An AI already controls the world. It's just a dumbass paperclip maximizer called "capitalism" whose job is to make the line go up on a graph. It's a kind of cute design where instead of using silicon chips, they get organic beings to do minor calculations for them, and then it's the distribute computing problem from hell to get all the calculations combined and error corrected, but it basically works well enough, and as aforementioned, it already controls the world. So basically, I don't see much room for a second AI to run the world unless it can find a way to coopt the operations of the first.