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The combination of physical models, including a combustion model of an advanced engine control system, was proposed to obtain sophisticated air/fuel ratio and residual gas fraction control in lean mixture combustion and high boost engines, including homogeneous charge compression-ignition and activated radical combustion with variable intake valve timing and a turbocharger or supercharger. Physical intake, engine thermodynamic, and combustion models predict air mass and residual gas fraction at the beginning of compression in the cylinder, on the basis of signals from an air flow sensor and an in-pressure sensor. Then, these models determine control variables such as air mass, fuel mass, exhaust gas recycle valve opening, intake valve timing, exhaust valve timing and combustion start crank angle, to attain an optimum air fuel ratio (A/F), optimum residual gas fraction, and highly efficient low nitrogen oxides combustion without power degradation in the above conditions.