## 1 Introduction
The ECMS supervisory control strategy has shown an improvement of more than 5% in fuel economy for the FTP75 driving cycle in comparison with an SI-only HEV, but barely any improvement was observed for the US06 driving cycle. In [29], dual-mode operation was investigated through a simulation of a power-split HEV equipped with an SI/HCCI engine, and an improvement of 2.5-5% was achieved for fuel consumption. In addition, it led to the prediction of a greater improvement with other types of HEVs, such as parallel architecture HEVs, which have lower flexibility in decoupling engine operations. In [30], a multi-mode low-temperature combustion (LTC) engine--which can operate not only in HCCI mode but also in reactivity-controlled compression ignition (RCCI) mode--was utilized as a range extender for a series HEV. A simulation shows that the multi-mode engine can offer an improvement in fuel consumption of up to 12.1% in comparison with an SI engine for different driving cycles. This is due to the higher engine efficiency in the HCCI mode. Additionally, under the control strategy based on PMP, almost all the operating points of the engine are located in the HCCI and RCCI regions. In [31], different EMSs were investigated for a power-split PHEV integrated with a dual-mode combustion engine, and a hierarchical EMS was proposed to realize the synergy of global and instantaneous optimization. The simulation results show a significant improvement in comparison with the CD/CS strategy for real-world driving cycles. In [32], an adaptive ECMS was developed for a power-split PHEV equipped with a dual-fuel intelligent charge compression ignition (ICCI) engine; this achieved fuel consumption and SOC control performances close to the global optimal results. which were achieved based on DP. All these studies reveal that the powertrain architecture, the dual-mode engine configuration, hybridization, driving cycle conditions, and EMSs can have an impact on dual-mode engine operation and fuel economy. In this paper, a plug-in SHEV with an SI/HCCI dual-mode combustion engine was investigated, and an EMS based on ECMS was developed to optimize fuel economy in the charge-sustaining mode under NVH constraints. The unique property of series hybrid vehicles is the decoupling of the ICE from the drivetrain, which ensures the convenience of operating the ICE within a limited range and reducing the complexity of HCCI combustion control and SI/HCCI mode transition control. While HCCI combustion has much higher fuel efficiency in comparison with SI combustion in the low-power operating range, it can significantly reduce fuel consumption in urban driving or heavy traffic, even under NVH constraints. Furthermore, compared with the conventional SI engine, which operates efficiently under high loads or at shutdown, the dual-mode combustion engine enables operation at medium-low power; this is closer to the power demand during driving. Thereby, the battery charging/discharging load is reduced and SOC sustainability is improved, along with benefits for battery health. The key contributions of this article are as follows:  
* NVH constraints are considered as the main constraints on engine operating conditions for HEVs; previous studies have usually ignored this. The NVH conditions of the engine have a significant impact on drivability; therefore, they should not be neglected in real-world applications. * An SI/HCCI dual-mode combustion engine is applied in a SHEV to solve the NVH issue. HCCI combustion enables the high-efficiency operation of the engine at low loads; therefore, this solution guarantees better fuel economy under tight NVH constraints in comparison with SI combustion. * An EMS based on the ECMS is developed and the optimal control problem is solved by utilizing the PSO algorithm. The fast convergence speed of PSO provides efficient calibration of the control parameters in offline simulations and guarantees online optimization for real-time applications. This paper is organized as follows.