## 6 Discussion  
In this paper, the speed optimization problem has been solved using DP. This technique guarantees the global optimal solution even if the problem has non-convex constraints. This is the advantage over other approaches such as Genetic Algorithms, because these methods could have a high probability to get the global optimal solution [33], but it is not actually guaranteed. So there are optimization techniques that can work with non-differentiable equations and restrictions but they require approximations and some of them do not guarantee reaching global optimum but local ones. The main drawback for DP is the exponential growth of calculation time caused by the number of inputs and states (curse of dimensionality). The calculation time increases with the length of the horizon and this fact makes onboard real-time optimization for a complete trip unfeasible when long distances are considered, so a stretch overlapping method has been used in order to shorten the road stretches length in which DP is performed. This method allows, on the one hand, real time execution that provides approximate solutions but very similar to the optimal ones. On the other hand, periodic modifications of weighting factors are made in the event that traffic conditions change or the driver has not followed the optimal speed profile. This approach provides an approximate solution but the overlapping distance has been chosen considering that differences between the approximate solution built concatenating stretches and the optimal one should be small. The selected distance D seems to be appropriate because these differences are quite reduced. Furthermore, the warning updates are frequent enough for counteracting any speed deviation during the trip. Other methods apart from DP could be used and can be found in previous research, but the problem type, the complexity of the system analyzed and the accuracy required make that DP is an adequate approach providing a better behaviour that other mathematical tools. For example, in Lagrangian methods, the constraint functions could have to be approximated in order to obtain features for differentiation and convexity. An energy consumption optimization for road vehicles contains several data sets (one of the most complex ones could be the engine map) into look-up table forms and these data could be hard to be fitted by a function without doing approximations. The differences on the results when the model functions are replaced by approximations are discussed in [74]. Furthermore, in [75], the author comments some disadvantages when a vehicle energy optimization is done using nonlinear programming. Regarding the system operation, it should be noted that the system does not provide any warnings when a traffic congestion situation is detected, because the driver could not follow them and he must adapt his speed to the traffic conditions. But the system recalculates the speed profile for completing the trip in the predefined travel time when these traffic conditions disappear. In general, under complex scenarios, the driver is not forced to follow the system indications so it will compensate any deviation afterwards. Another relevant topic that should be highlighted is the fact that the system, apart from traffic conditions and legal speed limits, considers other types of speed limits, such as safe speed limits that can differ from legal speed limits under certain circumstances (vehicle type, adverse weather conditions, _etc._). These safe speeds are calculated according to the method described in [76; 77] and they are stored in the digital map. Then, if variable conditions are detected during the trip and retrieved by wirelesscommunications, speed limits can be updated and the algorithm recalculates the optimal speed profile according to these new limits. Finally, the fuel minimization system has been applied on a real highway section and fuel savings of up to 4% were obtained with respect to a constant speed profile with the same travel time.