Thank you for reaching out to OSU Extension Service. You are correct, knotweed species are highly invasive. Chemical control is often required to manage knotweed. The following publication provides details about which herbicides are effective and common management mistakes, such as mowing and handpulling which create thicker stands. Biology and Management of Knotweeds in Oregon: https://catalog.extension.oregonstate.edu/sites/catalog/files/project/pdf/em9031.pdf
Additional herbicide information is available in our PNW Weed Management Handbook: https://pnwhandbooks.org/weed/problem-weeds/knotweed-bohemian-polygonum-bohemicum-japanese-polygonum...