My Sega Saturn USB Controller works on SF4 ULTRA PS4
Its the Official SLS SEGA Saturn USB Controller (Black Version with SEGA Logo). Don't believe you can buy them NEW anymore.
But there are replica ones on eBay quite cheap. (Also there are some "White Official SEGA Play" ones on sale on the internet (ebay, etc)
The SEGA pad lacks the extra buttons needed to access PS4 features (only has a START button) So the PS4 controller still has to be connected to access menu features. I had it connected wirelessly (didn't try wired connection)
Also by default only 2 buttons were working. Buttons have to be manually configured in the settings of game. Only SIX Face buttons can be changed (NOT the L/R Bumper buttons).
But after that the pad works great. Much better than the standard PS4 controller.