A robust model-based iterative feedback optimization methodolgy has been introduced in previous work for the steady-state optimization of chemical process operations without requiring cumbersome model updating. Here we extend the methodology to utilize differential equation models directly. The adjoint system method that is often used in dynamic optimization is modified to explicitly incorporate plant measurements in the gradient computation during each iteration, resulting in robustness with respect to model-plant mismatch. In the case that the states cannot be measured along the entire spatial direction, estimated profiles based on boundary measurements are utilized. The methodology is tested with simulations of an ammonia synthesis reactor in autothermal operation and is shown to be robust in the presence of modeling error, input error, and measurement noise.