Looking for management recommendations? Try the interactive Invasive Plant Control Database (by the Midwest Invasive Plant Network and the University of Wisconsin). It allows you to specify the species of interest, the time of year of treatment, the habitat, and other customizations.
The list below is an educational list of plants that can be invasive in natural areas. Some plants are regulated by the Minnesota Department of Agriculture as Noxious Weeds and that is noted in their descriptions.