What sort of cable do PS4 controllers use to charge? Is it a custom PS4 one or a generic sort?
The Xbox One uses a USB-microUSB cable, the generic sort most phone chargers use.
If the PS4 is the same, and acts the same, then connecting your controller to the PS4 with a charger cable should sync them up, and they should stay synced even if you unplug it.
Sorry if I misunderstand the issue. I haven't used a PS4 and am unsure what exactly syncing refers to, if not connedcting a wireless controller to the console.