## 3 Main Objective and Research Method  
The main objective of this work is to develop a system to warn the driver in real time of the optimal speed that should be maintained on every road segment in order to optimize the energy used and the fuel consumed while observing a time schedule. The system takes into account:  
* Orography contained in a detailed digital map that includes the vertical profile with slope values
* Speed limits, both fixed (signals contained in the digital map) and variable (because of weather conditions that can be transmitted to the vehicle in real time before the vehicle reaches that road section using V2V and V2I communications)
* Information about traffic congestion that occurs periodically
* Deviations from the optimal profile because of unexpected congestion (that can also be transmitted using communications) and, in general, when the driver does not follow the system speed suggestions  
In this paper, given the initial hypothesis that there is a specific speed profile whose fuel consumption is the minimum necessary amount for reaching the destination within a previously established time, the solution proposed here is to create this speed profile by concatenating vehicle speed transitions as required. This chain-form solution is found by applying Dynamic Programming (DP) optimization. Taking account of the road vertical profile, allowed speed limits and timing relevance, DP chooses each constitutive part of the solution from a speed transitions set. Data for fuel consumption and duration time are associated with each speed transition. These associated data are obtained using an energy and fuel consumption model for longitudinal dynamic simulation. Figure 1 shows the whole process scheme. In the optimization process, a driving state of a vehicle is described using the current speed and the gear engaged, and speed transitions can bring the vehicle from one state to another. When the state changes have been established, a model for energy and fuel consumption calculation provides the spent fuel and elapsed time for each transition. The fuel consumption model takes into account the road slope in each state change. When a transition (also called \"atomic case\") has been simulated, values for initial speed, initial gear, final speed, final gear, spent fuel, elapsed time and road slope are stored into a look-up table. From now on, this look-up table containing the whole set of simulated transitions and their associated data is called fuel consumption map. Then DP optimization technique is applied to find the optimal chain-form solution, _i.e._, the optimal speed profile. The optimal speed profile is created using an objective function to evaluate the speed transitions. The objective function considers spent fuel and elapsed time and contains weighting factors to assign different relevance to spent fuel and elapsed time. The optimal speed profile must satisfy the legal speed limits, with any speed transitions that exceed legal speed limits being excluded from the optimization process, and must consider the road vertical profile using the mathematical vehicle model. The weighting factor values are determined in order to meet a time schedule and to satisfy the destination arrival time. Because the computational time of the DP algorithm is quite high when considering long distances, we have proceeded to divide the trip into shorter sections that are chained by overlapping stretches that allow an optimal solution by linking one to the next. Then, the DP algorithm is executed at the beginning of each overlapping distance for that specific stretch instead of the whole trip. This strategy also allows the weighting factors to be modified if deviations between the optimal speed profile and the actual speed are found, in order to meet the schedule. This adjustment is made regardless of the vertical road profile and takes into account constant speeds between the road sections that have some type of restriction (fixed or variable limits, traffic congestion, _etc._).