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I believe it is natively supported even though I did not see it mentioned in the settings. I can attest I was extremely surprised when I noticed the DS4 rumbling. 
Since update release 1 I have been using the DS4 through steam which supports it natively as well. You can button map all the PS4 controls through steam and play exactly like Ace Combat on consoles.

Short answer yes. One way or another. 

alright thanks :)

how ?