Even more likely is stasis -- even if AI-managed systems had comprehensive control over everything (which is obviously a hat tip to the fictional notion of weather machines a la Karl Rove in his prime), if they pursued their own interest, they'd be pitted against each other, regarding us as just part of the environment, if they noticed us at all.
Close but is not the scenario I was referring to - it is the one posited by Gregory Benford in his five novels beginning with “In the Ocean of Night”.