Plants become invasive or noxious in many different way. They are brought from other countries to be planted as ornamentals, recommended by state and federal agencies as appropriate wildlife species or they sneak their way in as seed in a shipment. Eventually, these plants become listed as invasive or noxious when it becomes apparent that they’re overly aggressive in their new habitat and outcompete locally adapted plants.
More often than not, it’s very difficult to eliminate these “weeds” once they’re established. The first step to getting rid of invasive plants to to learn to identify them.
The following is a link to a very good publication by MSU-Extension, A Field Identification Guide to Invasive Plants in Michigan’s Natural Communities. In addition to viewing online, this booklet can also be purchased from MSU-E for $14.