The meltdown occurred when software incorrectly thought the plane was on a collision course with other aeroplanes.
The system was overloaded as it struggled to plot new courses for affected aircraft.
Hundreds of planes were grounded at Los Angeles International airport.
While the system was rebooted, dozens of flights were delayed at smaller airports across the area.Training operations
"On April 30 2014, an FAA air-traffic system that processes flight-plan information experienced problems while processing a flight plan filed for a U-2 aircraft that operates at very high altitudes under visual flight rules," FAA spokesman Lynn Lunsford said.
She added the computer system had "misinterpreted" the U-2 as a more typical low-altitude flight and become overwhelmed in trying to make sure its flight path did not conflict with other air traffic in the area.
"The FAA resolved the issue within an hour, and then immediately adjusted the system to now require specific altitude information for each flight plan," she added.
The agency said it had now added more flight-processing memory to the computer system.
The Pentagon confirmed on Monday that an Air Force U-2 spy plane had been conducting training operations in the area, adding that "all the proper flight plan paperwork" had been submitted.
The U-2 was used to fly reconnaissance missions during the Cold War, and there are plans to retire the planes within the next few years.