Optimal control of real driving emissions

Real driving emissions (RDE) testing is an important legislative tool to reduce the gap between type-approval and real-world emissions of internal combustion engines. Since low fuel consumption and low nitrogen oxides (NOx) emissions are conflicting objectives, the setpoints of a Diesel engine and its exhaust-gas aftertreatment system have to be optimised and controlled accordingly. To this end, several authors have developed a so-called supervisory controller. In order to comply with RDE legislation, most approaches use a conservative tuning and thus sacrifice performance. In this paper, we explicitly include the RDE requirements in the optimal control problem, which we then solve using direct multiple shooting and nonlinear programming. Using the optimal solution as a benchmark and comparing it to a conservative strategy, we find that fuel savings of up to 3% are possible in simulation. Furthermore, as a first step towards an online, RDE compliant, and optimal supervisory controller, we use Pontryagin’s minimum principle to derive the fact that the optimal costate related to the tailpipe NOx emissions is piecewise constant.