# Speed Advisor for Fuel Consumption Minimisation Under Real Driving Conditions
## 1 Introduction  
A substantial effort has been done during the last decades in order to reduce the fuel consumption and emissions in light duty vehicles by means of improved powertrain design and controls [1]. Nevertheless, noticeable discrepancies are still observed between declared and real driving consumption and pollutant figures [2, 3]. One of the main reasons for such a deviation is that the driving cycles considered by regulations only represent to some extent the set of conditions that a vehicle may face during their entire life. To make up for such a limitation, current regulations have introduced Real Driving Emission testing procedures as a method to reduce the gap between the declared performance and that perceived by users. In any case, those facts point out the important impact that the driving conditions, including traffic but also driving style, have on fuel consumption and emissions. Studies such as [4] show how the vehicle speed profile can be responsible of up to 30% of the fuel consumption. Other studies [5] point out that cruise control can reduce fuel consumption by about 5% compared to standard driving. For this reason, the optimization of the speed profile is a hot topic in the automotive control sector that has been approached during the last decades with different methods, e.g. in [6] with Model Predictive Control, in [7] by using look-ahead information or [8] with fuzzy-logic controllers. Another related research line is focused on how the driver should behave to minimise fuel consumption and emissions. Several publications address how to monitor the driver behaviour and promote eco-driving. An example of such a tool is presented by [9] wherethey propose to encourage economical driving behaviour by giving feedback to the driver with a light code showing his driving aggressiveness (product of velocity and acceleration), since an aggressive driving style will naturally lead to higher fuel consumption. A similar approach is presented and evaluated in [10]. Finally, a third line of study is aimed to obtain a vehicle speed profile to minimise fuel consumption in a given route. This is a problem that matches the field of Optimal Control (OC). In fact, OC has been applied to the speed profile optimization since 1977 in the work of [11], who calculated the optimal speed profile on a hill. From them, and specially during the last decade, several OC techniques have been applied to the vehicle speed trajectory optimization at different scenarios. Some of these approaches are Pontryagin Minimum Principle (PMP) like [12; 13; 14], Dynamic Programming (DP) in [15; 16; 17] and Direct Methods (DM) in [18; 19]. Due to the complexity of reproducing real driving conditions, most of them focus on particular driving conditions (highway, traffic lights,...) and address this topic from a modelling perspective. A comprehensive review of them can be found in [20; 21; 22]. In addition, few of the previous studies include the report of the optimal vehicle speed profile to the driver and the assessment of their impact on the fuel consumption. An example of such studies is [17] where authors propose a cloud-based optimization of the vehicle speed profile by DP that is downloaded in the vehicle for a given route. Similarly to the last work, the target of the present study is to explore the potential of speed profile optimisation in real driving conditions, assessing the suitability of an application which recommends the driver the optimal vehicle speed sequence that minimises the fuel consumption for a particular route. To this aim, there are three main aspects to consider:  
* The route: The optimal vehicle speed profile is route-dependent. In a final application, information about the route should be a priori available to allow the optimal trajectory computation.