Output control execution program of the output control method and a secondary battery control device and a secondary battery for a secondary battery

A rechargeable battery controller for controlling output of a rechargeable battery mounted on a vehicle having a power source including an internal combustion engine, a starter motor for starting the internal combustion engine, and a vehicle controller. The rechargeable battery controller includes a control circuit for setting an upper limit for discharge power output by the rechargeable battery in a set period of time and providing the upper limit to the vehicle controller. The control circuit is programmed to reset the upper limit to a value greater than or equal to a power value required to drive the starter motor when a first requirement in which power supply from the rechargeable battery to the starter motor is scheduled and a second requirement in which the upper limit is less than the power value required to drive the starter motor are both satisfied.