Exhaust purification system for internal combustion engine

An exhaust purification system for internal combustion engine comprising:

• a filter which is configured to trap particulate matters contained in exhaust gas of the internal combustion engine;
• an oxygen supply device which is configured to supply oxygen contained in intake air of the internal combustion engine to the filter;
• and
• a controller which is configured to execute filter regeneration processing to oxidize and remove the particulate matters deposited on the filter,
• wherein the filter regeneration processing includes regeneration processing during an engine stop that is executed during a shut-down of the internal combustion engine,
• wherein, in the regeneration processing during the engine stop, the controller is configured to:
• calculate a future temperature of the filter based on an accumulated amount of the particulate matters deposited on the filter, a present temperature of the filter, and an estimated pass amount of oxygen passing through the filter;
• and
• variably set an operation amount of the oxygen supply device based on a result of a comparison between the future temperature and an upper limit temperature of the filter.