## 1 Introduction  
Nowadays, plug-in hybrid electric vehicles (PHEVs) representing a positive research direction due to combination of a certain all electric range (AER) and hybrid drive, exhibit apparent advantages in environmental protection and petroleum savings over traditional hybrid electric vehicles (HEVs). Compared with HEVs, PHEVs are equipped with higher capacity energy storage systems that can be directly charged from the power grid [1; 2]. Currently, automotive manufacturers and research institutes are actively devoted to developing PHEVs and improving controlling performances. For PHEVs, an appropriate and effective energy management is critical to improve the vehicle's fuel economy and reduce emissions. For the energy management strategy, the main destination is to optimize the fuel economy. Since there exists some uncertainty for driving cycles, driver's habits, and weather conditions that can influence the energy distribution in the PHEV, from this point, it can be said that the energy management is a stochastic optimization problem. Actually, popular control candidates can be divided into four types: (1) rule based control method [3; 4; 5]; (2) intelligent control methods, including artificial neural network (ANN) [6; 7], fuzzy logic [8; 9], model predictive control (MPC) [10; 11], and machine learning algorithm [12; 13]; (3) analytic methods [14; 15]; and (4) optimization based control method, including deterministic dynamic programming (DP) [16; 17; 18; 19; 1], Pontryagin's Minimum Principle (PMP) [20; 21], quadratic programming (QP) [22; 23], and convex optimization [24; 25; 26]. These methods' purpose can include improving the fuel economy, reducing emissions [27; 28], prolonging cycling life of the battery pack [2; 29], minimizing the operation cost [30], etc. Among these methods, rule-based control methods are simpler and easier to implement, which have been widely applied in practical application [4; 31; 32]. It is relatively easy to implement with fixed control parameters according to experience and prior knowledge. The prevalent rule-based method is the charge depleting/charge sustaining (CD/CS) method. During the CD mode, the vehicle is powered by the motor which absorbs the energy from the battery. The CD mode tries to use up the energy stored in the battery until its state of charge (SOC) decreases to an allowable minimum value. After that, the vehicle operating mode turns to the CS mode, which is also called the hybrid mode. In this mode, the vehicle is powered by the motor and engine together and meanwhile the battery SOC maintains in the vicinity of the low threshold. Due to the complex coupling characteristic of driveline system of PHEVs, rule-based method may not achieve the optimal power split between the engine and the motor, even if it is simple and stable. The intelligent methods and the analytic method have been widely researched in the energy management of the PHEVs. In Ref. [9], a fuzzy logic energy management strategy of a series-PHEV is proposed to achieve the power split between the battery and the engine, based on the battery working state and vehicle power demand, and simultaneously to control the engine working in the economic region. Nonetheless, the fuzzy logic table and related rules should be defined with care. In Ref. [11], the power split of a PHEV which is equipped with a semi-active hybrid energy storage system and an assistance power unit, is regulated by the MPC method; however, it does not consider the engine ON/OFF power threshold and the trip length. In Ref. [12], a reinforcement learning-based method of a PHEV is raised, which takes the minimizing electricity consumption, real-time control and different conditions into account. In Ref. [14], based on modeling the electric driveline loss and applying the piecewise linear fuel consumption, an analytic method is applied to establish the energy management strategy to minimize the fuel consumption via finding the engine-on power and the optimal battery power commands.