For PS4, the keyboard needs to be set to "bios" mode. However, not all keyboards support bios mode and this is one of them. I don't think there's much you can do.
Alienware Keyboard 510K does not work with Sony Playstation 4. The keyboard lights up, USB passthrough with mouse attached works fine, but Playstation doesnot recognizes the keyboard or accepts input. Keyboard does work on PC and Xbox. Any tips or  workarounds?  
Playstation does not work with Alienware Keyboard 510K