An internal-combustion engine has an electronically-controlled one of a turbocharger and an exhaust-driven turbo supercharger coupled to an exhaust duct of the engine, and the engine is controlled during a shift event of a transmission coupled to an output shaft of the engine by determining a target engine speed at the end of the shift event, and controlling electrical energy supplied to an electric machine, rotatably coupled to a rotatable shaft that is rotatably coupled to the electronically-controlled turbocharger or exhaust-driven turbo supercharger, to control rotation of the rotatable shaft coupled to the turbocharger or exhaust-driven turbo supercharger to attain the target engine speed.