System for monitoring and controlling a motor-vehicle diesel internal combustion engine equipped with an electronic control unit, the engine comprising a double exhaust gas recirculation circuit comprising a low-pressure recirculation circuit (BPEGR) and a high-pressure recirculation circuit (HPEGR) each equipped with a respective recirculation valve (VHP, VBP), an exhaust valve, a turbocharger comprising a variable-nozzle turbine and a compressor, the references upstream and downstream being considered in the direction of gas circulation, wherein the electronic control unit is configured to control, in coordinated fashion, the opening positions of the valve of the high-pressure recirculation circuit (HPEGR), the variable nozzles of the turbine of the turbocharger, and of the exhaust valve, and comprises: - a recurrent neural network configured to model the type of the diesel engine, modelling non-linearly; characterized in that it furthermore comprises: - a linearizer configured to linearize the model of the recurrent neural network at the current operating point of the engine and deliver matrices (A, B, C) representative of the linearized model; - a state estimator configured to estimate the hidden states of the recurrent neural network, based on the recurrent neural network and on measurements of the pressure (P AVC) downstream of the intake air exchanger, on estimates of the fraction (X COLA) of gases burned in the intake collector (COLA), and on estimates of the fraction (X AVC) of gases burned upstream of the compressor of the turbocharger; and - a controller based on an MPC predictive control model for the evolution of the state of the engine, configured to estimate the commands for the opening positions of the valve of the high-pressure recirculation circuit (HPEGR), of the variable nozzles of the turbine of the turbocharger, and of the exhaust valve that minimize a mean squared error cost function in terms of setpoint tracking and MPC control variation while complying with setpoints of the pressure (P AVC) downstream of the intake air exchanger, of the fraction (X COLA) of gases burned in the intake collector (COLA), and of the fraction (X AVC) of gases burned upstream of the compressor of the turbocharger. - a recurrent neural network configured to model the type of the diesel engine, modelling non-linearly; - a linearizer configured to linearize the model of the recurrent neural network at the current operating point of the engine and deliver matrices (A, B, C) representative of the linearized model; - a state estimator configured to estimate the hidden states of the recurrent neural network, based on the recurrent neural network and on measurements of the pressure (P AVC) downstream of the intake air exchanger, on estimates of the fraction (X COLA) of gases burned in the intake collector (COLA), and on estimates of the fraction (X AVC) of gases burned upstream of the compressor of the turbocharger; and - a controller based on an MPC predictive control model for the evolution of the state of the engine, configured to estimate the commands for the opening positions of the valve of the high-pressure recirculation circuit (HPEGR), of the variable nozzles of the turbine of the turbocharger, and of the exhaust valve that minimize a mean squared error cost function in terms of setpoint tracking and MPC control variation while complying with setpoints of the pressure (P AVC) downstream of the intake air exchanger, of the fraction (X COLA) of gases burned in the intake collector (COLA), and of the fraction (X AVC) of gases burned upstream of the compressor of the turbocharger.