## 2 Materials and Methods
### Proposed Architecture of EMS  
The overall structure of the EMS presented in this paper, referred to as DP-ECMS, is shown in Figure 1. It relies on principles of optimal control to minimize fuel consumption considering look-ahead data. For this research, look-ahead data is a combination of traffic flow control devices (i.e., traffic light location and SPaT, stop signs) and road characteristics (i.e., speed limits, average traffic flow speed) obtained from sensors, including radar, camera, dedicated short range communication (DSRC), and GPS. All the look-ahead data is simulated and therefore assumed to be available at all times with no delays in data transmission. All modeling and simulation in this study is done using MATLAB and Simulink R2019b.  
Look-ahead data is used to obtain a speed limit prediction for the ego vehicle based on upcoming road conditions. This is done by layering different look-ahead data sources and finding the maximum safe speed. The average traffic flow speed is first compared to the legal speed limit. The effective speed limit is taken to be the minimum of the two. If the vehicle is in range of a connected intersection, SPaT is used to determine if the vehicle can pass on green. A simple rule-based method is used to find the speed needed to pass during a green window, where the speed is calculated by dividing the distance to the traffic light by the time left in the current phase. If the speed to pass on green does not violate the bounds set by traffic or the legal speed limit, it is taken as the effective speed limit. If speed constraints are violated, the effective speed limit at the traffic light is set to zero and the vehicle will be forced to stop. If there is no traffic and no traffic lights, the effective speed limit is simply the legal speed limit.  
The EMS shown in Figure 1 uses a modular control structure, which can be broken down into three key phases: the rollout algorithm-based MPC, a supervisory control and an EF predictor. The MPC uses the future speed limits obtained from the road data, SPaT and traffic to optimize the vehicle speed and battery SOC. It generates an optimal feedback control law for each control input, namely the total wheel torque and the torque split between the EM and internal combustion (IC) engine. The nonlinear MPC that uses DP as a solver cannot be executed at the rate of the powertrain controller due to computation time limitations. Additionally, the feedback law is not robust to stochastic uncertainties due to traffic. Hence, a supervisory controller is designed that uses the optimal feedback law obtained from nonlinear MPC in combination with adaptive ECMS. The supervisory controller uses the optimal feedback law to compute total wheel torque, but uses ECMS to compute the torque split ratio. Since there is no optimization in the supervisory controller, it can be executed at the rate of a typical powertrain controller. The key issue is that the ECMS requires an optimal equivalency factor that depends on the speed profile. Hence, a data-driven EF predictor is used which is based on the optimal speed and SOC trajectories obtained from a closed-loop simulation over the prediction horizon. An ANN is trained to generate an optimal EF for the expected future speed profile. It should be noted that all three phases are executed at different time rates. The supervisory controller is executed at the rate of 100 Hz. The MPC is executed once every 10 s, and the EF prediction is executed once every 30 s.