Can I get child support after my daugther has already turned 18 and there has never been a court order?

I'm in Illinois and I had a daughter with my then boyfriend in 1992. We lived together until she was 2 years old. Then we broke up and my boyfriend disappeared. No formal paternity action was ever instituted but his name is listed on her birth certificate as the father. No child support order was ever entered. In 2010, her father reappeared for the first time in 16 years just 2 months prior to her graduation from high school. My daughter had already turned 18 at this point. At this late date, is it still possible for me to pursue child support against her father?