Method of controlling the operation of an after-treatment system of a motor vehicle

Disclosed is a method of controlling the operation of an after-treatment system 270 of an internal combustion engine of a motor vehicle. The after-treatment system comprises a Lean NOx Trap (LNT) 285 and an exhaust line such as tail pipe 276, for conveying exhaust gasses from the LNT to the external environment. The method comprises the steps of calculating a value of a first parameter indicative of a NOx content in the exhaust gasses flowing in the tail pipe, calculating a value of a second parameter indicative of quantity of NOx stored in the LNT, calculating a value of a DeNOx request index as a function of the first parameter and the second parameter, calculating a raw threshold value of the DeNOx request index as a function of a LNT temperature and of an exhaust gas mass flow, calculating a corrected threshold value of the DeNOx, request index as a function of the raw threshold value of the DeNOx request index and of a correction factor, the correction factor being calculated as a function of a probability value of a successful completion of a DeNOx regeneration and starting a DeNOx regeneration if the calculated value of the DeNOx request index is larger than the corrected threshold value. Since the method includes a correction factor based on the probability of completing the DeNOx event the engine is able to operate efficiently and ensure the minimal use of a LNT DeNOx purge mode. Input parameters may include transmission gear and/or vehicle speed.