A control unit configured to control an electric turbocharger and an EGR valve. While an internal combustion engine is stopped, an oxygen-free period, which is a period during which oxygen surrounding an exhaust gas purifier used for an oxidation reaction runs out, is estimated based on a temperature of the exhaust gas purifier. Before entering the oxygen-free period, the EGR valve is opened and the electric turbocharger is driven. Air surrounding the exhaust gas purifier is replaced with fresh air. After replacement with the fresh air has been completed, the electric turbocharger is stopped.