A connected electric vehicle signal light intersection robust vehicle speed control method

Abstract

This invention discloses a robust speed control method for connected electric vehicles at traffic light intersections, belonging to the field of intelligent traffic control technology. The method first establishes an electric vehicle simulation model including the vehicle's longitudinal resistance, drive motor, and the RC equivalent circuit of the power battery. Then, it constructs a deterministic traffic light timing scenario model to characterize spatiotemporal constraints. Subsequently, it builds a spatial domain MPC speed planning framework, defines state and control variables and transition relationships, constructs a comprehensive objective function for battery charge consumption and lifespan degradation, approximates and simplifies the battery current, and sets multi-dimensional constraints. By establishing a truncated normally distributed random error model for traffic light timing, it employs a multi-scenario weighted random scenario MPC strategy for optimization, performing rolling optimization with a preset period and executing only the first control variable. This invention improves vehicle traffic efficiency, energy efficiency, and driving smoothness under uncertain traffic light timing scenarios, delays battery degradation, and achieves a multi-objective balance of safety, economy, and traffic efficiency.

Description

Technical Field

[0001] This invention relates to the field of intelligent traffic control technology, and in particular to a robust speed control method for connected electric vehicles at traffic light intersections. Background Technology

[0002] In current technologies, with the increasing severity of the energy crisis and environmental pollution, electric vehicles (EVs), with their zero emissions and high energy efficiency, have become an important direction for energy conservation and emission reduction in the transportation sector. However, in urban conditions, EVs still face problems such as short driving range and energy consumption significantly affected by driving behavior. Especially in areas with dense traffic lights, frequent starts, stops, accelerations, and decelerations lead to insufficient energy recovery, significantly reducing overall vehicle energy efficiency. Eco-driving is an effective way to achieve energy conservation and emission reduction by optimizing vehicle speed trajectories. Based on this, researching online-implementable energy-saving speed planning and control methods for traffic light scenarios is of great significance for improving the driving range of EVs and urban traffic energy efficiency.

[0003] Eco-driving strategies based on deterministic SPaT (Speed-Patient Response Time) have long been a mature technical approach, guiding vehicles to pass through intersections at appropriate speeds, thereby reducing stopping, waiting, and rapid acceleration.

[0004] However, most existing studies assume that SPaT information is completely deterministic and reliable, failing to adequately consider the uncertainties in traffic light phase and timing caused by factors such as communication delays and prediction errors. Some studies introduce probabilistic models combined with stochastic optimization or robust control methods to address these problems. For example, they predict the probability of a green light by using historical and real-time phase data and solve for the speed trajectory that maximizes the probability of passing through a green light; or they define the effective red light duration as a random variable and use data-driven chance constraint methods to construct robust optimization problems under unknown real distribution conditions, thereby improving the robustness of eco-driving under uncertain signal timing; some solutions also provide quasi-optimal rules for multi-signal passage in free-flow environments to replace numerically optimal solutions and meet real-time application requirements. However, these methods mostly focus on improving the probability of passage and do not delve into the trade-off mechanism between control robustness and real-time performance in scenarios with multiple uncertainties.

[0005] In addition, most of the research focuses on gasoline or hybrid vehicles, while there is a lack of research on robust speed optimization for pure electric vehicles in traffic light scenarios, especially in the systematic modeling of motor-battery coupling characteristics and battery life degradation. Summary of the Invention

[0006] The purpose of this invention is to provide a robust speed control method for connected electric vehicles at traffic light intersections. Targeting connected pure electric vehicles, it constructs a speed planning problem considering the spatiotemporal window constraints of traffic lights within a spatial domain MPC framework. Furthermore, it proposes a robust enhancement strategy for stochastic scenarios to address phase timing random prediction errors. The performance of the strategy is compared and evaluated through multi-intersection Monte Carlo simulations. This approach balances traffic safety, energy efficiency, and driving smoothness under uncertain signal timing conditions, providing a real-time robust planning approach for the ecological driving control of connected electric vehicles.

[0007] To achieve the above objectives, the present invention provides a robust speed control method for connected electric vehicles at traffic light intersections, comprising the following steps: S1. Establish an electric vehicle simulation model, which includes a vehicle longitudinal resistance model, a drive motor model, and a power battery RC equivalent circuit model, respectively characterizing the vehicle driving resistance characteristics, drive system power consumption characteristics, and battery dynamic charging and discharging and state of charge change characteristics. S2. Establish a deterministic traffic light scenario model. For roads with several traffic light-controlled intersections, define the timing parameters of each traffic light, solve the predicted green light time window and predicted red light time window of each traffic light within a specified period, and characterize the spatiotemporal constraints of vehicle passage. S3. Constructing a spatial domain model predictive control (MPC) speed planning framework: Define the state transition equation of the vehicle's nominal kinetic energy in the spatial domain, select system state variables and control variables and establish their state transition relationship, construct an objective function with the comprehensive goal of reducing battery charge consumption and slowing down battery life degradation, and further complete the construction of the spatial domain model predictive control (MPC) speed planning framework; perform nonlinear least squares regression approximation on the battery current in the objective function to reduce the difficulty of solving the problem. S4. Establish a random prediction error model for traffic light phase timing. Assume that the random prediction error for traffic light phase timing follows a normal distribution with a mean of zero. Define the timing prediction error for each traffic light. The timing prediction errors for traffic lights at all intersections share a random offset. Solve for the actual green light time window of the traffic lights after considering the error. S5. Based on the traffic light phase timing random prediction error model, a multi-scenario weighted random scenario MPC strategy is adopted to perform robust speed optimization control on connected electric vehicles. S6. The CasADi solver is used to solve the speed planning optimization problem of MPC strategy in random scenarios. The performance of the robust vehicle speed control strategy is verified by Monte Carlo simulation. During the optimization process, random timing offsets that follow a truncated normal distribution are generated independently. The real green light window of the traffic light is constructed, and the red light violation rate, energy consumption, average acceleration and deceleration, and charge throughput are selected as performance evaluation indicators.

[0008] Preferably, in S1, the vehicle resistance model is specifically represented as follows: (1); in, a To accelerate the vehicle; m For the overall vehicle weight; F out For vehicle control force; F res For vehicle driving resistance; F res Includes rolling resistance F roll Ramp resistance F grad air resistance F drag ; The expression for vehicle resistance is: (2); in, g It is the acceleration due to gravity; f This is the rolling resistance coefficient; The road slope angle; C D This refers to the air drag coefficient; A f The vehicle's frontal area; ρ air density; v The driving speed; The drive motor model is set to have a uniform distribution of driving force between the left and right wheels, and the total power consumption of the drive system is [not specified]. P prop Represented as: (3); in, T m and ω M These are the motor's output torque and angular velocity, respectively. Motor efficiency; superscript λ This indicates the motor's operating state; λ=-1 corresponds to the driving condition, and λ=1 corresponds to the braking energy recovery condition. In the aforementioned RC equivalent circuit model of the power battery, the battery output current... I b The calculation formula is as follows: (4); in, U oc This is the battery open-circuit voltage; R bat This refers to the battery's internal resistance. P bat= P prop The battery output power is the motor torque. T m With vehicle kinetic energy E v The function; The instantaneous rate of change of the battery's state of charge (SOC) is directly determined by the battery current, and its expression is: (5); in, Q bat This refers to the battery's rated capacity.

[0009] Preferably, S2 specifically includes the following: S21, Set the length to be L The road has I There are 1 traffic light-controlled intersections, of which the 1st i The location of each intersection is recorded as follows: Each traffic light follows a fixed timing scheme and operates on a periodic basis. C i It operates independently, with each signal cycle consisting of a fixed alternation of green and red light phases; S22, Definition of the i The timing parameters of each traffic light within a cycle include the start time of the green light phase. The green light lasts for 1 hour. Red light duration ; S23. Predicting the green light time window and red light time window: For the n The first cycle, the first i The predicted green light time window for each traffic light is: (6); Accordingly, the predicted red light time window is: (7).

[0010] Preferably, in S3, the construction of the spatial domain model predictive control (MPC) velocity planning framework includes the following steps: S31. Define the nominal kinetic energy of a vehicle in the spatial domain. E v for v 2 / 2 state transition equation: (8); S32. Select the system state variables and control variables as follows: (9); in, t For vehicle passage time; T b For mechanical braking torque; S33, Divide the spatial domain by step size Discretize, the discrete nodes are ;in k For discrete indexes in the distance domain, s p The vehicle's current location; S34. Define the following state transition relationship between system state variables and control variables: (10); (11); Among them, in equation (10) r The radius of the wheel; S35. The energy consumption of electric vehicles is related to the State of Charge (SOC) and depends on the instantaneous current. Furthermore, battery degradation, according to the current throughput model, depends on the absolute value of the instantaneous current. Therefore, the objective function is constructed as follows: (12); in, ω ={α} represents the system disturbance, i.e., the road slope; W d This is a weighting coefficient used to weigh the energy consumption cost against the battery life degradation cost; S36. Construct a spatial domain model predictive control (MPC) velocity planning framework: (13); in, E v,min , E v,max These represent the lower and upper bounds of kinetic energy under road speed limits; t ( k () represents the cumulative travel time of vehicles to spatial nodes. t des ( s k ) for in position s k The expected arrival time at the location; T m ( k ) represents the index in the spatial domain. k The torque control quantity of the drive motor at the location. T m,min , T m,max These are the upper and lower limits of the motor's permissible output torque; T b,min This is the lower limit of the mechanical braking torque;a min , a max These are the lower and upper limits of acceleration, respectively. t ( L i () represents the time of arrival at the intersection. That is, predicting the green light time window; The above inequalities include road speed limits, traffic efficiency, external characteristics of the drive motor, acceleration constraints, and safety constraints; Equation (13a) represents the interval constraint on kinetic energy; Equation (13b) is used to limit the vehicle arrival time to not exceed the expected value to ensure traffic efficiency; Equations (13c) and (13d) represent the constraints on the range of drive motor torque and mechanical braking torque; Equation (13e) limits the acceleration and deceleration amplitude to improve ride comfort and driving safety; Equation (13f) requires the vehicle arrival time to fall within the predicted green light time window to avoid running red lights.

[0011] Preferably, in S3, the nonlinear least squares regression approximation of the battery current in the objective function to reduce the difficulty of solving the problem specifically includes the following: S351, will I b Approximately expressed as kinetic energy E v and motor torque T m Fitting function: (14); in, This is an approximation of the battery current. b 1~ b 6 represents the fitting coefficient; S352. Substitute the fitted function into the equation and let each charge be a distance from the set point. The objective function (12) is approximated as: (15); S353, Introducing intermediate variables And impose constraints to handle absolute values: (16); S354, due to At the optimal solution, there is If true, the final objective function solution is transformed into: (17).

[0012] Preferably, the specific process in S4 is as follows: S41. The random prediction error for traffic light phase timing is assumed to approximately follow a normal distribution with a mean of zero in the time domain. Therefore, the first...i Each traffic light at a certain time t Timing prediction error Represented as: (18); in, Let be the standard deviation. To ensure the reasonableness of the error, the error distribution is set to be truncated within the interval [-2, 2] seconds, i.e. =2 seconds; S42. This error affects the actual green light time window of the traffic light. Relative to the prediction time window An overall offset occurred, but the traffic light cycle... C i Green light duration and red light duration All settings remain unchanged. To simplify the analysis and reflect the typical characteristics of regional signal coordination, the prediction error of traffic light timing at all intersections is set to follow a random offset. ξ ,Right now: (19); in, (20); S43. After considering the error, the first... The actual green light time window for each traffic light is represented as follows: (twenty one).

[0013] Preferably, S5 specifically includes the following: S51. The optimization objective of multi-scenario problems is transformed into minimizing the expected cost under all scenarios: (twenty two); In the formula: For the scene j The objective function value is as follows; w j The weights for this scenario satisfy... ; S52. Introduce unexpected constraints: require that at the current control moment, all scenarios adopt the same initial control quantity. u (0); The system only executes this initial control step, and the remaining predictive control variables are only used for rolling updates; S53. Generate random scene MPC and calculate the weight allocation error. ξ The probability distribution is: the error interval, which follows a standard normal distribution and is truncated to [-2, 2], is discretized at equal intervals as follows: S Each representative scenario j weight w j Equal to the probability mass within the neighborhood interval of this node: (twenty three); in,[ a j ,b j ] is the first j The neighborhood interval of each point This is the cumulative distribution function of the standard normal distribution.

[0014] The present invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the robust speed control method for connected electric vehicles at traffic light intersections.

[0015] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the robust speed control method for connected electric vehicles at traffic light intersections.

[0016] Therefore, this invention adopts the above-mentioned robust speed control method for connected electric vehicles at traffic light intersections and proposes a stochastic scenario MPC strategy to achieve the optimal balance of multiple objectives in speed control of connected electric vehicles at traffic light intersections. The risk of running red lights is extremely low. It breaks through the excessive constraints of conservative MPC with almost no sacrifice in safety, improves traffic efficiency, reduces energy consumption, and suppresses battery life degradation. At the same time, it significantly improves driving smoothness, has strong robustness to random errors in traffic light timing, adapts to different urban road conditions, and is more in line with actual application needs.

[0017] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0018] Figure 1 This is the model predictive control principle of this invention embodiment; Figure 2 This is a comparison result between the fitted surface and the sampling points in an embodiment of the present invention; Figure 3 This is the signal light timing prediction error distribution according to an embodiment of the present invention; Figure 4 This is the simulation test route of an embodiment of the present invention; Figure 5 This is a comparison of travel time and travel distance in scenario one of the embodiments of the present invention; Figure 6 This is a comparison of motor torque response in scenario one of the embodiments of the present invention; Figure 7 This is a scenario 1 of the present invention, showing the distribution of motor operating points; Figure 8This is a comparison of the speed planning results in scenario one of the embodiments of the present invention; Figure 9 This is a comparison of travel time and travel distance in scenario two of this embodiment of the invention; Figure 10 This is a comparison of motor torque response in scenario two of the embodiments of the present invention; Figure 11 This is the distribution of motor operating points in scenario two of this embodiment of the invention; Figure 12 This is a comparison of the speed planning results in scenario two of the embodiments of the present invention; Figure 13 This is the Monte Carlo statistical result of scenario one in this embodiment of the invention; Figure 14 This is the Monte Carlo statistical result of scenario two in this embodiment of the invention; Figure 15 This is a flowchart of the method according to an embodiment of the present invention. Detailed Implementation

[0019] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0020] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0021] Example 1 This invention provides a robust speed control method for connected electric vehicles at traffic light intersections, the overall process of which is as follows: Figure 15 As shown, it includes the following steps: S1. Establish an electric vehicle simulation model, which includes a vehicle longitudinal resistance model, a drive motor model, and a power battery RC equivalent circuit model, respectively characterizing the vehicle's driving resistance characteristics, the drive system's power consumption characteristics, and the battery's dynamic charging and discharging and state of charge change characteristics.

[0022] The vehicle's longitudinal resistance model is as follows: Since speed planning is the primary task of eco-driving control, the lateral and vertical dynamics of the vehicle are generally ignored. Therefore, the following longitudinal dynamics model of the vehicle is established: (1); in, a To accelerate the vehicle; m For the overall vehicle weight; F out For vehicle control force; F res This refers to the resistance force on the vehicle. F res Includes rolling resistance F roll Ramp resistance F grad air resistance F drag .

[0023] The expression for vehicle resistance is: (2); in, g It is the acceleration due to gravity; f This is the rolling resistance coefficient; The road slope angle; C D This refers to the air drag coefficient; A f The vehicle's frontal area; ρ air density; v This refers to the driving speed.

[0024] The drive motor model is as follows: The drive motor model is set to distribute the driving force evenly between the left and right wheels, and the total power consumption of the drive system is... P prop Represented as: (3); in, T m and ω M These are the motor's output torque and angular velocity, respectively. Motor efficiency; superscript λ This indicates the motor's operating state. λ=-1 corresponds to the driving condition, and λ=1 corresponds to the braking energy recovery condition.

[0025] In this embodiment, two Protean PD18 permanent magnet synchronous hub motors are arranged on the front axle to provide power; the motors are equipped with integrated inverters, and the maximum power of a single motor is 78kW and the maximum torque is 1250N·m.

[0026] The RC equivalent circuit model of the power battery is as follows: To accurately calculate energy consumption and charge changes, this method constructs an RC equivalent circuit model of a power battery to simulate its dynamic characteristics. Using its open-circuit voltage and equivalent internal resistance parameters, the battery output current is calculated. I b It can be obtained from the power balance relationship: (4); in, U oc This is the battery open-circuit voltage; R bat This refers to the battery's internal resistance. P bat = P prop The battery output power is the motor torque. T m With vehicle kinetic energy E v The function.

[0027] The instantaneous rate of change of the battery's state of charge (SOC) is directly determined by the battery current, and its expression is: (5); in, Q bat This refers to the battery's rated capacity. Open-circuit voltage. U oc With equivalent internal resistance R bat It varies with SOC.

[0028] S2. Establish a deterministic traffic light timing scenario model to characterize the spatiotemporal constraints of vehicle passage. For roads with several traffic light-controlled intersections, define the timing parameters of each traffic light, solve for the predicted green light time window and predicted red light time window of each traffic light within a specified cycle, and characterize the spatiotemporal constraints of vehicle passage. The specific content is as follows: S21, Set the length to be L The road has I There are 1 traffic light-controlled intersections, of which the 1st i The location of each intersection is recorded as follows: Each traffic light follows a fixed timing scheme and operates on a periodic basis. C i It operates independently, with each signal cycle consisting of a fixed alternation of green and red light phases; S22, Definition of the i The timing parameters of each traffic light within a cycle include the start time of the green light phase. The green light lasts for 1 hour. Red light duration ; S23. Predicting the green light time window and red light time window: For the n The first cycle, the first i The predicted green light time window for each traffic light is: (6); Accordingly, the predicted red light time window is: (7).

[0029] S3. Constructing a spatial domain model predictive control (MPC) speed planning framework: Define the state transition equation of the vehicle's nominal kinetic energy in the spatial domain, select system state variables and control variables and establish their state transition relationship, construct an objective function with the comprehensive goal of reducing battery charge consumption and slowing down battery life degradation, and further complete the construction of the spatial domain model predictive control (MPC) speed planning framework; perform nonlinear least squares regression approximation on the battery current in the objective function to reduce the difficulty of solving.

[0030] MPC is a rolling time-domain control strategy based on a dynamic model, such as Figure 1 As shown, this method utilizes the current vehicle state and environmental information within the predicted time domain to solve the optimal control problem in the finite time domain online and executes only the first control variable. Compared to global planning, MPC has superior real-time performance, constraint handling capabilities, and robustness. The MPC speed planning framework constructed by this method aims to control the vehicle while reducing energy consumption and lifespan degradation, and ensuring sufficient smoothness and safety when passing through multiple traffic light intersections.

[0031] The construction of the spatial domain model predictive control (MPC) velocity planning framework includes the following steps: S31. Define the nominal kinetic energy of a vehicle in the spatial domain. E v for v 2 / 2 state transition equation: (8).

[0032] S32. Select the system state variables and control variables as follows: (9); in, t For vehicle passage time; T b It is the mechanical braking torque.

[0033] S33, Divide the spatial domain by step size Discretize, the discrete nodes are ;in k For discrete indexes in the distance domain,s p This indicates the vehicle's current location.

[0034] S34. Define the following state transition relationship between system state variables and control variables: (10); (11); Among them, in equation (10) r The radius is the wheel radius.

[0035] S35. The energy consumption of electric vehicles is related to the State of Charge (SOC) and depends on the instantaneous current. Furthermore, battery degradation, according to the current throughput model, depends on the absolute value of the instantaneous current. Therefore, the objective function is constructed as follows: (12); in, ω ={α} represents the system disturbance, i.e., the road slope; W d This is a weighting coefficient used to balance the cost of energy consumption with the cost of battery life degradation.

[0036] In S35, battery current I b It is the key quantity in the objective function (12), obtained according to equation (4). I b The calculation requires coupling the motor efficiency diagram, battery open-circuit voltage, and equivalent resistance, resulting in highly nonlinear computation. Direct optimization leads to solution difficulties and struggles to meet the real-time requirements of MPC. Therefore, this method incorporates battery current... I b To reduce the difficulty of solving the problem, nonlinear least squares regression approximation is performed, specifically including the following: S351, will I b Approximately expressed as kinetic energy E v and motor torque T m Fitting function: (14) in, This is an approximation of the battery current. b 1~ b 6 represents the fitting coefficient; Figure 2 To compare the fitted surface with the sampling points in this embodiment, the root mean square error (RMSE) of the fitting result is 0.1755, and the coefficient of determination is... R 2 The value of 0.9999 indicates good fitting accuracy.

[0037] S352. Substitute the fitted function into the equation and let each charge be a distance from the set point. The objective function (12) is approximated as: (15) S353, Introducing intermediate variables And impose constraints to handle absolute values: (16) S354, due to At the optimal solution, there is If true, the final objective function solution is transformed into: (17).

[0038] S36. Construct a spatial domain model predictive control (MPC) velocity planning framework: (13); in, E v,min , E v,max These represent the lower and upper bounds of kinetic energy under road speed limits; t ( k () represents the cumulative travel time of vehicles to spatial nodes. t des ( s k ) for in position s k The expected arrival time at the location; T m ( k ) represents the index in the spatial domain. k The torque control quantity of the drive motor at the location. T m,min , T m,max These are the upper and lower limits of the motor's permissible output torque; T b,min This is the lower limit of the mechanical braking torque; a min , a max These are the lower and upper limits of acceleration, respectively. t ( L i () represents the time of arrival at the intersection. This refers to predicting the green light time window.

[0039] The above inequalities include road speed limits, traffic efficiency, external characteristics of the drive motor, acceleration constraints, and safety constraints; Equation (13a) represents the interval constraint on kinetic energy; Equation (13b) is used to limit the vehicle arrival time to not exceed the expected value to ensure traffic efficiency; Equations (13c) and (13d) represent the constraints on the range of drive motor torque and mechanical braking torque; Equation (13e) limits the acceleration and deceleration amplitude to improve ride comfort and driving safety; Equation (13f) requires the vehicle arrival time to fall within the predicted green light time window to avoid running red lights.

[0040] S4. The SPAT information received by connected vehicles is usually provided by a cloud-based prediction system, which inevitably contains prediction errors. To study the impact of these errors on green wave traffic strategies, a stochastic prediction error model for traffic light phase timing needs to be established. Assuming that the stochastic prediction error for traffic light phase timing follows a normal distribution with a mean of zero, the timing prediction error for each traffic light is defined, and the timing prediction errors for all intersections share a random offset. The actual green light time window for the traffic lights after considering these errors is then calculated. The specific process is as follows: S41. The random prediction error for traffic light phase timing is assumed to approximately follow a normal distribution with a mean of zero in the time domain. Therefore, the first... i Each traffic light at a certain time t Timing prediction error Represented as: (18); in, For the standard deviation, in this embodiment, we take... =1s; To ensure the reasonableness of the error, the error distribution is set to be truncated within the interval [-2, 2] seconds, that is... =2 seconds.

[0041] S42. This error affects the actual green light time window of the traffic light. Relative to the prediction time window An overall offset occurred, but the traffic light cycle... C i Green light duration and red light duration All settings remain unchanged. To simplify the analysis and reflect the typical characteristics of regional signal coordination, the prediction error of traffic light timing at all intersections is set to follow a random offset. ξ ,like Figure 3 As shown, that is: (19); in, (20); S43. After considering the error, the first... The actual green light time window for each traffic light is represented as follows: (twenty one).

[0042] S5. Based on the aforementioned traffic light phase timing stochastic prediction error model, a multi-scenario weighted stochastic scenario MPC strategy is adopted to perform robust speed optimization control for connected electric vehicles. The stochastic scenario MPC strategy discretizes continuous random disturbances into a finite number of representative scenarios, transforming the stochastic optimization problem into a solvable deterministic multi-scenario optimization problem, achieving a trade-off between safety and conservatism. Specifically, it includes the following: S51. The optimization objective of multi-scenario problems is transformed into minimizing the expected cost under all scenarios: (twenty two); In the formula: For the scene j The objective function value is as follows; w j The weights for this scenario satisfy... ; S52. To ensure the feasibility of rolling optimization, an unexpected constraint is introduced: requiring that at the current control moment, all scenarios adopt the same initial control quantity. u (0); The system only executes the first step of control, and the remaining predictive control quantities are only used for rolling updates, thereby approximating uncertainty in multiple scenarios, effectively reducing excessive conservatism, and improving traffic efficiency under average working conditions.

[0043] S53. Generate random scene MPC and calculate the weight allocation error. ξ The probability distribution is: the error interval, which follows a standard normal distribution and is truncated to [-2, 2], is discretized at equal intervals as follows: S Each representative scenario j weight w j Equal to the probability mass within the neighborhood interval of this node: (twenty three); in,[ a j ,b j ] is the first j The neighborhood interval of each point This is the cumulative distribution function of the standard normal distribution.

[0044] The MPC strategy for random scenarios uses the cumulative probability of an interval rather than the probability density of a single point to determine the weights, ensuring the normalization of the weights and better reflecting the statistical characteristics of the truncated distribution. Detailed pseudocode of the algorithm is shown in Table 1.

[0045] Table 1. Pseudocode for Random Scenario MPC

[0046] S6. The CasADi solver is used to solve the speed planning optimization problem of MPC strategy in random scenarios. The performance of the robust vehicle speed control strategy is verified by Monte Carlo simulation. During the optimization process, random timing offsets that follow a truncated normal distribution are generated independently. The real green light window of the traffic light is constructed, and the red light violation rate, energy consumption, average acceleration and deceleration, and charge throughput are selected as performance evaluation indicators.

[0047] In this embodiment, to evaluate the applicability and robustness of the proposed control strategy in actual urban roads, a simulation study was conducted on a road scenario in a city in my country to verify the effectiveness of the method in improving traffic efficiency, safety, and economy.

[0048] (1) Simulation parameter settings: Scenario 1 selects a section of urban road with a length of L=1200m and a maximum speed limit of 60km / h, such as Figure 4 As shown in (a), the road segment has three traffic light-controlled intersections in sequence. Their locations and the prediction baseline parameters obtainable from the vehicle end are shown in Table 2. The MPC spatial prediction domain length is 500m, and rolling optimization updates are performed with a period of 1s.

[0049] Scenario 2 corresponds to the real road section as follows: Figure 4 As shown in (b), the length is L=2600m, and the maximum speed limit is 60km / h. Table 3 gives the timing reference parameters for this scenario. The MPC prediction domain is extended to 700m to cope with longer planning requirements, and the rolling update cycle is still 1s.

[0050] The two scenarios described above represent two typical urban operating conditions: "short-distance side roads" and "long-distance multi-intersection main roads," respectively. They exhibit significant differences in traffic light distribution density and timing parameters. By unifying vehicle models and control parameters in both scenarios, we can systematically evaluate the robustness, energy economy, and ride comfort performance of MPC, Intelligent Driver Model (IDM), conservative MPC, and the scenario MPC strategy described in this method under different signal layouts and road conditions in fixed traffic light scenarios.

[0051] Table 2. Benchmark parameters for traffic light timing prediction in scenario 1

[0052] Table 3. Benchmark parameters for traffic light timing prediction in scenario 2

[0053] (2) Simulation methods and evaluation indicators To evaluate the policy performance under random signal errors, the Monte Carlo method was used for simulation verification. Each simulation independently generated a policy that obeyed the following rules. Furthermore, a random timing offset truncated at [-2, 2] seconds is superimposed on the timing reference information of each intersection to construct a true green light window. Subsequently, it is verified whether the actual passage time of vehicles under different control strategies falls within the true green light time window.

[0054] The different strategies are handled in Monte Carlo verification as follows: Conservative MPC and stochastic scenario MPC strategies are planned only based on the predicted signal time window and do not utilize the random errors during simulation. The values ​​are selected to verify its inherent robustness under uncertain conditions; for IDM, its driving behavior changes in real time with the actual signal timing, and each test will produce a different trajectory, so its performance index is represented by the mean.

[0055] To comprehensively compare the advantages and disadvantages of different strategies, the following indicators were selected: Red light violation rate Characterizes security. In M In this simulation, the number of times the vehicle failed to pass through the real green light window. M red The proportion is (twenty four); Energy consumption Characterizes economic efficiency. Calculates the vehicle's net battery energy output throughout the entire journey. The vehicle's state is updated in a 1-second cycle, with the execution step index determined by... p express( The battery output energy is defined as... (25); Average acceleration / deceleration: characterizes ride comfort, based on longitudinal acceleration. a p Total travel time is The average acceleration and average deceleration are defined as follows: (26); (27).

[0056] Charge throughput: characterizes the degree of battery aging. (28).

[0057] (3) Results Analysis 1000 Monte Carlo simulations were performed on scenario one, and the results are shown below. Figures 5-8 See Table 4.

[0058] Figure 5 This indicates that both the conservative MPC and stochastic scenario MPC strategies can pass through three intersections consecutively without stopping, taking 95-97 seconds; the torque response is as follows: Figure 6 As shown, the torque variation of MPC-type strategies is smoother overall, which is beneficial for energy consumption control and component lifespan. Figure 7As shown, the operating points of both types of MPC converge significantly towards the efficient region of 85%–92%, achieving optimal economic cruise control. Figure 8 The comparison shows that MPC-type strategies avoid complete stops by slowing down in advance, resulting in more continuous speed changes and effectively improving traffic efficiency and comfort.

[0059] Table 4 further presents the statistical results of 1000 Monte Carlo simulations. Comparing the performance indicators of each strategy, it can be concluded that Scenario-based MPC exhibits superior performance in delaying battery degradation, with a charge throughput as low as 1.50 Ah, a significant reduction of 19.4% compared to IDM, and outperforming conservative MPC and fixed MPC. Scenario-based MPC avoids excessive conservatism caused by tightening the worst-case scenario without significantly sacrificing efficiency. When the number of scenarios increases to 9, it further reduces the risk of non-compliance to 2.3% while maintaining low energy consumption and low battery loss, demonstrating an effective trade-off between safety, economy, and battery life.

[0060] Table 4 Performance Comparison of Various Strategies in Scenario 1

[0061] Scenario 2 uses the same time-matched random offset distribution for 1000 Monte Carlo simulations. The results are shown below. Figures 9-12 See Table 5.

[0062] like Figure 9 As shown, scenario-based MPC effectively avoids overly conservative behavior, resulting in a shorter process time compared to conservative MPC. According to... Figure 10 It can be seen that the torque of both types of MPC is generally stable, and both reduce torque near the second intersection to achieve the expected arrival time. However, the conservative MPC has a higher braking peak and exhibits prolonged low-load fluctuations, reflecting its conservative characteristics. Figure 11 As shown, with increasing road conditions, the MPC robustness is optimal in random scenarios, with operating points consistently clustering tightly within the high-efficiency range of 300-600 r / min. This smoothing of torque fluctuations enables efficient utilization of battery energy. Figure 12 It can be concluded that the overall speed change of the scene MPC is smoother, and it has stable performance under different scene numbers.

[0063] Table 5 shows that Scenario-based MPC significantly suppresses battery life degradation by optimizing driving smoothness. Its average acceleration is reduced by approximately 30.0% compared to conservative MPC, and its energy consumption reduction is approximately 1.5% higher; charge throughput is significantly reduced by 44.4% compared to IDM. With an increase in the number of selected scenarios, energy consumption decreases, while the red-light violation rate slightly increases, demonstrating a trade-off between adjustable risk and performance. With increasing road network complexity and the number of signals, Scenario-based MPC achieves superior energy consumption and smoothness under controllable low-probability defaults, thus achieving optimal suppression of battery aging.

[0064] Table 5 Performance Comparison of Various Strategies in Scenario 2

[0065] To summarize, compare the two scenarios: 1) Fixed MPC is extremely sensitive to signal timing prediction errors and cannot guarantee traffic safety; Conservative MPC and scenario MPC can effectively suppress disturbances and significantly reduce unnecessary frequent start-stop and high-amplitude acceleration and deceleration compared to IDM. This not only greatly reduces SOC consumption but also significantly reduces charge throughput and effectively delays battery aging.

[0066] 2) Scenario-based MPC effectively avoids overly conservative behavior by tolerating extremely low probability of violations. It achieves the lowest possible charge throughput, resulting in optimal suppression of battery life degradation. With a red light violation rate close to 0%, its energy consumption and traffic efficiency are similar to or slightly better than conservative MPC, demonstrating optimization of driving smoothness and battery life while ensuring robustness.

[0067] (4) Monte Carlo statistical analysis Figure 13 and Figure 14 Demonstrates prediction errors under different signal timings ξ Below, the performance improvement of the random scenario MPC strategy compared to the traditional IDM model is shown. Error bars represent the 5%–95th percentile interval. The histogram showing consistently positive values ​​indicates that, under all error scenarios, random scenario MPC significantly reduces energy consumption and travel time compared to IDM, while suppressing speed fluctuations and effectively delaying lifetime decay. The narrow quantile interval confirms the stability of performance gains under different error conditions.

[0068] From a trend perspective, with ξ The shift from negative to positive indicates a slight, monotonically increasing difference in energy consumption and travel time in Scenario 1, suggesting a gradual expansion of the energy consumption and travel efficiency advantages. The advantages in average acceleration / deceleration and battery life degradation decrease slightly. In Scenario 2, the differences in charge throughput, average acceleration, and travel time show a positive correlation with timing errors, indicating that the phase switching lag has a significant impact on the IDM model, easily triggering rapid acceleration / deceleration and leading to accelerated battery life degradation. Unlike the above indicators, in the long-distance Scenario 2, the energy consumption difference... ξ The energy consumption peak occurs in the range [-1, 0], indicating that the IDM is more sensitive to disturbances in this error range under this scenario, which can easily lead to additional energy consumption. However, overall, the energy consumption of this type of MPC strategy will not change due to timing prediction errors, and it can maintain stable energy-saving benefits.

[0069] Therefore, the present invention adopts the above-mentioned robust speed control method for connected electric vehicles at traffic light intersections. The proposed random scenario MPC strategy has a comprehensive performance that is closer to the actual application requirements. Without sacrificing safety, it achieves energy efficiency and smoothness that are similar to or even better than conservative MPC, thus realizing a balance between safety, economy, traffic efficiency and battery life.

[0070] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A robust speed control method for connected electric vehicles at traffic light intersections, characterized in that, Includes the following steps: S1. Establish an electric vehicle simulation model, which includes a vehicle longitudinal resistance model, a drive motor model, and a power battery RC equivalent circuit model, respectively characterizing the vehicle driving resistance characteristics, drive system power consumption characteristics, and battery dynamic charging and discharging and state of charge change characteristics. S2. Establish a deterministic traffic light scenario model. For roads with several traffic light-controlled intersections, define the timing parameters of each traffic light, solve the predicted green light time window and predicted red light time window of each traffic light within a specified period, and characterize the spatiotemporal constraints of vehicle passage. S3. Constructing a spatial domain model predictive control (MPC) speed planning framework: Define the state transition equation of the vehicle's nominal kinetic energy in the spatial domain, select system state variables and control variables and establish their state transition relationship, construct an objective function with the comprehensive goal of reducing battery charge consumption and slowing down battery life degradation, and further complete the construction of the spatial domain model predictive control (MPC) speed planning framework; perform nonlinear least squares regression approximation on the battery current in the objective function to reduce the difficulty of solving the problem. S4. Establish a random prediction error model for traffic light phase timing. Assume that the random prediction error for traffic light phase timing follows a normal distribution with a mean of zero. Define the timing prediction error for each traffic light. The timing prediction errors for traffic lights at all intersections share a random offset. Solve for the actual green light time window of the traffic lights after considering the error. S5. Based on the traffic light phase timing random prediction error model, a multi-scenario weighted random scenario MPC strategy is adopted to perform robust speed optimization control on connected electric vehicles. S6. The CasADi solver is used to solve the speed planning optimization problem of MPC strategy in random scenarios. The performance of the robust vehicle speed control strategy is verified by Monte Carlo simulation. During the optimization process, random timing offsets that follow a truncated normal distribution are generated independently. The real green light window of the traffic light is constructed, and the red light violation rate, energy consumption, average acceleration and deceleration, and charge throughput are selected as performance evaluation indicators.

2. The robust speed control method for connected electric vehicles at traffic light intersections according to claim 1, characterized in that, In S1, the vehicle longitudinal resistance model is specifically represented as follows: (1)； in, a To accelerate the vehicle; m For the overall vehicle weight; F out For vehicle control force; F res For vehicle driving resistance; F res Includes rolling resistance F roll Ramp resistance F grad air resistance F drag ; The expression for vehicle resistance is: (2)； in, g It is the acceleration due to gravity; f This is the rolling resistance coefficient; The road slope angle; C D This refers to the air drag coefficient; A f The vehicle's frontal area; ρ air density; v The driving speed; The drive motor model is set to have a uniform distribution of driving force between the left and right wheels, and the total power consumption of the drive system is [not specified]. P prop Represented as: (3)； in, T m and ω M These are the motor's output torque and angular velocity, respectively. Motor efficiency; superscript λ This indicates the motor's operating state; λ=-1 corresponds to the driving condition, and λ=1 corresponds to the braking energy recovery condition. In the aforementioned RC equivalent circuit model of the power battery, the battery output current... I b The calculation formula is as follows: (4)； in, U oc This is the battery open-circuit voltage; R bat This refers to the battery's internal resistance. P bat = P prop The battery output power is the motor torque. T m With vehicle kinetic energy E v The function; The instantaneous rate of change of the battery's state of charge (SOC) is directly determined by the battery current, and its expression is: (5)； in, Q bat This refers to the battery's rated capacity.

3. The robust speed control method for connected electric vehicles at traffic light intersections according to claim 2, characterized in that, S2 specifically includes the following: S21, Set the length to be L The road has I There are 1 traffic light-controlled intersections, of which the 1st i The location of each intersection is recorded as follows: Each traffic light follows a fixed timing scheme and operates on a periodic basis. C i It operates independently, with each signal cycle consisting of a fixed alternation of green and red light phases; S22, Definition of the i The timing parameters of each traffic light within a cycle include the start time of the green light phase. The green light lasts for 1 hour. Red light duration ; S23. Predicting the green light time window and red light time window: For the n The first cycle, the first i The predicted green light time window for each traffic light is: (6)； Accordingly, the predicted red light time window is: (7)。 4. The robust speed control method for connected electric vehicles at traffic light intersections according to claim 3, characterized in that, In S3, the construction of the spatial domain model predictive control (MPC) velocity planning framework includes the following steps: S31. Define the nominal kinetic energy of a vehicle in the spatial domain. E v for v 2 / 2 state transition equation: (8)； S32. Select the system state variables and control variables as follows: (9)； in, t For vehicle passage time; T b For mechanical braking torque; S33, Divide the spatial domain by step size Discretize, the discrete nodes are ;in k For discrete indexes in the distance domain, s p The vehicle's current location; S34. Define the following state transition relationship between system state variables and control variables: (10)； (11)； Among them, in equation (10) r The radius of the wheel; S35. The energy consumption of electric vehicles is related to the State of Charge (SOC) and depends on the instantaneous current. Furthermore, battery degradation, according to the current throughput model, depends on the absolute value of the instantaneous current. Therefore, the objective function is constructed as follows: (12)； in, ω ={α} represents the system disturbance, i.e., the road slope; W d This is a weighting coefficient used to weigh the energy consumption cost against the battery life degradation cost; S36. Construct a spatial domain model predictive control (MPC) velocity planning framework: (13)； in, E v,min , E v,max These represent the lower and upper bounds of kinetic energy under road speed limits; t ( k () represents the cumulative travel time of vehicles to spatial nodes. t des ( s k ) for in position s k The expected arrival time at the location; T m ( k ) represents the index in the spatial domain. k The torque control quantity of the drive motor at the location. T m,min , T m,max These are the upper and lower limits of the motor's permissible output torque; T b,min This is the lower limit of the mechanical braking torque; a min , a max These are the lower and upper limits of acceleration, respectively. t ( L i () represents the time of arrival at the intersection. That is, predicting the green light time window; The above inequalities include road speed limits, traffic efficiency, external characteristics of the drive motor, acceleration constraints, and safety constraints; Equation (13a) represents the interval constraint on kinetic energy; Equation (13b) is used to limit the vehicle arrival time to not exceed the expected value to ensure traffic efficiency; Equations (13c) and (13d) represent the constraints on the range of drive motor torque and mechanical braking torque; Equation (13e) limits the acceleration and deceleration amplitude to improve ride comfort and driving safety; Equation (13f) requires the vehicle arrival time to fall within the predicted green light time window to avoid running red lights.

5. The robust speed control method for connected electric vehicles at traffic light intersections according to claim 4, characterized in that, In S3, the nonlinear least squares regression approximation of the battery current in the objective function is used to reduce the difficulty of solving the problem. Specifically, this includes the following: S351, will I b Approximately expressed as kinetic energy E v and motor torque T m Fitting function: (14)； in, This is an approximation of the battery current. b 1~ b 6 represents the fitting coefficient; S352. Substitute the fitted function into the equation and let each charge be a distance from the set point. The objective function (12) is approximated as: (15)； S353, Introducing intermediate variables And impose constraints to handle absolute values: (16)； S354, due to At the optimal solution, there is If true, the final objective function solution is transformed into: (17)。 6. The robust speed control method for connected electric vehicles at traffic light intersections according to claim 5, characterized in that, The specific process in S4 is as follows: S41. The random prediction error for traffic light phase timing is assumed to approximately follow a normal distribution with a mean of zero in the time domain. Therefore, the first... i Each traffic light at a certain time t Timing prediction error Represented as: (18)； in, Let be the standard deviation. To ensure the reasonableness of the error, the error distribution is set to be truncated within the interval [-2, 2] seconds, i.e. =2 seconds; S42. This error affects the actual green light time window of the traffic light. Relative to the prediction time window An overall offset occurred, but the traffic light cycle... C i Green light duration and red light duration All settings remain unchanged. To simplify the analysis and reflect the typical characteristics of regional signal coordination, the prediction error of traffic light timing at all intersections is set to follow a random offset. ξ ,Right now: (19)； in, (20); S43. After considering the error, the first... The actual green light time window for each traffic light is represented as follows: (21)。 7. The robust speed control method for connected electric vehicles at traffic light intersections according to claim 6, characterized in that, S5 specifically includes the following: S51. The optimization objective of multi-scenario problems is transformed into minimizing the expected cost under all scenarios: (twenty two); In the formula: For the scene j The objective function value is as follows; w j The weights for this scenario satisfy... ; S52. Introduce unexpected constraints: require that at the current control moment, all scenarios adopt the same initial control quantity. u (0); The system only executes this initial control step, and the remaining predictive control variables are only used for rolling updates; S53. Generate random scene MPC and calculate the weight allocation error. ξ The probability distribution is: the error interval, which follows a standard normal distribution and is truncated to [-2, 2], is discretized at equal intervals as follows: S Each representative scenario j weight w j Equal to the probability mass within the neighborhood interval of this node: (23)； in,[ a j ,b j ] is the first j The neighborhood interval of each point This is the cumulative distribution function of the standard normal distribution.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the robust speed control method for connected electric vehicles at traffic light intersections as described in any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the robust speed control method for connected electric vehicles at traffic light intersections as described in any one of claims 1-7.

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