The legal puzzle of declaring war without a named target nation is precedented. See following notes from Slate:

Under Article I, Section 8 of the U.S. Constitution, Congress is constitutionally empowered to declare war on terrorists and is not obligated to name a host country. Article I authorizes Congress to "define and punish Piracies, Felonies committed on the High Seas, and Offenses against the Law of Nations." Piracy was such a significant threat at the time of the founding that the power to punish pirates is explicitly laid out in addition to the congressional power to declare war.

There is also historical precedent for congressional action against terrorists. For instance, in 1801, President Thomas Jefferson was authorized by Congress to send the Navy to the Mediterranean to curb the depredations of the Barbary pirates operating along the coast of northern Africa. These Corsairs--in the manner of terrorists everywhere--persecuted innocents while working in league with existing nation-states. The lack of a Barbary national anthem or embassy was not an obstacle.

Regards,

A.