Alpha Control was an agency of Earth's United States of America, responsible for launching the ill-fated Jupiter 2 mission October 16, 1997. ("The Reluctant Stowaway")
When Will Robinson briefly returned to Earth in 1998, he attempted to establish contact with Alpha Control. ("Return from Outer Space")
Over a year after the launch of the Jupiter 2, the crew managed to make contact with Alpha Control and inform them that they were still alive. ("Wild Adventure")
Around late 1999, Will Robinson again came close to Earth while aboard Zalto's spaceship and unsuccessfully attempted to contact Alpha Control. ("Rocket to Earth")