## 1 Introduction
In addition, the control variable is simplified to the torque distribution of the two power sources. However, this method limits the adjustment range of the motor's operating point and increases the overall energy consumption of the vehicle under certain harsh working conditions. Aimed at the P2 configuration hybrid vehicle with continuously variable transmission (CVT), in [15], the authors determined the CVT speed ratio using instantaneous optimization during each calculation step of the dynamic programming. The control variable is simplified to the engine torque, and the problem of two degrees of freedom is thus converted into a one-degree problem. However, the weight coefficient during instantaneous optimization depends on engineering experience, which leads to a discrepancy between the instantaneous optimization solution and the global optimal solution. Dynamic programming needs to predict all the information of driving conditions and does not have a real-time performance. However, the minimum strategy for the equivalent fuel consumption derived from PMP achieves a good real-time performance, and has therefore been widely used [16; 17; 18; 19]. A single variable of the equivalent factor can be used to calculate the battery consumption or recovered energy equivalent to the fuel consumption, and the optimal solution of each instant can be solved by minimizing the equivalent fuel. Therefore, some researchers have combined DP and ECMS. For example, [20] uses the DP algorithm to optimize the vehicle operating parameters (under the best fuel economy in the entire cycle), uses these parameters to solve the equivalent factor, and selects the best equivalent factor according to the different initial conditions of the car. However, the equivalent factor obtained by this method is fixed and cannot be adjusted in real time according to practical working conditions, so the robustness and fuel economy are poor. Moreover, [21] uses DP to match the equivalent factors, construct the best equivalent factor map diagram under different SOC, and adjust the equivalent factor in real time, according to the current SOC of the vehicle. However, this method only considers the influence of SOC on the equivalent factor and does not consider the driving conditions, which is too limited. In [22; 23; 24; 25; 26], the authors proposed the approximate equivalent fuel consumption minimization strategy (A-ECMS) based on the approximate minimum principle (A-PMP). The motor output torque is constrained in a set of five optional values, which greatly simplifies the calculation cost, and its reliability has been proved in an actual vehicle experiment. Based on this, this study nests the A-ECMS into DP to form an improved dynamic programming algorithm with an equivalent factor as the single control variable. Firstly, the A-ECMS model is established, where the output torque of the motor is constrained to a limited number of optional values by numerically fitting the efficiency of the engine and the motor. The instantaneous energy distribution is obtained by A-ECMS of different equivalent factors at each instant, and the SOC variation under the energy distribution is calculated. Then, the DP global optimization model is established, in which the equivalent factor is the control variable, the battery SOC is the state variable, and the cumulative fuel consumption is the global optimization goal. Therefore, the DP-A-ECMS algorithm is formed. In order to verify the algorithm proposed in this paper, a PHEV computer simulation model was built to simulate under different driving conditions, and the optimal equivalent factor sequence was obtained. Finally, in order to realize the online application of DP-A-ECMS, a BP neural network was used to extract the nonlinear correlation between the optimal equivalent factor and real-time operating conditions, and the optimal equivalent factor sequence was transformed from a set of time-varying sequences to a set of state-varying sequences. By doing this, an online control strategy could be established.