Methods relating to exhaust after-treatment devices

A vehicle system, comprising:

• an electric machine;
• an internal combustion engine having an intake-air tract, an exhaust tract, an exhaust-gas after-treatment device arranged in the exhaust tract, an exhaust-gas recirculation tract for conducting exhaust gas from the exhaust tract, downstream of the exhaust-gas after-treatment device, to the intake-air tract via a loop, and a valve coupled to each of the intake-air tract and the exhaust-gas recirculation tract;
• a hybrid drivetrain comprising the electric machine and the internal combustion engine;
• and
• a controller with computer readable instructions stored on non-transitory memory for:
• in response to an actual value of the exhaust-gas after-treatment device deviating from a setpoint value, adjusting the valve to recirculate exhaust gas to the engine while controlling the electric machine during an overrun operation of the engine.