## 1 Introduction  
Lithium-ion batteries currently represent the most commonly employed energy storage systems on-board hybrid electric vehicles (HEVs) and pure electric vehicles [1, 2]. They allow the storage of electrical energy for subsequent use as vehicle propelling energy. However, they present some critical issues that currently contribute to restricting the widespread diffusion of electrified powertrains. As an example, the current high cost of Li-ion battery packs (250-2500 $/kWh [3]) is a major factor in making the retail price of electrified vehicles considerably higher compared with vehicles equipped with traditional propulsion systems, i.e., based solely on internal combustion engines (_ICEs_) [4]. Moreover, Li-ion battery packs notably suffer from degradation of performance throughout their lifetime: their internal resistance increases, their capacity reduces, and their charge and discharge power capabilities consequently decrease [5]. Battery degradation worsens the performance of the electrified vehicle both in terms of fuel economy and acceleration capability [6]. Cyclic ageing that occurs during effective battery operation is normally considered the most critical ageingaspect [7]. The rate of cyclic ageing depends on given battery operating factors such as the C-rate, state-of-charge (_SOC_), and battery temperature as examples [8; 9; 10]. In general, the more critical the battery operating conditions, the more rapidly the battery approaches its end-of-life (_EOL_). However, defining the battery _EOL_ is not a trivial operation. Indeed, the battery _EOL_ is not simply related to the effective maximum number of charging and discharging cycles that a battery can supply, but rather to a more subtle concept of battery charge throughput (often expressed as Ah-throughput). The total number of allowed battery cycles loses relevance as the nominal capacity decreases below a certain value. The progression of the battery towards its _EOL_ is normally monitored by the battery state-of-health (_SOH_) and it ends when the effective battery capacity is reduced to 80% of its initial nominal value [11]. Progressive capacity loss in Li-ion energy storage systems involves specific chemical processes that take place within the cells. For example, a solid electrolyte interface (SEI) layer gradually grows on the anode with a rate that particularly accelerates at high temperatures above 35 \({}^{\circ}\)C [12]. Battery ageing is also due to lithium plating at the anode, which principally occurs at low temperatures below 15 \({}^{\circ}\)C [13]. However, battery ageing also occurs when the temperature of the battery is between 15 \({}^{\circ}\)C and 35 \({}^{\circ}\)C at a rate that depends on the battery C-rate, _SOC_ swing, and battery temperature itself [14]. Developing battery _SOH_ sensitive EMSs for HEVs has become a topic of growing interest in the literature. In 2012, [PERSON] et al. first adopted the concept of _SOH_ for controlling battery ageing using a throughput-based capacity fading model. They simulated different driving missions by means of a quasi-static HEV model controlled by an equivalent consumption minimization strategy (ECMS) [15]. Similar considerations were made by [PERSON] et al. in the same year, who introduced a severity factor in place of the battery _SOH_[16]. Further battery _SOH_ sensitive energy management approaches were then introduced in the following years. The concept of dual-objective ECMS for controlling fuel consumption and battery ageing was further extended in 2015 [17] and in 2019 [18]. These investigations demonstrated that considerable economic saving can be achieved by preserving the same battery pack for the entire vehicle lifetime. Different battery _SOH_ sensitive HEV energy management approaches were developed, including convex optimization [19], model-predictive control [20], and dynamic programming [21; 22]. The above studies assumed that battery temperature was kept constant by the conditioning system throughout the entire simulated driving missions.