## 3 Energy Management Strategies for HEVs
### Optimization-Based Control Strategy
#### 3.2.1 Global Optimization  
Among the most notable EMSs, those rooted in global optimization encompass the DP control approach, the stochastic dynamic programming (SDP) methodology, the linear programming (LP) technique, the PMP control method, as well as hybrid strategies that incorporate various intelligent control methods. These global optimization-based energy management techniques predominantly oversee the allocation of energy for a designated duty cycle, wherein the vehicular fuel economy is inherently reliant on the particular duty cycle, thereby posing certain inherent constraints. (a) Dynamic Programming. The optimization challenge in the decision-making process is solved mathematically by the dynamic planning-based energy management approach. [PERSON] first developed this technique in the 1950s. It entails breaking down a complicated problem into several of single-step optimization decisions [114]. The basic principle of DP is illustrated in Figure 7. It involves optimizing the process by finding the lowest-cost path from A to F. Although it can achieve global optimization under specific conditions, it is challenging to apply directly to real-time vehicle control due to the necessity of predicting cyclic conditions and the 'dimensionality catastrophe' from high computational demands [113]. However, it remains valuable for finding the optimal solution within the model's predictive control range, offering a crucial reference for energy management, optimizing energy efficiency, and enhancing system performance [115]. [PERSON] et al. (2013) [116] proposed a new DP method that utilizes an inverse simulation model to evaluate state constraints, avoiding demand interpolation and improving planning accuracy. [PERSON] et al. (2012) [117] developed an energy management system based on machine learning for online training of neural networks for predicting traffic congestion and road types, which improves the energy management efficiency of hybrid vehicles. [PERSON] et al. (2019) [118] presented a Receding Horizon Control technique based on DP for multi-mode HEV power splitting and mode selection. [PERSON] et al. [100] (2020) compared reinforcement learning with DP control approaches for energy management in HEVs. [PERSON] et al. (2020) [119] developed a DP strategy for simultaneous identification and control in series HEVs to balance conflicting objectives. [PERSON] (2020) [120] compared DP with GAs for power management in a parallel plug-in HEV. [PERSON] et al. (2020) [121] mainly solved the optimization problem of energy allocation for power-split hybrid vehicles using dynamic planning, which improved the transmission efficiency and thus the performance and fuel economy of the vehicle. [PERSON] et al. (2020) [122] applied DPto solve the energy management problem in an HEV with three driving modes. [PERSON] et al. (2021) [123] investigated optimal mesh discretization in DP for HEVs, aiming to enhance both calculation times and accuracy. [PERSON] et al. (2021) [124] proposed an iterative DP algorithm for transient powertrain control in HEVs. [PERSON] et al. (2021) [125] consider parallel HEVs and propose a dual EMS that combines long-term DP and short-term online optimization. Long-term planning calculates the SOC trajectory by DP and generates an intelligent SOC reference model with neural networks. For short-term optimization, a deep neural network is constructed to predict speed, and energy management is achieved by MPC and neighborhood search techniques. [PERSON] et al. (2022) [126] employed a deterministic DP approach to study energy-optimal regulatory control strategies for parallel HEVs. This method aims to maximize energy efficiency and offers an accurate and reliable optimization path for regulatory control systems. [PERSON] (2022) [127] highlighted DP as the optimal energy management approach for HEVs with constraints on battery SOC, SOH, and smooth driving. [PERSON] et al.