Drone Riots occur when the numbers of Drones at a base exceeds the number of Talents. During Riots, citizens will continue to feed themselves, but no production will take place and no surplus energy will be produced.
To end the Drone Riots, you will have to restore the balance of Drones and Talents.
Drone Riots can be prevented (or ended) by one of several methods: (a) building psych-related facilities such as Recreation Commons will reduce the numbers of Drones at a base. (b) if your social engineering POLICE rating is high enough, you can place military units in your base to serve as "police" and impose order. (c) Converting some workers to Doctors will increase the number of Talents, balancing out the drones. (d) if your base produces enough energy, increasing your energy allocation to Psych will increase the number of Talents at your base (one talent for every two points of Psych produced), thereby restoring balance.