Methods for adapting system variation for an engine system having an after-treatment system. Measured characteristics of the after-treatment system may be used to predict a model value(s) that is compared to a measured value(s) of the after-treatment system to provide a comparison value. Information relating to high frequency uncertainties in characteristics of the after-treatment system are removed from the comparison value to provide an estimated system variation value. The estimated system variation value may then be used to adapt a system command of a controller. Further, information relating to high frequency uncertainties in characteristics of the after-treatment system may be used by a feed-back controller to determine high frequency adaptation values that may also be used to adjust the system command. The inclusion of the estimated system variation may eliminate reliance on the feed-back controller to provide system adjustments for both high and low frequency uncertainties.