An energy management method for fuel cell vehicles based on the equivalent consumption minimization strategy

By adopting a combination method of equivalent consumption minimum strategy and LSTM model in fuel cell vehicles, the power distribution of fuel cells and power cells is optimized in real time, and the problem that energy management methods in the prior art are difficult to achieve real-time optimal solutions, improving the economy and energy-saving potential of the automobile.

CN114771293BActive Publication Date: 2025-06-17YANSHAN UNIV
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Patent Information

Application Number
CN202210359338.0
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-04-06
Publication Date
2025-06-17
Estimated Expiration
2042-04-06

AI Technical Summary

Technical Problem

The existing fuel cell vehicle energy management methods are difficult to achieve global optimal solutions in real-time control, and at the same time, the calculation is large and cannot be applied in real-time.

Method used

The online energy management method based on the equivalent consumption minimum strategy (ECMS) is adopted, combined with the Pontriajin minimum value principle and the LSTM model, the optimal comorphosis variable and vehicle state information are predicted in real time, and the power distribution between the fuel cell and the power cell is optimized.

Benefits of technology

Energy management can be applied in real time while ensuring the optimization results are close to optimal, improving the overall economic and energy-saving potential of fuel cell vehicles.

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Abstract

The present invention discloses an online energy management method for fuel cell vehicles based on the equivalent consumption minimum strategy, which relates to the field of new energy vehicles. This method includes an offline part and an online part. The offline part includes: obtaining vehicle driving condition data; establishing a fuel cell hybrid vehicle model; based on the Pontryagin minimum principle, establishing a Hamiltonian function from the objective function and obtaining the optimal solution of historical condition data using the shooting method; using the obtained optimal solution as a sample set to train an LSTM model. The online part includes: online predicting the future short-term speed of the vehicle based on networked information; obtaining the optimal co-state variable in real time using the trained LSTM model; obtaining the optimal equivalent factor according to the relationship between PMP and ECMS; and solving the optimal power distribution of the fuel cell vehicle in real time through ECMS. The results of the present invention have good global optimality, high computational efficiency, and good real-time performance; comprehensively consider the influence of vehicle historical information and future information, and improve fuel economy and the robustness of the management strategy.
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Description

Technical Field

[0001] The present invention relates to the technical field of new energy vehicles, and particularly to an online energy management method for fuel cell vehicles based on the equivalent consumption minimum strategy (ECMS). Background Art

[0002] In recent years, with the rapid growth of the number of motor vehicles, problems such as air pollution and energy crisis have become increasingly serious. New energy vehicles such as hybrid electric vehicles, battery electric vehicles, and fuel cell vehicles have received more and more attention. Among them, fuel cell hybrid vehicles (FCHVs) have received more and more attention from automobile manufacturers due to their advantages such as high efficiency, clean and pollution-free, and long driving range.

[0003] Energy management is one of the key technologies for fuel cell vehicles. The current energy management strategies (EMS) include strategies based on global optimization algorithms such as dynamic programming (DP) and Pontryagin's minimum principle (PMP). Although this kind of strategy can obtain the global optimal solution, it needs to obtain global prior information, and the calculation amount is large, so it cannot be applied in real time.

[0004] The equivalent consumption minimum strategy (ECMS) does not require prior information, can be solved in real time, and can be applied to real-time control. However, this kind of strategy can only obtain a local optimal solution, and its optimality cannot be guaranteed.

[0005] Therefore, it is necessary to design a new fuel cell energy management method to meet the requirements of fuel cell vehicles for real-time performance and optimality. At the same time, with the development of intelligent network connection technology, it has become easier to obtain data such as the driving conditions of the vehicle itself and external information such as road traffic information. How to use artificial intelligence technology to mine effective information from the huge amount of data and apply it to the fuel cell energy management method to make the performance of the energy management method better is also a problem worthy of consideration. Summary of the Invention

[0006] In view of this, the purpose of the present invention is to provide an online energy management method for fuel cell vehicles based on the equivalent consumption minimum strategy (ECMS), which can be applied in real time while ensuring that the optimization result is close to optimality, and improve the overall economy of fuel cell vehicles. At the same time, mine the effective information of traffic data in the networked environment to further improve the optimization and robustness of the energy management strategy.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] An online energy management method for a fuel cell vehicle based on an equivalent consumption minimum strategy, specifically comprising the following steps:

[0009] Step 1: Obtain multi-dimensional road condition information of the fuel cell hybrid vehicle during historical driving;

[0010] Step 2: Based on the power system structure of the fuel cell hybrid vehicle, establish a vehicle power system model for the fuel cell hybrid vehicle; the vehicle power system model for the fuel cell hybrid vehicle includes: a vehicle dynamics model, a fuel cell hydrogen consumption model and efficiency model, and a power battery model;

[0011] Step 3: Taking the total hydrogen consumption as the objective, establish an objective function, and determine the constraint conditions of the state variables and control variables; based on the Pontryagin minimum principle, establish a Hamiltonian function from the objective function, and use the shooting method to solve the multi-dimensional road condition information of the fuel cell hybrid vehicle obtained in Step 1 during historical driving to obtain the optimal co-state variable and its corresponding vehicle state information, and the corresponding vehicle state information includes: vehicle speed, SOC trajectory, and demand power;

[0012] Step 4: Use the optimal co-state variable and its corresponding vehicle state information obtained in Step 3 as a sample set to train an LSTM-based optimal co-state variable prediction model;

[0013] Step 5: Use the road traffic information obtained in Step 1 to online predict the vehicle speed of the vehicle in the next 1s, 2s, 3s, 4s, and 5s through an LSTM-based vehicle speed prediction model; the LSTM-based vehicle speed prediction model uses the road traffic information obtained in Step 1 as the model input and the vehicle speed of the vehicle as the model output;

[0014] Step 6: Use the trained LSTM-based optimal co-state variable prediction model in Step 4 to online and real-time predict the optimal co-state variable;

[0015] Step 7: According to the relationship between the Pontryagin minimum principle and the equivalent consumption minimum strategy, obtain the optimal equivalent factor from the optimal co-state variable obtained in Step 6; the relationship between the Pontryagin minimum principle and the equivalent consumption minimum strategy is:

[0016]

[0017] In the formula, S(t) is the adaptive equivalent factor, is the lower calorific value of hydrogen, U OC is the open-circuit voltage of the power battery, Q bat is the power battery capacity, and λ(t) is the co-state variable;

[0018] Step 8: Based on the equivalent consumption minimization strategy, with the goal of minimizing the real-time total energy consumption, establish an objective function, where the objective function is:

[0019]

[0020] In the formula, is the equivalent hydrogen consumption; is the change rate of the state of charge of the power battery; is the hydrogen consumption rate;

[0021] Apply the optimal equivalent factor obtained in Step 7 to the objective function, and find the optimal solution that minimizes the objective function, which is the optimal power distribution between the fuel cell and the power battery.

[0022] Furthermore, the multi-dimensional road condition information includes: vehicle speed, acceleration, the speed of the vehicle in front, the acceleration of the vehicle in front, road gradient, and traffic light information passed through during the route.

[0023] Furthermore, the vehicle dynamics model is:

[0024]

[0025] In the formula, P dem is the required power, v h is the vehicle speed of this vehicle, m is the vehicle weight, ρ is the air density, A is the vehicle frontal area, C d is the air resistance coefficient, g is the acceleration due to gravity, μ r is the rolling resistance coefficient, θ is the road gradient, η m is the motor efficiency;

[0026] P dem = P fc + P bat ;

[0027] In the formula, P fc is the fuel cell stack power, P bat is the power battery power.

[0028] Furthermore, the fuel cell hydrogen consumption model is:

[0029]

[0030] In the formula, is the hydrogen consumption rate, N fc is the number of fuel cell monomers in the fuel cell stack, is the molar mass of hydrogen, I fc is the fuel cell current, n e is the number of electrons transferred in the electrochemical reaction, and F is the Faraday constant;

[0031] The fuel cell efficiency model is as follows:

[0032]

[0033] where η fc is the fuel cell efficiency, and

[0034] is the lower heating value of hydrogen.

[0035]

[0036] where I bat is the power battery current, U OC is the open-circuit voltage of the power battery, and R bat is the internal resistance of the power battery;

[0037]

[0038] where is the rate of change of the state of charge of the power battery, and Q bat is the capacity of the power battery.

[0039] Furthermore, taking the total hydrogen consumption as the objective function and based on the Pontryagin minimum principle, the Hamiltonian function is established as follows:

[0040]

[0041] where H(SOC(t), P fc (t), λ(t)) is the value of the Hamiltonian function, and λ(t) is the co-state variable.

[0042] Furthermore, taking the optimal co-state variable obtained in step 3 and the corresponding vehicle state information as the sample set to train the optimal co-state variable prediction model based on LSTM, including:

[0043] Taking the vehicle speed, SOC trajectory, and required power obtained in step 3 as the input variables of the optimal co-state variable prediction model based on LSTM, and taking the optimal co-state variable as the output variable of the optimal co-state variable prediction model based on LSTM;

[0044] Constructing the network structure of the optimal co-state variable prediction model based on LSTM, where the network structure includes an input layer, an LSTM layer, and an output layer, and determining the number of neurons in each layer of the network;

[0045] Normalizing the input variables and output variables, and performing offline training on the optimal co-state variable prediction model based on LSTM to obtain the co-state variable prediction model.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] (1) The present invention designs an energy management method for fuel cell vehicles by utilizing the relationship between PMP and ECMS. The optimization result is close to the global optimum, and at the same time, it has high computational efficiency, good real-time performance, and can be used for real-time control.

[0048] (2) The present invention uses the LSTM model to predict the optimal co-state variable, considering the problem that the predicted variable is highly correlated with the time series, and the prediction result is more accurate.

[0049] (3) When predicting the co-state variable, the present invention considers the vehicle speed in the short term in the future, taking into account the impact of future information on the optimization result, and further enhancing the energy-saving potential of fuel cell vehicles.

[0050] (4) The present invention uses artificial intelligence methods to extract effective information from the huge traffic data in the connected environment and applies it to the proposed energy management method, improving the global optimality and robustness of the energy management method, and providing a new idea for the research of energy management methods based on the connected environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0052] Figure 1 is a flowchart of an energy management method for a fuel cell vehicle based on the equivalent consumption minimization strategy in an embodiment of the present invention;

[0053] Figure 2 is a structural diagram of the power system of a fuel cell vehicle in an embodiment of the present invention;

[0054] Figure 3 is a schematic structural diagram of an optimal co-state variable prediction model based on LSTM in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0055] In order to enable those skilled in the art to better understand the solutions of the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0056] It should be noted that the terms "first", "second", etc. in the description, claims and above-mentioned drawings of the present invention are used to distinguish similar objects, and do not necessarily have to be used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances, so that the embodiments of the present invention described here can be implemented in an order other than those illustrated or described here. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0057] As Figure 1 shown, the embodiment of the present invention provides a fuel cell vehicle energy management method based on the equivalent consumption minimum strategy, which specifically includes the following steps:

[0058] Step 1, obtain multi-dimensional road condition information of the fuel cell hybrid vehicle during historical driving;

[0059] Among them, the multi-dimensional road condition information specifically includes: the vehicle state information, including: vehicle speed, vehicle acceleration and other information; the road traffic information, including: the speed of the vehicle in front, the acceleration of the vehicle in front, the road slope, the timing and phase information of the traffic lights passed through during the route, etc.

[0060] Step 2, based on the power system structure of the fuel cell hybrid vehicle, establish a vehicle power system model of the fuel cell vehicle;

[0061] As Figure 2 shown, the power system structure of the fuel cell hybrid vehicle includes: a fuel cell system, an auxiliary system, a DC / DC bidirectional converter, a power battery system, a vehicle controller, an inverter, a motor controller and a motor. Among them, the fuel cell system, the DC / DC bidirectional converter, the power battery system, the inverter and the motor controller all perform bidirectional signal transmission and reception with the vehicle controller. The energy is provided by the fuel supply and is transmitted and flows among the fuel cell system, the auxiliary system, the DC / DC bidirectional converter, the power battery system, the inverter, the motor controller and the motor. The present invention makes the energy consumption of the fuel cell hybrid vehicle minimum by reasonably allocating the power between the fuel cell and the power battery.

[0062] Establishing a vehicle power system model of the fuel cell vehicle includes establishing a vehicle dynamics model, a fuel cell hydrogen consumption model, an efficiency model and a power battery model. Specifically, it includes the following steps:

[0063] Step 2.1, build the vehicle dynamics model as:

[0064]

[0065] Wherein, P dem is the required power, v h is the vehicle speed of this vehicle, m is the vehicle weight, ρ is the air density, A is the vehicle frontal area, C d is the air drag coefficient, g is the acceleration due to gravity, μ r is the rolling resistance coefficient, θ is the road slope, η m is the motor efficiency.

[0066] P dem = P fc + P bat ;

[0067] Wherein, P fc is the fuel cell stack power, P bat is the power battery power.

[0068] Step 2.2: Build the fuel cell hydrogen consumption model and efficiency model respectively as:

[0069]

[0070] Wherein, is the hydrogen consumption rate, N fc is the number of fuel cell monomers in the fuel cell stack, is the molar mass of hydrogen, I fc is the fuel cell current, n e is the number of electrons transferred in the electrochemical reaction, F is the Faraday constant.

[0071]

[0072] Wherein, η fc is the fuel cell efficiency, is the lower heating value of hydrogen.

[0073] Step 2.3: Build the power battery model as:

[0074]

[0075] Wherein, I bat is the power battery current, U OC is the open-circuit voltage of the power battery, R bat is the internal resistance of the power battery.

[0076]

[0077] Wherein, is the rate of change of the state of charge of the power battery, Q bat is the capacity of the power battery.

[0078] Step 3: Based on the Pontryagin minimum principle, establish the Hamiltonian function from the objective function, and solve the historical data obtained in Step 1 using the shooting method, that is, continuously try different initial co-state values to make the result approach the optimum, and obtain the optimal co-state variables;

[0079] Co-state variables are auxiliary variables used in the solution of the Pontryagin minimum principle.

[0080] Specifically, it includes the following steps:

[0081] Step 3.1: Taking the total hydrogen consumption as the objective, establish the objective function as:

[0082]

[0083] The constraint conditions for the state variables and control variables are:

[0084]

[0085] Step 3.2: Based on the Pontryagin principle, the Hamiltonian function established from the objective function is:

[0086]

[0087] In the formula, H(SOC(t), P fc (t), λt()) is the value of the Hamiltonian function, and λ(t) is the co-state variable.

[0088] Step 3.3: Use the shooting method to find the optimal solution for the working conditions obtained in Step 1, and obtain the optimal co-state variables and the corresponding vehicle state information, including: vehicle speed, SOC trajectory, and required power.

[0089] Step 4: Use the optimal co-state variables obtained in Step 3 and the state information corresponding to the optimal co-state variables as a sample set to train the LSTM (Long Short-Term Memory) model;

[0090] Specifically, it includes the following steps:

[0091] Step 4.1: Use the vehicle speed, SOC trajectory, and required power obtained in Step 3 as the input of the LSTM, and use the optimal co-state variables as the output of the LSTM;

[0092] Step 4.2: As Figure 3As shown in the figure, an LSTM network structure is constructed, including an input layer, an LSTM layer, and an output layer, and the number of neurons in each layer of the network is determined. Among them, the number of neurons in the input layer is 3, the LSTM layer has two layers, and the number of neurons in each layer is 30 and 10 respectively, and the number of neurons in the output layer is 1.

[0093] Step 4.3: Normalize the input and output quantities, and perform offline training on the LSTM model to obtain a co-state variable prediction model.

[0094] Step 5: Use the road traffic information obtained in Step 1 to online predict the vehicle speed of the vehicle in the next 1s, 2s, 3s, 4s, and 5s.

[0095] Step 6: Take the real-time state information of the vehicle, including the SOC value, the required power, and the online predicted future speed of the vehicle, as the input and feed it to the trained LSTM model to online predict the optimal co-state variable.

[0096] Step 7: Use the predicted optimal co-state variable to calculate the adaptive equivalent factor in real time according to the relationship between the Pontryagin minimum principle (PMP) and the equivalent consumption minimum strategy (ECMS). The relationship is as follows:

[0097]

[0098] In the formula, S(t) is the adaptive equivalent factor.

[0099] Step 8: Based on ECMS, with the real-time total energy consumption as the goal, establish an objective function, and feed the optimal equivalent factor obtained in Step 7 to ECMS to obtain the optimal power distribution between the fuel cell and the power battery. Specifically, it includes the following steps:

[0100] Step 8.1: Based on ECMS, with the real-time total energy consumption as the goal, establish an objective function:

[0101]

[0102] In the formula, is the equivalent hydrogen consumption.

[0103] Step 8.2: Feed the obtained adaptive equivalent factor to ECMS, and find the optimal solution to obtain the optimal power distribution between the fuel cell and the power battery.

[0104] Among them, Steps 1 to 4 can be performed offline, and Steps 5 to 8 are performed online.

[0105] An energy management method for a fuel cell vehicle based on the equivalent consumption minimum strategy in the embodiments of the present invention has the following beneficial effects:

[0106] (1) The present invention designs an energy management method for fuel cell vehicles by utilizing the relationship between PMP and ECMS. The optimization result is close to the global optimum, while having high computational efficiency and good real-time performance, and can be used for real-time control.

[0107] (2) The present invention uses an LSTM model to predict the optimal co-state variable, considering the problem that the predicted variable is highly correlated with the time series, and the prediction result is more accurate.

[0108] (3) When predicting the co-state variable, the present invention takes into account the vehicle speed in the short term in the future, considering the influence of future information on the optimization result, and further enhancing the energy-saving potential of fuel cell vehicles.

[0109] (4) The present invention uses artificial intelligence methods to extract effective information from the huge traffic data in the connected environment and applies it to the proposed energy management method, enhancing the global optimality and robustness of the energy management method, and providing a new idea for the research of energy management methods based on the connected environment.

[0110] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An online energy management method for fuel cell vehicles based on the equivalent consumption minimum strategy, characterized in that, Including: Step 1: Obtain multi-dimensional road condition information during the historical driving process of a fuel cell hybrid vehicle; Step 2: Based on the power system structure of the fuel cell hybrid vehicle, establish a vehicle power system model for the fuel cell hybrid vehicle; the vehicle power system model for the fuel cell hybrid vehicle includes: a vehicle dynamics model, a fuel cell hydrogen consumption model, an efficiency model, and a power battery model; Step 3: Taking the total hydrogen consumption as the objective, establish an objective function, and determine the constraint conditions for the state variables and control variables; based on the Pontryagin minimum principle, establish a Hamiltonian function from the objective function, and use the shooting method to solve the multi-dimensional road condition information of the fuel cell hybrid vehicle obtained in Step 1 during the historical driving process to obtain the optimal co-state variables and their corresponding vehicle state information, and the corresponding vehicle state information includes: vehicle speed, SOC trajectory, and demand power; Step 4: Use the optimal co-state variables and their corresponding vehicle state information obtained in Step 3 as a sample set to train an LSTM-based optimal co-state variable prediction model; Step 5: Use the road traffic information obtained in Step 1 to online predict the vehicle speed of the vehicle in the next 1s, 2s, 3s, 4s, and 5s through an LSTM-based vehicle speed prediction model; the LSTM-based vehicle speed prediction model uses the road traffic information obtained in Step 1 as the model input and the vehicle speed of the vehicle as the model output; Step 6: Use the trained LSTM-based optimal co-state variable prediction model in Step 4 to online and real-time predict the optimal co-state variables; Step 7: According to the relationship between the Pontryagin minimum principle and the equivalent consumption minimum strategy, obtain the optimal equivalent factor from the optimal co-state variables obtained in Step 6; the relationship between the Pontryagin minimum principle and the equivalent consumption minimum strategy is: where \(S(t)\) is the adaptive equivalent factor, is the lower heating value of hydrogen, \(U\) OC is the open-circuit voltage of the power battery, \(Q\) bat is the capacity of the power battery, and \(\lambda(t)\) is the co-state variable; Step 8: Based on the equivalent consumption minimum strategy, taking the minimum of the real-time total energy consumption as the objective, establish an objective function, and the objective function is: In the formula, is the equivalent hydrogen consumption; is the change rate of the state of charge of the power battery; is the hydrogen consumption rate; Apply the optimal equivalent factor obtained in Step 7 to the objective function, and obtain the optimal solution that minimizes the objective function as the optimal power distribution between the fuel cell and the power battery.

2. The online energy management method for fuel cell vehicles based on the equivalent consumption minimum strategy according to claim 1, characterized in that, The multi-dimensional road condition information includes: vehicle speed, acceleration, the speed of the vehicle in front, the acceleration of the vehicle in front, road slope, and traffic light information passed through during the route.

3. The online energy management method for fuel cell vehicles based on the equivalent consumption minimum strategy according to claim 1, characterized in that, The vehicle dynamics model is: Where, P dem is the required power, v h is the vehicle speed, m is the vehicle weight, ρ is the air density, A is the frontal area of the vehicle, C d is the air drag coefficient, g is the acceleration due to gravity, μ r is the rolling resistance coefficient, θ is the road gradient, η m is the motor efficiency; P dem = P fc + P bat ; Wherein, P fc is the power of the fuel cell stack, and P bat is the power of the power battery.

4. The online energy management method for fuel cell vehicles based on the equivalent consumption minimum strategy according to claim 3, characterized in that, The fuel cell hydrogen consumption model is: Wherein, is the hydrogen consumption rate, N fc is the number of fuel cell monomers in the fuel cell stack, is the molar mass of hydrogen, I fc is the fuel cell current, n e is the number of electrons transferred in the electrochemical reaction, and F is the Faraday constant; The fuel cell efficiency model is: where η fc is the fuel cell efficiency, and is the low heating value of hydrogen.

5. The online energy management method for fuel cell vehicles based on the equivalent consumption minimum strategy according to claim 3, characterized in that, The power battery model is: Where, I bat is the current of the power battery, U OC is the open-circuit voltage of the power battery, and R bat is the internal resistance of the power battery; In the formula, is the change rate of the state of charge of the power battery, and Q bat is the capacity of the power battery.

6. A method for online energy management of a fuel cell vehicle based on an equivalent consumption minimization strategy according to claim 1, wherein, Taking the total hydrogen consumption as the objective function and based on the Pontryagin minimum principle, the established Hamiltonian function is: where H(SOC(t), P fc (t), λt()) is the value of the Hamiltonian function, and λ(t) is the co-state variable.

7. A method for online energy management of a fuel cell vehicle based on an equivalent consumption minimization strategy according to claim 1, wherein, Using the optimal co-state variables and their corresponding vehicle state information obtained in Step 3 as a sample set to train an LSTM-based optimal co-state variable prediction model includes: Taking the vehicle speed, SOC trajectory, and demand power obtained in Step 3 as the input variables of the LSTM-based optimal co-state variable prediction model, and taking the optimal co-state variables as the output variables of the LSTM-based optimal co-state variable prediction model; Construct the network structure of the LSTM-based optimal co-state variable prediction model, and the network structure includes an input layer, an LSTM layer, and an output layer, and determine the number of neurons in each layer of the network; Normalize the input and output quantities, and perform offline training on the optimal co-state variable prediction model based on LSTM to obtain the co-state variable prediction model.

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