## 3 Energy Management Strategy for HEV/PHEVs
### Optimization-Based EMS
#### 3.2.1 Real-Time Optimization Methods  
Real-time strategies aim to determine the allocation of power sources at each time step while simultaneously minimizing the cost function (e.g., fuel economy, power, and emissions). This class of strategy has been widely developed in recent years due to its relative ease of implementation. It can be subdivided as follows:  
* Pontryagin's Maximum Principle (PMP), which is the main method in optimal control theory, obtains the optimal control variable by solving the extreme values of the Hamilton function at each moment. It is easily implemented in order to find the optimal control; see [12,13].
* Equivalent Consumption Minimization (ECM) is an approach that calculates the total fuel consumption by combining the fuel used by an ICE and the equivalent fuel consumption of the electric motor. This unifies the calculation of power from both sources [14]. It is also a form of PMP that has been proven to yield a maximum fuel  
Figure 7: Classification of HEV/PHEV control strategies [6].  
economy under certain conditions [15]. An adaptive method [16] has been developed based on ECM. This method continually updates the equivalent factor by taking into account changing driving conditions, and it calculates the equivalent consumption in real-time as a function of the current system output. This allows the system to operate without future driving condition information [17].
* Model Predictive Control (MPC) is an advanced process control method that adheres to a set of constraints. In the context of EMSs for HEV/PHEVs, it is a strategy that combines online system parameter updates with optimal control to predict future velocities and optimize fuel consumption based on them. A typical example can be found in [18], where the authors formulated the energy management problem of a combined HEV as a nonlinear Optimal Control Problem with constraints. Two different cost functions were defined, and the MPC strategy was used to determine the power split between the IC Engine and electrical machines at each sample time. The results demonstrated a significant improvement in fuel economy compared to a commercially available controller in the Powertrain System Analysis Toolkit (PSAT) software. For more reviews of MPC-based EMS, please refer to [19].
* Machine learning, in recent years, has become a popular and useful technique for addressing various problems in many research fields, including as an EMSs method for HEV/PHEVs. It has great potential to improve the computation process and adaptability. The applications of machine learning to energy management can be generally classified into two categories [20]. The first involves using a single algorithm, such as reinforcement learning algorithms [21; 22], to derive the energy management policy. The second category involves combining other information or algorithms with machine learning methods, such as predictive algorithms, trip information, and MPC [23; 24; 25; 26].
* Metaheuristic algorithms are a type of computational intelligence paradigm that are especially useful for solving complex optimization problems with a vast search space of potential solutions [27]. They use general methods that can be applied to different types of optimization problems, without relying on specific knowledge, and aim to find near-optimal solutions within a reasonable amount of computation time. They are widely used in engineering, science, and business to tackle a range of optimization problems, including those encountered in HEV/PHEV EMSs. The most commonly used metaheuristic algorithms in HEV/PHEVs EMSs are Simulated Annealing(SA), the Genetic Algorithm(GA), and Particle Swarm Optimization (PSO) [28; 29; 30]. These algorithms do not require the calculation of derivatives, but instead use alternative methods to identify candidates for the optimal solution. This search for the optimal solution is guided by certain parameters that help to overcome local minima, although convergence to global optima cannot be generally guaranteed [11].