Various methods and systems are provided for controlling air flow through an engine by adjusting an electric turbocharger of a vehicle. In one embodiment, a system for a vehicle comprises an electric turbocharger comprising a compressor, an exhaust turbine coupled to the compressor via a shaft, and an electric machine mechanically coupled to the shaft; and a controller including a processor and instructions stored on a non-transient memory of the controller that, when executed, cause the controller to: adjust an amount of power provided to or extracted from the shaft by the electric machine based on at least one of a speed of the electric turbocharger, a cylinder pressure, and an exhaust gas temperature. By adjusting the amount of power provided to or extracted from the electric machine, the exhaust gas temperature and the speed of the electric turbocharger may be efficiently maintained within a desired operating range.