Are there any Targaryen Bastards?

[norwaywolf123]

Aerys:

 "He loved music, dancing and masked balls, and was exceedingly fond of young beautiful women, filling the court with fair maidens from across the kingdoms. Some say he had as many mistresses as Aegon the Unworthy, though most historians highly doubt that. Whatever the case, Aerys always lost interests in his lovers fairly quickly.^[4] "

It seems that Aerys had many mistresses or lovers there sould be some bastards? But we never hear anything about targ bastards? Did Aerys have week sead or are we missing information?

 

R+L=J, According to this theory Jon Snow is not the bastard of Eddard but instead the bastard of Rhaegar Targaryen and Eddards sister Lyanna.