## 1 Introduction
[32] proposed three distributed DRL-based energy and emission management strategies to achieve near-optimal fuel economy and outstanding computational efficiency, regarding a DP strategy as the optimal benchmark. In the DRL-based strategies, the engine's fuel consumption and emission model are still modeled by steady-state engine performance maps. As can be seen, these existing studies tried to use steady-state engine performance data measured on a laboratory engine bench to construct emission models. However, under real driving conditions, the engine operating state and control parameters change instantaneously, and transient pollutant emissions differ from those under stable engine operating conditions on the test bench [33]. Many existing studies have revealed that the dynamic characteristics of the engine's operating conditions influence exhaust pollutant emissions [34]. On-road driving tests have also verified that the real driving pollutant emissions in the aggressive driving style are significantly higher than those under the smooth driving style [35; 36; 37]. Evidently, emission models based on steady-state engine performance test data are much less likely to characterize the severe emissionsresulting from extreme transient changes of engine states in the engine's start-up, making it challenging to consider exhaust emissions in energy management strategies for EREV. This study aims to develop a dynamic model of engine pollutant emissions to fully reflect the emission deterioration caused by engine start-stop during real driving conditions of EREVs and to optimize energy management strategies with strict constraints on pollutant emissions. This study investigates the real driving emissions of an EREV based on regulatory test procedures and determines the engine start-up events that lead to abnormal pollutant emissions under real driving conditions. Inspired by real driving emission characteristics, an interpolated-startup-corrected method is proposed to construct the real driving emission model of EREV, which approximates the engine non-start-up conditions to the steady operating conditions and corrects the engine start-up emissions. Then, an optimization problem is constructed with real driving emissions as the constraints and minimum fuel consumption as the objective. Using the penalty function method, the emission constraints are assembled with the objective function to guide the optimization solution toward satisfying the emission constraints. Next, the DP algorithm embodying the interpolated-startup-corrected emission models is developed by inventing multiple interpolation operations in the value-space and action-space domains, which is used to solve the optimal engine operating sequence to obtain the lowest fuel consumption under the given emission limits. This study creates a new pathway to combine fuel economy-centered strategies and emission pollution-limited strategies for the energy management of EREVs. This paper is organized as follows: Section 2 introduces the EREV real driving emission tests based on the regulatory test procedures, demonstrates the modeling methodology and model validation of the interpolation-startup-correction emission model, and proposes the DP algorithm embedding the real driving emission model for energy management strategy optimization. The start-stop reduction strategies and condition migration strategies resulting from the DP algorithm are analyzed, explained, and discussed in Section 3. Finally, conclusions are drawn in Section 4.