Controller for internal combustion engine

A controller configured to control an internal combustion engine, wherein

• the internal combustion engine includes:
• a tank that stores fuel, a fuel injection valve that is provided on the internal combustion engine and supplies fuel to a cylinder, a fuel passage that connects the tank to the fuel injection valve, and an electromagnetic valve that is provided in the fuel passage so as to selectively open and close the fuel passage,
• in response to a request to operate at idle, the controller is configured to perform a fuel pressure control of adjusting a fuel pressure downstream of the electromagnetic valve in a flow direction of fuel in the fuel passage to a prescribed pressure lower than a fuel pressure upstream of the electromagnetic valve by first closing the electromagnetic valve until the fuel pressure downstream of the electromagnetic valve decreases to the prescribed pressure, then repeatedly performing opening and closing operations of the electromagnetic valve,
• the controller comprises processing circuitry, and
• the processing circuitry is configured to execute a process of setting opening and closing time points of the electromagnetic valve such that a valve opening period of the electromagnetic valve during execution of the fuel pressure control overlaps with a valve opening period of the fuel injection valve.