Sunchokes - or Jerusalem Artichokes - have you actually eaten those things? Once you get them started, you may never be rid of them again! When I was a kid, we decided we didn't like them boiled, fried or baked as they have kind of an earthy taste. We pulled up the rest of the crop and gave it to the cow, who relished both the tubers and leaves. However, after the tiller went though the garden next spring, we realized that there were lots of tubers left. The tiller shredded them and every tiny bit grew! It was a nightmare getting rid of the dang things!
Not quite kudzu, but . . .