Shade is the best biological control.
Triclopyr is an EPA-approved, effective herbicide when used as directed.
Lilly-Miller sells it under the name of "Image"- Fred Meyer carries it.
Late afternoon, Springtime application to growing vines, and/or autumn.
Goats will eat the young, green leaves; but the roots survive to re-sprout - once the goats leave.
Little else is of value... I know, I've tried.