The top figure is a plot of the target or reference velocity field at the nondimensionalized time t = 0.5. The bottom figure is the optimal velocity field at that same time instant.
By this time, the velocity field of the optimal flow has become practically indistiguishable from the velocity field of the target flow. This situation is mantained at susequent times. Thus, we see that the optimal control strategy has very effectively steered the flow towards the target flow.
The initial target and initial optimal velocity fields
The target and optimal velocity fields at t = 0.1
The target and optimal velocity fields at t = 0.3
The target and optimal velocity fields at t = 0.4
The norm of the difference between the target and optimal velocities vs. time
The norm of the control vs. time