###### Contents  
* 1 Introduction
* 2.1 Introduction
* 2.2 The reduction of emissions related to road transport is a challenge that is being faced all over the world. In the EU, passenger cars and vans (\"light commercial vehicles\") are responsible for around 12% and 2.5%, respectively, of the total EU emissions of carbon dioxide (CO\({}_{2}\)), the main greenhouse gas [1]. On 21 January 2020, the European Parliament and the Council modified the Regulation (EU) 2019/631 (adopted on 17 April 2019) setting CO\({}_{2}\) emission performance standards for new passenger cars and for new vans in the EU [2]. It sets new EU fleet-wide CO\({}_{2}\) emission targets for the years 2025 and 2030, both for newly registered passenger cars and for newly registered vans. These targets are defined as a percentage reduction from the 2021 starting points. For cars, it aims for a 15% reduction from 2025 onwards and a 37.5% reduction from 2030 onwards. To adhere to these regulations, downsized engines, powertrain electrification, lower rolling resistance tire and the use of lightweight materials have been investigated intensively over the past few decades. Hybridization is a viable step toward powertrain electrification [3]. Apart from hybridization, since most of the future powertrain systems will continue to have a combustion engine (conventional powertrain and HEV as well), it should be noted that it is still fundamental to develop new technologies for combustion engines to improve the efficiency and the engine emissions level [4; 5]. To take advantage of the emission reduction potential of hybrid electric vehicles (HEVs), appropriate design of their energy management systems (EMSs) to control the power flow between the engine and the battery is essential. In a conventional (non-hybrid) vehicle, there is no need for an energy management strategy: the driver decides the instant power delivery using the brake and accelerator pedals and, in manual transmission vehicles, decides which gear is engaged at any time. In a hybrid vehicle, on the other hand, there is an additional decision that must be taken due to its ability to recover energy during braking or driving downhill: how much power is delivered by each of the energy sources on-board of the vehicle. The recovered energy can be stored in the battery and deployed at a later time to assist the prime mover to provide tractive power. This is why all hybrid vehicles include an energy management controller, interposed between the driver and the component controllers. As mentioned, the aim of the energy management system is to determine the optimal power split between the on-board energy sources. The decision regarding what to consider optimal depends on the specific application: in most cases, the strategies tend to minimize the fuel consumption, but optimization objectives could also include the minimization of pollutant emissions, maximization of battery life or--in general--a compromise among all the above goals [6]. Apparently, the optimal control policy depends on the characteristics of the drive cycle. Computing the optimal control sequence, it is thus essential to know the power and velocity requests in advance [7]. Therefore, the optimal control depends explicitly on the power requests and engine velocity. Although the optimal control cannot be implemented in real time, its determination is necessary for several reasons: (1) to evaluate the fuel consumption reduction potential of a hybrid vehicle; (2) to benchmark real-time control strategies; and (3) to improve the optimality of a real-time strategy using predicted trajectories. Then, at first glance, the easiest way to get a hybrid vehicle up and running with a real-time implemented strategy is to define a set of rules that decide when to use the electric machine and when not to use it [7]. This is known as rule-based (RB) EMS. The RB EMSs can be sub-classified into deterministic and fuzzy-logic strategies. Apart from this, optimal control-based approaches have been explored as well to determine the optimal control policy.