Like all invasive non-native submersed weeds, there are several methods to control them.
Fanwort is an herbaceous perennial that spreads primarily by stem fragments or rhizomes. The erect shoots are upturned extensions of horizontal rhizomes. The species forms large clones as new rhizomes and floating shoots arise as axillary branches. The rhizomes are fragile and easily broken, facilitating vegetative spread and transport to new water bodies. The plants flower from May to September in the southeastern U.S., fanwort is self-pollinating and seeds readily germinate. Seeds collected from New Jersey failed to germinate, and no seedlings have been observed in the field; therefore, reproduction by seed in New Jersey is of little or no importance. ( from http://www.ecy.wa.gov/programs/wq/plants/weeds/aqua006.html)