## 2 Fuzzy Energy Management Strategy (F-EMS) of HEVs  
Unlike the control strategy based on deterministic rules, fuzzy control does not describe the controlled system from the perspective of a precise mathematical expression, but rather determines some fuzzy control rules based on experience, experimental data analysis, and cognitive reasoning of the process, as well as obtaining the control parameters by controlling the output error of the system and the reasoning of the fuzzy rules, thereby not depending on the mathematical model of the controlled object, but realizing the complex control object with uncertainty. Therefore, for high-order complex systems that are difficult to implement with traditional control methods, the advantages of fuzzy control are very evident. Fuzzy control has strong robustness and adaptability to uncertain factors, such as electric vehicle parameters and driving conditions. The control rules that are difficult to accurately quantify in the EMS of HEV can be realized by fuzzy logic [12; 23; 24]. The core of fuzzy control is the fuzzy control rules, which are expressed in the form of human language. For example, if an electric vehicle requires more power, the output power of the battery and engine is greater. Rules are easily accepted and understood; in addition, fuzzy control algorithms are easy to implement digitally. These distinctive features allowed fuzzy control theory to develop rapidly in recent decades and become an active field in intelligent control [8; 9; 25; 26]. In the fuzzy system, there are two main representations of the fuzzy model: one is that the latter part of the fuzzy rule is a fuzzy set of outputs, called the standard model of the fuzzy system or the Mamdani model; the other is that the latter part of the fuzzy rule is a function of the input linguistic variable, called the Takagi-Sugeno model of the fuzzy system. Obviously, the Mamdani model should be used for the energy management or torque distribution control strategy of HEVs. The principle of the Mamdani fuzzy logic system, which is based on the standard model, is shown in Figure 1. In the process of realizing fuzzy control, a fuzzy controller is the carrier of a fuzzy control algorithm, which is mainly composed of the rule base, input fuzzification, fuzzy reasoning, and clear output [10; 11]. The fuzzy control rules of the Mamdani fuzzy controller are represented by a series of fuzzy conditional statement with \"if..., then... \". The basic form of the fuzzy rule language of the fuzzy controller is as follows:  
\[\text{If }x_{1}\text{ is }A_{1}\text{ and }x_{2}\text{ is }A_{2}\text{ and }\ldots\text{ and }x_{n}\text{ is }A_{n}\text{, }\text{ then }y\text{ is }B\text{,} \tag{1}\]  
where \(x_{i}\) and \(A_{i}\) (\(i=1,\,2,\,\ldots\,\,n\)) are the input fuzzy linguistic variables and their values, respectively, whereas \(y\) and \(B\) are the output linguistic variables and their values. In this paper, the fuzzy control strategy selects the SOC of the power battery and the total demand torque as the reference input of the fuzzy controller; that is, the state signals (such as SOC and demand torque) are converted into a set of fuzzy quantities expressed by membership degree, and the switching state of the engine and the magnitude of the output torque are determined by fuzzy rules according to the operating efficiency curve of the engine. The design ideas of the fuzzy EMS are described below. (1) When the battery is fully charged and the demand torque is large, the HEV operates in the hybrid drive mode. At this point, the engine works near the optimal efficiency curve, and the residual torque is provided by the motor; when the demand torque is relatively large and less than the optimal efficiency torque of the engine, the HEV is separately driven by the engine, and the motor does not work;  
Figure 1: Composition of the fuzzy controller. (2) When the battery is relatively full and the demand torque is large, the HEV operates in engine drive mode or hybrid drive mode.