I want to ask if someone is familiar with the schematics

There are multiple versions of DS4 with different boards. GIS seems to indicate that's a JDM-055, but confirm that before doing anything.

Acid Mods Forum has some reverse-engineered info. The "Bottom Identifications" indicate what I think is your component as C11:

a surface mount capacitor. Unfortunately the schematic they have is incomplete and does not include a value for C11 (in the lower left in C9; the pdf on the linked page is better quality than the image I posted here):

but if you have access to a similar controller you should be able to get a part number off C11. You'll need either some kind of magnifying lens or much better eyes than most people. If the letters are faded, rub some chalk on the cap then blow it off. Surface mount capacitor identification. If you don't have access to another JDM-055, there's probably a solid chance C11 has the same value as C10 right next to it, but it's up to you if you want to roll the dice on that.

Good luck!

Per that schematic and the PCB traced my guess is those are the capacitors next to the battery connector on the schematic.

I can't read the values, but I would guess they are both the same, so measure the remaining one and go from there or read the value if you can. Voltage would be about 20% higher than the battery voltage.