Saying Adon Olam at End of Davening

How far back does the practice of singing Adon Olam at the end of davening go? Also, why is it that in Nusach Sefard of the Chassidim, Adon Olam is not said as is the case in many Nusach Ashkenaz kehilios that follow what we term the "Yeshivishe" world and on what authority are they somech to omit it?

Thanks,

Steven

At KAJ/WH, they omit it. They also do not say Yigdal on Leil Shabbos.