AIR FUEL RATIO CONTROLLING APPARATUS

An air feed ratio controlling apparatus can include a predictor for predicting an air fuel ratio on the downstream side of a catalyst calculates a predicted air fuel ratio at least based on an actual air fuel ratio from an oxygen sensor and a history of a first correction coefficient. The air fuel ratio controlling apparatus can also include an adaptive model corrector which determines the deviation between the actual air fuel ratio and the predicted air fuel ratio as a prediction error ERPRE, and superposes a second correction coefficient on the first correction coefficient so that the prediction error may be reduced to zero.