In Physical Access Control lingo, the term Edge controller typically refers to a device that is installed at the door (or in close proximity to the door) and that has all of the components needed to fully control the door with only and IP connection running back for communications to the front end system.
Typically Edge access controllers are PoE so that there is no need to provide a separate power feed to the device, they also provide power to all the components that comprise the door control (door lock, REX etc)
Continuum does not have a physical access controller that can be considered an Edge access controller.
The Continuum access controller that come closest is the CX9702, although it is NOT a PoE controller.
Click HERE to see the specs of the CX9702.