Prioritized multi-objective optimization has been widely used within the operational space inverse dynamics control framework. In this paper, we present a constrained prioritized multi-objective optimization-base control formulation that extends to impedance control, including the `simple' impedance controller, which does not require the dynamic model. The main contribution of this paper is the dynamic-model-free prioritized feedback control formulation which encompasses arbitrary number of priority levels and takes the saturation constraints on the control inputs rigorously into account. The utility of the proposed formulation is demonstrated by a combined inverse dynamics impedance controller used to simulate stable locomotion of a planar anthropometric biped robot.