This paper introduces a continuous-time constrained control strategy, which mimics the behavior of a traditional model predictive control scheme using dynamic feedback. The approach is based on the idea that the solution of the optimal control problem can be embedded in the internal states of a dynamic control law running in parallel to the system. Using input-to-state stability arguments, it is shown that if the controller dynamics are sufficiently fast with respect to the plant dynamics, the interconnection between the two systems is asymptotically stable. Additionally, it is shown that, by augmenting the proposed scheme with an add-on unit known as an explicit reference governor, it is possible to guarantee recursive feasibility and limit the residual of the optimal control problem, regardless of any changes in the desired set point. Numerical examples featuring aerospace applications demonstrate the effectiveness of the proposed scheme.