Parameters which are related to the rate at which particulate matter accumulates and is reburnt, are monitored and the time at which a regeneration is required and/or the length of time a regeneration should be induced, are derived based on the same. The temperature at the inlet and outlet of a trap in which particulate matter is accumulated are monitored and measures such as throttling the induction and exhaust are implement in addition to energizing a heater disposed immediately upstream of the trap as required in order to elevate the trap temperature and to induce and maintain the reburning during a trap regeneration. The pressure differential across the trap can be used to determine the amount of incombustible matter (ash) which has accumulated in the trap and to modify the regeneration timing. When the temperature of the exhaust gases cannot be raised sufficiently, a by-pass is opened to attenuate cooling of the trap by the low temperature gases.