To begin, we do have a feature request in to expose the current input controller in the FKey data, used for input. You can follow it here:
Since it is backlogged, there is no way to know when it will be looked at. The good news is that UE4 uses a library called SDL ( Simple direct media layer ), which will expose an array of attached controllers. You can technically use this to get the type of contoller(s) attached to the computer at any given time, though it will take some effort on your end.
As an example, this user created a plugin that uses SDL to get joystick support:
This should give you a good example of where to start and how to get access to the connected controllers.