This looks like a close relative to giant knotweed, Japanese knotweed (Fallopia japonica), though hybrids of the two are possible and treatment is the same. Both Japanese knotweed and giant knotweed are aggressive perennials that reproduces both by rhizomes (underground stems) and by seed. They are often found in shaded to partially shaded habitats on moist, nutrient-rich soils, though it can thrive in gardens and on roadsides as well.
Repeated chopping or digging may eventually deplete underground reserves thus reducing the competitive edge of Japanese knotweed, however it is expected to take several growing seasons to achieve eradication and unfortunately, success is rare. Both root and stem fragments can root and result in new plants, therefore any plant material removed for control should be placed in the trash headed to the landfill and not in yard waste or compost. Mulching is not an effective means of suppressing Japanese knotweed. Mowing is not recommended as it can spread the infestation.
Repeated herbicide applications of glyphosate or various brush killers, such as triclopyr (Garlon, Pathfinder, Brush-B-Gon), picloram (Tordon, Pathway) or triclopyr + 2,4-D (Crossbow) should help keep this plant under control. Chemical applications can be made to cut stems for more effective treatment of small populations, see herbicide labels for details. Glyphosate (e.g. Roundup Weed and Grass Killer concentrate) is probably the best choice for homeowners because of its safety, ease of application and lack of residual activity in the soil. Glyphosate is most effective for perennial control in the fall (now) but can be applied anytime the plants are actively growing (temperatures consistently above 50F). Repeat applications will be necessary.
When using products containing glyphosate there are a few important points to consider. First, as with any pesticide, remember to read and follow all labeled instructions to maximize effectiveness and ensure environmental and personal safety. Second, glyphosate is a broad-spectrum herbicide, meaning it will injure or kill other plants contacted during the application, so care is needed to avoid green plant material, exposed roots, and injured bark of desired plants. Third, glyphosate is relatively safe in the environment when used as labeled. It adsorbs strongly to the soil in most cases (i.e. clay and organic matter), allowing even sensitive crops to be planted shortly after application; meaning no carry-over issues are expected. Fourth, glyphosate alone can take up to 14 days to show full activity under ideal growing conditions. Retreatment of the area may be needed depending on the degree of infestation. Glyphosate is most effective for perennial control in the fall but can be applied anytime the plants are actively growing (temperatures consistently above 50F). Finally, be sure that the product you choose has only the active ingredient glyphosate or glyphosate + pelargonic acid. Products with additional active ingredients may have other unwanted effects and may delay the planting of other plants in the coming season(s).