## 6 Results and Discussion  
The potential of the proposed strategy is assessed by comparing its performance with two extreme cases. On the one hand, the DP solution of the complete driving cycle is considered as best-case scenario, where the complete driving cycle is a priori known and the optimal power split can be computed. On the other hand, the widespread ECMS is employed as a reference technique with online capability. The \(s\) factor is calibrated with the reference loop (_ref_), and this value is applied during the complete driving cycle. In the case at hand, the first loop registered by the bus was considered as reference (_ref_) for both ECMS and the rollout algorithms, and was removed from the evaluated driving cycle. Since differences between the reference loop and the rest may lead the ECMS to fail in its aim of sustaining the charge, a feedback from _SoE_ is considered, so the reference \(s\) is used in the _SoE_ range between 0.3 and 0.7, while its value increases if _SoE_ falls below 0.3 and decreases if _SoE_ rises above 0.7. Figure 8 shows the evolution of the fuel consumption and _SoE_ during the complete driving cycle for the three strategies compared. It can be observed how the three methods are able to sustain the charge. Of course, DP succeeds in keeping the _SoE_ within the allowed range of 0.3 to 0.7 and leads to a final _SoE_ of 0.48, near the initial value of 0.5, to minimize the cost in (14), since it exploits the full knowledge of the complete driving cycle. The ECMS with the \(s\) parameter calibrated from a single loop frequently hits the _SoE_ limits, and only is able to keep its value within the required range by applying corrections to the \(s\) parameter. In any case, the ECMS shows how, since the beginning of the route, the strategy struggles to keep the _SoE_ above 0.3 and leads to a progressive deviation from the optimal fuel consumption obtained from DP. The result clearly shows that some calibration effort is needed to overcome this issue. Regarding the proposed strategy (rollout), results show the _SoE_ evolves well within the limits of 0.3 and 0.7, showing an evolution more similar to the DP and leading to a final _SoE_ of 0.47. Figure 9 shows the probability distribution of the difference between the optimal _SoE_ evolution obtained by DP and those obtained with the two evaluated methods (rollout and ECMS). It can be clearly noticed how despite both methods being online applicable and requiring the same information, i.e., the optimization of a single representative loop, the rollout algorithm provides better tracking of the optimal _SoE_ evolution. Due to the differences between optimal _SoE_ evolution and those obtained with the online-assessed capable strategies, at the end of the cycle, the ECMS shows an increase in fuel consumption of 11% with respect to the DP, while this figure is reduced to 1.9% by the proposed strategy based on rollout, as pointed out by the lower plot of Figure 8.  
Figure 7: Block diagram of the proposed algorithm. The fuel saving provided by the rollout strategy with respect to the standard ECMS is based on the operation of the ICE and batteries in more efficient conditions. Contour lines in Figure 10 show the efficiency levels in the ICE depending on the engine speed and demanded torque, while the color scale represents the observed frequency in the engine operating conditions obtained with ECMS (left), rollout (center) and DP (right). For instance, in the standard ECMS case, the ICE operates frequently outside the high-efficiency area, particularly in the area of middle load (with an efficiency around 40%) and low load (with an efficiency around 30%) due to the \(SoE\) excursions towards 0.3 that force the engine to start in order to avoid battery depletion, while for the rollout case most operating conditions are placed in the high-efficiency region, and there are only a few operating points in the area of medium and low efficiency.