Automatic engine stop and start system with detection of brake operation

An automatic engine stop and start system monitors a booster negative pressure (PB) and a braking operation (BS). A combination of the booster negative pressure (PB) and the brake operation (BS) can effectively indicate that a booster negative pressure (PB) will be insufficient to ensure a brake function. The controller (17) evaluates the booster negative pressure (PB) and the brake operation (BS), and restarts the engine when it is estimated that the booster negative pressure may be decreased below a threshold (PBth). As a result, it is possible to restart the engine before the booster negative pressure (PB) is decreased.