Dynamic Programming for Integrated Emission Management in Diesel Engines

Abstract

Integrated Emission Management (IEM) is a supervisory control strategy that aims at minimizing the operational costs of diesel engines with an aftertreatment system, while satisfying emission constraints imposed by legislation. In previous work on IEM, a suboptimal real-time implementable solution was proposed, which was based on Pontryagin's Minimum Principle (PMP). In this paper, we compute the optimal solution using Dynamic Programming (DP). As the emission legislation imposes a terminal state constraint, standard DP algorithms are sensitive to numerical errors that appear close to the boundary of the backward reachable sets. To avoid these numerical errors, we propose Boundary Surface Dynamic Programming (BSDP), which is an extension to Boundary Line Dynamic Programming and uses an approximation of the backward reachable sets. We also make an approximation of the forward reachable sets to reduce the grid size over time. Using a simulation study of a cold-start World Harmonized Transient Cycle for a Euro VI engine, we show that BSDP results in the best approximation of the optimal cost, when compared to existing DP methods, and that the real-time implementable solution only deviates 0.16 [%] from the optimal cost obtained using BSDP. cop. IFAC.