## 1 Introduction
From the research perspective, many articles have been published base on the recent and cutting edge issues in the field of hybrid vehicles as in [10; 11], which has led to advancements in control strategies and optimization methods. The function of the EMSs in HEVs is to allocate power demand to the vehicle's power sources efficiently. Research institutions have widely adopted EMSs for more than 20 years, and they are considered nonlinear and time-varying control problems [8]. Implementing these EMSs in HEVs has significantly improved fuel efficiency and reduced CO\({}_{2}\) emissions. These advancements have contributed to the widespread adoption of HEVs as a viable solution in transportation electrification compared to ICE vehicles. The EMSs have been adopted for efficient performance based on the durability of HEV components and optimal fuel consumption, and reducing emissions [12]. EMSs are generally classified into rule-based, optimization-based, and learning-based [8]. Rule-based facilitates integration in embedded controllers and presents excellent real-time performance. Rule-based EMSs are simple to implement [13], but requires human experience for better control effects. Optimization-based offers excellent performance but hinders implementation in real time. Learning-based offers outstanding potential for real-time implementation and provides a satisfactory control solution. However, it requires too much training time due to the large datasets, the training process is unstable, and there is difficulty in setting the objective functions [8]. Optimization-based EMSs have received wide attention in the context of scientific manuscripts. The commonly used optimization-base EMSs are the model predictive control (MPC), dynamic programming (DP), genetic algorithms (GA), particle swarm optimization (PSO), bacterial foraging optimization algorithm (BFOA), control theory [14], etc. For example PSO was proposed in [15] as EMS for multi-objective optimization for plug-in HEV, GA in [16], and adaptive dynamic programming (ADP) was proposed in [17] for a series-parallel HEV and a robust fuel economy was realized. In recent years, nonlinear control algorithms have been the pioneering control philosophy utilized in electric vehicles for optimal fuel economy and reduced emissions. A nonlinear model predictive control (NMPC) was proposed in [18] and neural network (NN) in [19] for optimal fuel economy for plug-in HEV. In [20] NN was proposed for improving fuel economy in HEV. The NN has been a pioneering control strategy in the field of nonlinear control system like quadrotor [21]. In [22] an interval type-2 fuzzy Takagi-Sugeno-Kang (IT2 TSK) was proposed to reduce the fuel usage in HEV. The proposed algorithm assessed on the basis of the engine and motor torques and the battery's SOC could save up to 19.03%, 12.54%, and 7.14%, respectively. The study in [23] proposed a deep learning (DL) algorithm for optimal fuel consumption in HEV. The suggested method is 12.2% and 6.4% better compared to rule-based and equivalent consumption minimization strategies. Predictive cruise control (PCC) was proposed in [24] for HEV based on the hierarchical control architecture to minimize fuel consumption. The study in [25] proposed two robust sliding mode controllers (SMCs) on a series HEV in order to optimize the system efficiency on the basis of speed and torque, respectively. The proposed controllers are promising and yield realistic performance for the HEV. A super-twisting sliding mode control (TSMC) was proposed in [26] to optimise the state of charge (SOC) in parallel HEV to reduce fuel consumption and emissions. The simulation results demonstrated the STSMC algorithm as a promising and alternative control technique suitable for optimal fuel consumption in HEVs. In [27] a new offline-online hybrid deep reinforcement learning (DRL) strategy was proposed to improve the fuel economy in HEV. The simulation results demonstrated that the proposed approach is promising and relatively better than only the online learning algorithms.