We would especially like suggestions which are plausible given technology that normal scientists would expect in the next 15 years.

Why wait 15 years? A Stuxnet-like technology is something that is already available and is likely to be a no-brainer for a super-intelligence. With it you can take over a lot of the current tech, from avionics and robotic factories to manufacturing orders, shipping manifestos and troop deployment. There is no need to bribe or blackmail anyone, humans already happily do what they are told without thinking too much about it. It is not hard to divert enough resources to build a robotic compound without anyone noticing. Doesn't even need to be done on a global scale, finding a weakness in the order management software of just one large company like Samsung, BP or GE is enough to kickstart a covert skunkworks project.