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.

A control device for an internal combustion engine includes an in-cylinder pressure detector, an output shaft torque calculator, a target torque calculator, an input torque parameter calculator, and a controller. The output shaft torque calculator is to calculate an output shaft torque of an output shaft of the internal combustion engine based on an in-cylinder pressure. The target torque calculator is to calculate a target torque of the output shaft torque. The input torque parameter calculator is to calculate an input torque parameter representing an input torque such that the output shaft torque becomes equal to the target torque using a feedback control algorithm which is based on a controlled object model which models a controlled object that receives the input torque parameter as input and produces the output shaft torque as output. The controller is to control the output shaft torque using the input torque parameter.

A control apparatus of an engine system, the engine system including an engine, a VGT configured to control a boost pressure applied to the engine by adjust an angle of a vane provided in a turbine, and an EGR valve configured to control an amount of a recirculated exhaust gas, includes a target value determiner determining a target boost pressure and a target intake air amount based on an engine speed and a fuel injection amount, an EGR valve controller calculating a target EGR mass flow rate based on the target boost pressure and the target intake air amount and determining an EGR valve opening rate, and a turbocharger controller performing a sliding mode control using the calculated target EGR mass flow rate as a parameter to calculate a target compressor power and a target turbocharger mass flow rate and determining a turbine vane opening rate.