1 ) A method for controlling a combustion engine ( 1 ) equipped with a supercharging system, said supercharging system comprising a turbocharger ( 2 ) and a positive-displacement compressor ( 3 ) for compressing a gas mixture at the intake of said combustion engine ( 1 ) and a by-pass circuit arranged parallel to said positive-displacement compressor, comprising a controllable by-pass valve ( 4 ), said positive-displacement compressor ( 3 ) being driven by an electric motor ( 11 ), characterized in that the following stages are carried out: a) acquiring a boost pressure setpoint P sural sp ; b) constructing a filling model for the supercharge volume contained between the intake valves of said engine ( 1 ) on the one hand and positive-displacement compressor ( 3 ) and by-pass valve ( 4 ) on the other; c) converting said boost pressure setpoint P sural sp to a rotational speed setpoint N cpr sp for said positive-displacement compressor ( 3 ) using said supercharge volume filling model, and d) controlling said electric motor ( 11 ) according to said rotational speed setpoint N cpr sp of said positive-displacement compressor ( 3 ).