## 5 Discussion  
An NLP-based ECMS that can determine an appropriate equivalent factor for an A-ECMS was proposed. The NLP-based ECMS used a reference SOC trajectory to control the equivalent factor. The NOCP was designed to calculate the reference SOC trajectory. The NOCP includes ICE torque, EM torque, and battery SOC as state variables, and the system models for these variables were applied in a simplified form to increase calculation speed. The NOCP also includes a cost function, which was designed through surface-fitting to the fuel-consumption-rate map. The solution closest to the global optimal with a short computation time through NLP-based ECMS was preferred. In addition, the proposed method was able to respond to infeasible solutions that occurred in NLP by using a strategy involving the equivalent factor. The performance of the proposed method, which was verified in an Autonomie simulation environment, was superior to those of a DP-based ECMS and rule-based EMS in terms of calculation time and fuel consumption. The proposed NLP-based ECMS completed its tasks rapidly in a desktop-computer simulation. However, the hybrid or electric control unit of an actual vehicle likely has far fewer computational resources. To apply an NLP-based ECMS to a real-world environment, a solver that can be applied to embedded system is therefore required. In this paper, the possibility that NLP-based ECMS can reduce fuel consumption close to the global optimal solution (DP result) is confirmed. However, empirical research on NLP-based ECMS is also important. For empirical verification, it is necessary to compare NLP-based ECMS with other online optimization approaches, such as PSO [21; 22; 23] or NN-based method [27; 28; 29; 30; 31]. We are conducting a follow-up study for empirical verification of NLP-based ECMS. In conclusion, follow-up studies are required to apply NLP-based ECMS to embedded systems. NLP-based ECMS includes NLP, which is a challenge when applied to embedded systems. To apply NLP-based ECMS to embedded systems, two representative follow-up studies are needed. The first is to improve the computational speed and computational stability of NLP. To improve the computational performance of NLP, it is necessary to simplify OCP. Simplifying OCP means softening constraints on road information (speed profile, grade profile, etc.) or vehicle models (degree of surface fitting polynomial for engine/motor map). It is important to determine the appropriate prediction/control horizon through this process. Improving computational stability means considering the infeasible region of the NLP. NLP can derive infeasible solutions because of the exceptional driving situation, like a cut-in. The second is to develop a NLP solver suitable for embedded systems. Various studies have been actively conducted on the research subject [43; 44; 45], such as SQP or interior-point method. NLP requires a very large amount of computation because it uses \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & **Fuel** & **Fuel** & **Final** & **Simulation** \\  & **Consumption** & **Improvement** & **SOC** & **Time** \\ \hline DP & 0.512 [kg] & – & – & – \\ \hline Ruel-based & 0.595 [kg] & 0.0 [\%] & 0.61 [-] & 73.79 [s] \\ \hline
0 & 0.527 [kg] & 11.4 [\%] & 0.61 [-] & 2553.18 [s] \\ \hline
2 & 0.527 [kg] & 11.4 [\%] & 0.61 [-] & 281.49 [s] \\ \hline
5 & 0.533 [kg] & 10.4 [\%] & 0.61 [-] & 90.39 [s] \\ \hline
6 & 0.536 [kg] & 9.9 [\%] & 0.61 [-] & 81.00 [s] \\ \hline NLP & 0.531 [kg] & 10.8 [\%] & 0.61 [-] & 74.18 [s] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Analysis of Autonomie simulation results: Fuel Improvement and Simulation Time. numerical and recursive methods. Therefore, it is necessary to optimize the amount of computation through solution space analysis. The solution space is determined by an operation characteristic or a driving situation of the HEV. The proposed NLP-based ECMS does not consider clutch and transmission effects.