Japanese Knot Weed
As with any invasive, a multi-pronged long term approach is needed to eradicate the plant. More info about these options are included in the article below.
You will see that there are chemical products that can be applied to the cut canes which will help kill some of the roots. However, your best bet may be to cut back the growth and cover with a heavy plastic weighted down with heavy bricks. This will prevent the Knotweed from getting the sunlight it needs to keep growing. You may need to leave the plastic down for several growing seasons. Use the chemical product on any stray upshoots around the plastic.
The only professionals that I can think of to help you with this would be a landscaper with a chemical applicator license. Or perhaps you can find out more from the Midwest Invasive Species Information Network. Link to the web site below. Hope that helps.