## 4 Conclusions  
The paper aims at providing a straightforward and clear procedure to model and select the suitable powertrain mode and the operating condition for each actuator, based on the power-weighted efficiency concept. The main conclusions can be summarized in the following points:  
* Hybrid powertrains can be controlled by actuators whose nature is extremely different in terms of efficiency and dynamic characteristics. An energy management strategy relying only on the individual efficiency map of each actuator does not provide a satisfying power distribution, since it limits or completely excludes the actuators with lower maximum efficiency, i.e., the ICE. The power-weighted efficiency provides a unique parameter that normalize the overall efficiency contribution of each actuator based on the power flow requested during a specific vehicle working condition which is not correlated to a specific driving cycle.
* There are multiple solutions, in terms of actuator torque distribution, for a given set of boundary conditions in terms of road slope, vehicle speed, and acceleration. The power-weighted efficiency could represent a valid parameter to discriminate and select the best working map for each actuator that satisfies the minimum energy loss principle. However, this solution would not prevent from undesirable working conditions where part of the power is addressed to accelerate or decelerate one or more powertrain components. Aiming at minimizing the variation of the powertrain kinetic energy, a penalty factor is introduced into the definition of the power-weighted efficiency that always guarantees high efficiency, though slightly lower than the maximum possible value, with a more targeted power flow towards the vehicle and/or the battery.
* This methodology also considers the effect of the road inclination, which modifies the admissible vehicle acceleration range. This approach is able to regulate the operative condition of each actuator and to switch the two electric machine modes between generator and motor, thus taking advantage or compensating the road inclination influence.  
This paper represents an initial step towards the validation of the effectiveness of the presented methodology which would require a further investigation in terms of comparison against other conventional strategies as well as a fair experimental campaign to assess the efficiency and dynamic performance of the new formulation, based on the power-weighted efficiency.  
Figure 16: Resulting powertrain mode map for the two-mode hybrid system for a \(\alpha=-10\%\) (**left**), \(\alpha=0\%\) (**center**) and \(\alpha=10\%\) (**right**) road slope.  
**Author Contributions:** Conceptualization, A.T., E.G., A.V., and M.V.; Data curation, A.T.; Formal analysis, A.T.; Methodology, A.T., E.G., A.V., and M.V.; Software, A.T., E.G.; Supervision, M.V.; Writing--original draft, A.T.; Writing--review and editing, E.G., A.V., L.D., and M.V. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.