The name Falken is a nod to an aircraft of the same name in Ace Combat, even though the said aircraft probably never existed in the Trek Universe.
It was also a compromise, because I originally wanted to name this variant Falcon, but upon seeing that this name has been used quite a bit in fanon, decided to go with Falken, hoping that it would be less common, or even unused.
Unless, the Falken later used an AI later in the Ace Combat series after 5, you have the wrong reference (I haven't been able to play any of the later games due to not having a XBOX 360, and did they ever even make any of the later games playable on the PS3?).
For the most part, if the Aventine doesn't have it in her inventory, the Falken and her kin doesn't have it either, due to being built at around the same time, so unless the Vesta has an AI, the Falken doesn't.