rate.