Distributed vehicle cooperative oscillation wave absorption method based on multi-objective optimization

Abstract

This invention discloses a distributed convoy cooperative oscillation absorption method based on multi-objective optimization. The steps include: S1 acquiring a scenario of mixed-flow convoys passing through an oscillation zone, dividing long convoys, and determining key parameters; S2 constructing an optimization control model to solve for the optimal convoy splitting point and splitting the mixed convoys; S3 using an improved AS-OCD distributed trajectory optimization algorithm to synchronously control each sub-convoy to completely absorb traffic oscillations. This method solves the problem of frequent traffic oscillations in high-saturation traffic flow or urban expressways. Through distributed cooperative optimization, it achieves state sharing and boundary coordination among sub-convoys, enhancing the system's adaptability and robustness in high-density and complex traffic environments, ensuring speed coordination and safe following distances between convoys, reducing the risk of traffic conflicts, and improving the overall stability and operational efficiency of the traffic system.

Description

Technical Field

[0001] This invention belongs to the field of intelligent traffic control technology, and in particular relates to a distributed vehicle fleet cooperative oscillation wave absorption method based on multi-objective optimization. Background Technology

[0002] With the rapid growth of urban motor vehicle ownership, urban expressways face prominent problems such as high traffic density, limited lane resources, and drastic fluctuations in traffic demand, leading to continuously increasing pressure on the traffic system. Against this backdrop, traffic sway waves, a typical nonlinear traffic disturbance phenomenon, have become a significant factor inducing decreased traffic efficiency and frequent traffic accidents. Sway waves exhibit periodic acceleration and deceleration behavior in traffic flow, easily causing queuing, delays, and even chain-reaction rear-end collisions in bottleneck areas, severely impacting road service levels. To mitigate the impact of sway waves, existing research often employs connected and automated vehicles (CAVs) to adjust their speeds to absorb disturbances, indirectly improving following stability by guiding individual vehicles to adopt gentle deceleration / acceleration strategies. However, in urban expressway environments with high traffic saturation or limited road length, these methods, due to limited spatiotemporal control, struggle to cut off the upstream propagation path of sway waves at the system level. Instead, inappropriate intervention timing or magnitude may induce secondary sway waves, forming moving bottlenecks that spread upstream, exacerbating traffic instability and conflict risks.

[0003] Meanwhile, with the development of vehicle-to-everything (V2X) sensing networks and intelligent driving technologies, traffic control systems are gradually evolving from centralized control to a distributed, cooperative control architecture. Traditional centralized control strategies based on single-fleet traffic are limited by vehicle heterogeneity, communication latency, and overall computational complexity, making it difficult to achieve multi-objective cooperative optimization of disturbance absorption, queue stability, and traffic efficiency when dealing with large-scale disturbances. Therefore, there is an urgent need to construct a highly adaptable and scalable cooperative control framework for the high-density mixed traffic environment of urban expressways, in order to effectively eliminate traffic ripples and improve road traffic efficiency and the operational resilience of the traffic system.

[0004] To address the aforementioned issues, scholars both domestically and internationally have conducted numerous studies on vehicle fleet stability and oscillation control, proposing methods including model predictive control, nonlinear control, trajectory planning, and fuzzy coordinated control. They have also gradually introduced dynamic vehicle fleet splitting and distributed control mechanisms to improve system robustness and adaptability. However, existing methods still suffer from limitations in control scale, coordination efficiency, and computational complexity in high-density, short-segment, and real-time-critical urban expressway scenarios, making it difficult to achieve efficient absorption of traffic oscillations and coordinated optimization of vehicle fleet operation. Summary of the Invention

[0005] The purpose of this invention is to provide a distributed vehicle fleet cooperative oscillation wave absorption method based on multi-objective optimization to solve the problem of frequent traffic oscillation waves in high-saturation traffic flow or urban expressways.

[0006] The technical solution adopted in this invention is a distributed vehicle fleet cooperative oscillation wave absorption method based on multi-objective optimization, the steps of which include:

[0007] Step S1: Obtain the scene of the mixed flow vehicle passing through the oscillation zone, divide the long vehicle fleet, and determine the key parameters;

[0008] Step S2: Construct an optimization control model to solve for the optimal vehicle splitting point and split the mixed vehicle fleet.

[0009] Step S3: Based on the improved AS-OCD distributed trajectory optimization algorithm, synchronize the control of each sub-vehicle group to completely absorb traffic shock waves.

[0010] Furthermore, the specific steps of S1 are as follows:

[0011] S11, Determine the spacing between vehicles within the sub-platform and the number of vehicles following in the sub-platform:

[0012] For CAVs, the maximum number of vehicles following is... The number of information transmission layers in the vehicle topology Directly determines the expected distance between two adjacent vehicles within a sub-team. ≥ The distance the vehicle travels within the maximum delay is equal to the expected safe distance. sum;

[0013] For HDV, the maximum number of following vehicles The effective communication range of the vehicle is It was decided that the total length of the sub-vehicle group would be less than or equal to the effective communication distance. ;

[0014] Maximum number of cars following a sub-team In the formula, This indicates taking the minimum value;

[0015] S12, determine the distance between sub-platforms; the lead vehicle of an adjacent sub-platform must be within the effective communication range. Within the vehicle, the expected following distance D between sub-vehicle groups must be greater than the length of the preceding sub-vehicle group;

[0016] S13, determine the number of sub-teams. In a multi-team system, the maximum number of sub-teams is determined by the number of sub-teams affected by the topology. and the number of sub-vehicle fleets affected by controller stability Common restrictions, In the formula, np,max This represents the maximum number of sub-teams. This indicates taking the minimum value.

[0017] Furthermore, the specific steps of S2 are as follows:

[0018] S21, Introducing a binary variable The location of the convoy split point is described by i=1, which means that the convoy splits before the first car, i=N means that the convoy splits between the (N-1)th car and the Nth car, and i=N+1 means that the convoy splits after the Nth car. To ensure the rationality and effectiveness of the split strategy, the convoy is subject to a unique split point constraint, a latest passing constraint for the preceding sub-convoy, and an earliest passing constraint for the following sub-convoy.

[0019] S22, determine the safe time interval and the speed difference between the last car in the leading sub-group and the first car in the following sub-group, using the following formula:

[0020] ;

[0021] Among them, L i Indicates CAV i The length plus the minimum following distance, τ is the baseline safe following distance, δ1 is the following conservative coefficient, δ2τ(v i (t)-v i-1 (t) represents the velocity difference, and δ2 is the velocity difference coefficient. Indicates CAV i-1 At the position at time t Indicates CAV i At the position at time t Indicates CAV i The velocity at time t, Indicates CAV i-1 The velocity at time t, CAV i Let vehicle i be a connected autonomous vehicle (CAV). i-1 This indicates that vehicle i-1 is a connected autonomous vehicle;

[0022] S23, based on S21~S22, constructs the objective function for the fleet splitting algorithm. The formula is as follows:

[0023] ;

[0024] In the formula, This indicates taking the minimum value. It is the energy consumption objective function. This is the risk objective function, where α1 and α2 represent the objective functions respectively. , The weighting coefficients, It is the speed of vehicle i at time t; It is the acceleration of vehicle i at time t.

[0025] Furthermore, the unique split point constraint requires that there must be one and only one split point in the mixed-flow vehicle fleet, and all binary variables... There is exactly one value of 1, and the rest are 0;

[0026] The latest constraint for the preceding sub-team is: the split point is i, and the last car (CAV) of the preceding sub-team passes through. i-1 It must be at the end of its oscillation time Previously, it was based on the corresponding end point of the oscillation. ;

[0027] The earliest vehicle in the rear sub-convoy passes the constraint: the split point is i, and the first vehicle (CAV) of the rear sub-convoy... i When its oscillation ends At that time, it must not pass through its corresponding oscillation end position. .

[0028] Furthermore, the specific steps of S3 are as follows:

[0029] S31, based on the operating status of the lead vehicle in the convoy, initializes the AS-OCD algorithm, incorporates the constraints satisfying the boundary conditions into the activity set and Lagrange multipliers, initializes the activity set, solves the initial optimization problem, outputs the initial solution and the Lagrange multipliers corresponding to various constraints, and clarifies the equality constraints that are currently activated and truly affect the safety and stability of vehicle operation. The formulas are as follows:

[0030] ;

[0031] ;

[0032] In the formula, It is a vehicle acceleration, It is a vehicle acceleration, This indicates constraints involving two or more vehicles, which are processed into equations when activated. Represents the hard constraints of a single vehicle;

[0033] S32, Activity set iteration, traverses all constraints of CAV for dynamic filtering, identifies and marks constraints triggered in the current running state as candidate activations, adds candidate constraints to the activity set and enforces them in the form of equations; if the corresponding Lagrange multiplier in the activity set becomes negative, it is removed and restored to an inactive constraint.

[0034] S33, optimal condition decomposition and solution: constructing KKT conditions and their matrix approximations, and using the distributed Newton iteration method for solution. By iteratively optimizing the distributed control input and Lagrange multipliers of the CAV, the constraints in equation S23 are satisfied, while simultaneously minimizing the objective function value. The formula is as follows:

[0035] ;

[0036] ;

[0037] ;

[0038] ;

[0039] ;

[0040] In the formula, It is the Lagrangian function derived from the objective function J; and It is a Lagrange multiplier. This represents the search direction vector for all vehicles. The acceleration vector representing all vehicles is a decision variable. These are the weights of the constraints. These are the weights of the equality constraints, and T represents the transpose. Represents the gradient operator. Represents the Hessian matrix;

[0041] Approximating the KKT matrix K as CAV i matrix blocks The details are as follows:

[0042] ;

[0043] ;

[0044] ;

[0045] In the formula, Indicates CAV i The search direction vector, Indicates CAV i The residual vector, Indicates CAV i The corresponding submatrix block, where N represents the Nth vehicle, Represents structural approximation operations;

[0046] S34, Synchronization and Global Update: Each CAV communicates across vehicles via the vehicle network, sharing its own operating status information in real time and aligning all involved constraints. Adjacent vehicles exchange optimized control inputs and status data to correct their respective boundary conditions and generate a control input sequence that is consistent globally and conforms to all coupling constraints.

[0047] S35, Convergence check and termination: During the iteration process, check whether the objective function value tends to stabilize, and evaluate whether all key constraints are satisfied. If the optimization result reaches the preset convergence criterion, the algorithm terminates; otherwise, return to step S32 to continue the activity set update and optimization iteration.

[0048] S36, Optimal control input execution: After the optimization process is completed, the output optimal control input sequence will be sent to each vehicle in the sub-team, so that they can adjust their speed and distance according to the planning results, ensuring the smoothness and consistency of the platoon operation.

[0049] The beneficial effects of this invention are:

[0050] 1. The distributed fleet splitting method proposed in this invention dynamically divides long fleets into multiple sub-fleets with adaptive boundaries, realizing hierarchical management of fleets, improving the flexibility and scalability of control strategies, and alleviating the limitations of traditional centralized control in terms of computational complexity and real-time performance.

[0051] 2. This invention is based on a multi-objective optimization trajectory optimization strategy, which independently adjusts the speed and distance of each sub-vehicle group, comprehensively taking into account traffic efficiency, safety and energy consumption, significantly enhancing the ability to suppress traffic shock waves, and improving the stability and safety of vehicle group cooperative operation.

[0052] 3. This invention achieves state sharing and boundary coordination among sub-vehicle groups through distributed collaborative optimization, which enhances the system's adaptability and robustness in high-density and complex traffic environments, ensures speed coordination and safe distances among vehicle groups, reduces the risk of traffic conflicts, and improves the stability and operational efficiency of the overall traffic system. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 This is a diagram of the cooperative oscillation wave absorption strategy for mixed traffic flow vehicle fleets in an embodiment of the present invention.

[0055] Figure 2 This is a schematic diagram of a vehicle convoy in the oscillation zone according to an embodiment of the present invention.

[0056] Figure 3 These are spatiotemporal trajectory diagrams of vehicles under different control strategies in embodiments of the present invention, wherein (a) is without control, (b) is the WT-JAD strategy, (c) is the full JAD strategy, (d) is the WT-WOA oscillation absorption strategy, and (e) is the strategy of the present invention.

[0057] Figure 4 The diagram shows the vehicle speed variation under different control strategies in the embodiments of the present invention, where (a) is no control, (b) is the WT-JAD strategy, and (c) is the fleet cooperative oscillation absorption strategy.

[0058] Figure 5 The diagram shows the changes in vehicle acceleration under different control strategies in the embodiments of the present invention, where (a) is without control, (b) is the WT-JAD strategy, and (c) is the vehicle convoy cooperative oscillation absorption strategy.

[0059] Figure 6 This is a comparison of the temporal evolution and spatial distribution of the speed standard deviation under different oscillation absorption strategies in the embodiments of the present invention, wherein (a) is the speed standard deviation at each time point under different strategies, and (b) is the speed standard deviation of each vehicle under different strategies. Detailed Implementation

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0061] Example 1

[0062] Embodiments of the present invention provide a distributed vehicle fleet cooperative oscillation wave absorption method based on multi-objective optimization, wherein the absorption strategy is as follows: Figure 1 As shown, the steps include:

[0063] Step S1: Obtain the scene of a mixed-flow convoy passing through a sloshing zone on an urban expressway, segment the long convoy, and determine key parameters. Figure 2Taking the scenario shown as an example, the mixed-flow convoy consists of CAVs and HDVs (Human-Driven Vehicles). The CAV convoy can choose to follow the lead HDV or drive freely. Within the CAV convoy, a network topology for communication between vehicles is employed to minimize communication latency. CAVs in the preceding and following convoys exchange information via V2V (Vehicle-to-Vehicle Communication) when there are no communication failures, ensuring real-time coordination and preventing unbounded latency. It is assumed that the CAVs at the rear of the preceding convoy are within communication range of the lead vehicle in the following convoy and can maintain effective communication. Furthermore, the driving behavior of the HDVs can be detected by onboard sensors in adjacent CAV convoys, enhancing the convoy's responsiveness and coordination. The specific steps for dividing a long convoy are as follows:

[0064] S11 determines the spacing between vehicles within the sub-platform and the number of vehicles following in the sub-platform. The expected distance within the sub-platform is mainly affected by vehicle energy consumption and safety. Its core objective is to maximize energy consumption while ensuring safety. Since CAV vehicles employ autonomous driving functions, driver reaction time can be ignored. The safe distance mainly depends on the distance the vehicle travels at its original speed during the time delay. Under stable multi-platform driving conditions, the cruising speed of the sub-platform will not exceed the expected cruising speed of the lead vehicle. The expected distance between adjacent vehicles within the sub-platform... The following relationship should be satisfied:

[0065] ;

[0066] In the formula, d0 is the desired safety clearance in meters (m). The maximum delay is expressed in seconds (s). The desired cruising speed is expressed in m / s.

[0067] For HDV, due to the limited communication range of vehicle-to-vehicle communication technology and its susceptibility to interference from road environmental factors, to ensure communication connectivity within the convoy, all following vehicles must be able to receive information from the lead vehicle. Let the effective communication range of the vehicles be... The length of vehicle i is The following distance is The maximum number of following vehicles in a sub-team under communication constraints. The following conditions must be met:

[0068] ;

[0069] The communication between vehicles within a CAV convoy is constrained by the network topology. This topology constraint refers to the accessibility of vehicles within a sub-convoy to information about the leading vehicle. When the sub-convoy is too long, some following vehicles cannot reliably obtain information from the lead vehicle through communication or sensing links, thus affecting control performance and stability. Therefore, it is necessary to limit the maximum number of following vehicles. Based on the convoy communication topology type (e.g., forward chain, bidirectional chain, or local neighbor topology), the number of forward information transmission layers that each vehicle can reliably receive is set. The formula for calculating the maximum number of vehicles that can stably follow is as follows:

[0070] ;

[0071] In the formula, This represents the maximum number of following vehicles in a sub-platform constrained by the network topology, determined by the number of information transmission layers in the vehicle topology. Directly determines the corresponding topological structures This can be determined through simulation verification or communication performance testing. Indicates the average vehicle length. Indicates the average vehicle spacing. This indicates rounding down to the nearest integer.

[0072] In summary, the maximum number of cars following a sub-team is... for:

[0073] ;

[0074] In the formula, This indicates taking the minimum value.

[0075] S12, determine the distance between sub-platforms. The expected following distance between sub-platforms is limited by communication range and safety. The lead vehicle of adjacent sub-platforms must remain within the effective communication range. At the same time, the expected following distance between sub-platforms must be greater than the length of the preceding sub-platform to avoid collision risk. Therefore, the expected following distance D between sub-platforms must meet the following conditions:

[0076] ;

[0077] In the formula, This represents the expected distance between two adjacent vehicles within a sub-team. This represents the number of vehicles corresponding to the optimal length of the sub-platform (subtracted by 1 during calculation). It is derived by using a traffic flow-communication collaborative simulation method on both the AC simulation platform and the Internet simulation platform to simultaneously simulate the dynamic behavior and communication constraints of vehicles in a unified scenario, coupled with the communication stability indices of different sub-platforms (vehicle speed fluctuation attenuation rate, distance maintenance error, and energy consumption level). This represents the length of vehicle i. Indicates the maximum delay. Indicates the desired cruising speed. Indicates the effective communication range of the vehicle.

[0078] S13, determine the number of sub-teams. In a multi-team system, the maximum number of sub-teams is determined by the number of sub-teams affected by the topology. and the number of sub-vehicle fleets affected by controller stability Common constraints, the formula is as follows:

[0079] ;

[0080] In the formula, n p,max This represents the maximum number of sub-teams. This indicates taking the minimum value.

[0081] calculate First, by analyzing the fleet communication topology (such as forward chain, bidirectional chain, local neighbor), the maximum number of layers Lp that vehicles can maintain a stable communication link is determined. Then, the maximum number of sub-fleets is calculated based on the average vehicle length and vehicle spacing. First, controller stability analysis (such as Lyapunov stability or eigenvalue determination) is used to obtain the maximum allowable fleet size under certain control gain and communication delay conditions, which is then converted into the maximum number of sub-fleets. Therefore, Derived from communication topology analysis, Both are derived from controller stability analysis and can be clearly obtained through simulation or theoretical derivation.

[0082] In the initial phase, the lead vehicle collects information from following vehicles, determines control objectives, and adjusts control parameters. When the convoy status changes, the dynamic decision-making module updates the lead vehicle's cruising speed and safe distance, adjusts parameters such as following distance, and broadcasts the updated information to ensure the system can flexibly respond to dynamic environments.

[0083] Step S2 involves employing Mixed-Integer Nonlinear Programming (MINLP) to construct an optimal control model that, while satisfying vehicle dynamics constraints, comprehensively considers key factors such as fleet operating status, speed and acceleration constraints, fleet length, and energy consumption. This model aims to solve for the optimal fleet splitting point and split the mixed fleet. The specific steps are as follows:

[0084] S21, Introducing a binary variable Let i = 1 represent the split point of the convoy, i = N represent the split between the (N-1)th and Nth vehicles, and i = N+1 represent the split after the Nth vehicle. To improve the applicability of the control strategy and reduce computational complexity, the convoy is divided into only two sub-convoys at each split, and this process is repeated until all vehicles have passed through the oscillation zone, thus ensuring the feasibility and stability of the split process. To ensure the rationality and effectiveness of the split strategy, the following constraints are imposed:

[0085] 1) Unique Split Point Constraint: Requires that there must be one and only one split point in the mixed-flow vehicle fleet, i.e., all binary variables. There is one and only one value that is 1 (split), and the rest are 0 (not split), as shown below:

[0086] ;

[0087] 2) The latest passage constraint for the first sub-vehicle group: If the split point is i, then the first sub-vehicle group (CAV1 to CAV) generated from this point must pass through the constraint i. i-1 The last CAV train i-1 It must be at the end of its oscillation time Previously, it was based on the corresponding end point of the oscillation. ,Right now:

[0088] ;

[0089] 3) The earliest sub-vehicle group passes the constraint: if the split point is i, then the resulting sub-vehicle group (CAV) is the first to pass the constraint. i To CAV N The first CAV i When its oscillation ends At that time, it must not pass through its corresponding oscillation end position. ,Right now:

[0090] ;

[0091] In the formula, express CAV Time i-1 Location, express CAV Time i Location, Let i represent the set of vehicle splitting points.

[0092] S22 determines the safe time interval and the speed difference between the last vehicle in the preceding sub-platform and the first vehicle in the following sub-platform to ensure driving safety and increase traffic throughput. The formula is as follows:

[0093] ;

[0094] Among them, L i Indicates CAV i The length plus the minimum following distance, in meters; τ is the baseline safe following distance, in seconds; δ1 is the following safety factor, δ1 ≥ 1; δ2τ(v i (t)-v i-1 (t) represents the speed difference, and δ2 is the speed difference coefficient. δ2 ≥ 0. When the vehicle in front is faster than the vehicle behind, the safety distance is adaptively reduced to improve road capacity. Conversely, the safety distance is increased to ensure driving safety. Additional safety margin, unit: meters (m); Indicates CAV i-1 At the position at time t Indicates CAV i At the position at time t Indicates CAV i The velocity at time t, in m / s; Indicates CAV i-1 The velocity at time t, in m / s, CAV i Let vehicle i be a connected autonomous vehicle (CAV). i-1 This indicates that vehicle i-1 is a connected autonomous vehicle.

[0095] S23, based on S21~S22, constructs the objective function for the fleet splitting algorithm. The formula is as follows:

[0096] ;

[0097] ;

[0098] ;

[0099] The boundary conditions for each variable in the objective function are: , , , , , .

[0100] In the formula, This indicates taking the minimum value. The duration of the shock wave; The fuel consumption of vehicle i at time t, in units ; The following risk term for vehicle i is obtained by dividing the difference between the collision exposure time of vehicle i under uncontrolled conditions and the collision exposure time after implementing the control strategy of this invention by the collision exposure time under controlled conditions. The collision risk term for vehicle i is obtained by dividing the difference between the collision contact time of vehicle i under uncontrolled conditions and the collision contact time after implementing the control strategy of this invention by the collision contact time under controlled conditions. This represents the earliest time when the oscillation began; The latest time for the end of the oscillation; a max Let a be the maximum acceleration of the vehicle. min v is the minimum acceleration of the vehicle. max v is the maximum speed of the vehicle. min This is the minimum speed of the vehicle. It is the energy consumption objective function. This is the risk objective function, where α1 and α2 represent the objective functions respectively. , The weighting coefficients, It is the speed of vehicle i at time t; Let M be the acceleration of vehicle i at time t; M is a sufficiently large constant used to constrain linearization. It is the fuel consumption rate of vehicle i at time t.

[0101] For HDVs, they are treated as uncontrollable vehicles and used as boundary conditions or internal constraints when dividing the sub-teams. The control inputs are dynamically adjusted by the CAV based on the operating status of the HDVs.

[0102] Step S3: Based on the improved AS-OCD (Active-set Based Optimal Condition Decomposition Algorithm) distributed trajectory optimization algorithm, synchronous control is performed on each sub-vehicle group to achieve complete absorption of traffic sway waves. In traditional control, when the lead vehicle implements the sway absorption strategy, secondary ripples may be induced due to response delays or control incoordination between vehicles, exacerbating traffic instability. The improved AS-OCD algorithm of this invention introduces active set filtering and distributed KKT condition decomposition, which can accurately identify the constraints that are currently in effect and locally optimize the control input within each sub-vehicle group, maintaining a reasonable safe distance and speed coordination between vehicles, thereby effectively suppressing the formation of secondary waves. In this process, the algorithm combines the propagation mechanism of sway waves, vehicle dynamics constraints, and vehicle-to-everything (V2X) communication characteristics to dynamically adjust the speed and trajectory of each vehicle, ensuring that compression waves and dissipation waves meet and cancel each other out at the appropriate time, ultimately achieving traffic flow smoothing. The specific steps are as follows:

[0103] S31, based on the operating status of the lead vehicle in the convoy, initializes the AS-OCD algorithm by incorporating constraints satisfying the boundary conditions into the activity set and Lagrange multipliers (for both uncoupled and coupled constraints). The activity set is used to dynamically track constraints actually in effect under the current oscillation wave. During the initialization phase, all inequality constraints are initially marked as "inactive." By solving the initial optimization problem, the initial solution and the Lagrange multipliers corresponding to various constraints are output, clarifying the equality constraints that are currently activated and truly affect the safety and stability of vehicle operation. The formulas are as follows:

[0104] ;

[0105] ;

[0106] In the formula, It is a vehicle acceleration, It is a vehicle acceleration, This indicates that constraints involving two or more vehicles (such as safety distance constraints) are processed into equations when activated. Hard constraints (such as velocity and acceleration boundary conditions) for a single vehicle are always expressed as equations. It is an active coupling constraint used to describe the safe distance and speed coordination relationship between two or more CAVs. It is a key constraint to prevent shock waves from spreading upstream. "=0" means that the safety constraint is added to the active set in the form of an equation when it is activated, while its general form is "≥0" when it is not activated. It is an active uncoupled constraint that acts only on a single CAV (such as acceleration or speed limit), reflects the physical limits of a single vehicle, and ensures that the vehicle will not become unstable due to excessive control. "=0" indicates an equality constraint that a single CAV must always satisfy, such as speed or acceleration limit. This type of constraint does not need to be activated and always exists in the form of an equality.

[0107] S32, Activity Set Iteration: This process iterates through all constraints of the CAV, dynamically filtering and identifying constraints triggered in the current operating state as candidate activations. Specifically, it checks all constraints for each CAV, selecting the currently active constraints to form a new activity set, which serves as the constraint conditions for subsequent optimization. These candidate constraints are added to the activity set and enforced in equation form. For constraints whose corresponding Lagrange multipliers in the activity set become negative, indicating that the constraint no longer restricts the optimal solution, they are removed and restored to inactive constraints. This iterative process allows the activity set to reflect in real-time constraint changes caused by traffic disturbances such as sudden deceleration of the preceding vehicle, insertion, or compression of distance, providing accurate boundary conditions for subsequent trajectory optimization.

[0108] S33, optimal condition decomposition and solution: Construct the KKT (Karush-Kuhn-Tucker) conditions and their matrix approximations, and solve using the distributed Newton iteration method. Iterative optimization of the distributed control input and Lagrange multipliers of the CAV is used to satisfy the constraints in equation S23 while minimizing the objective function value. The formula is as follows:

[0109] ;

[0110] ;

[0111] ;

[0112] ;

[0113] ;

[0114] In the formula, It is the Lagrangian function derived from the objective function J; and It is the Lagrange multiplier, used to characterize the effect of constraints; This represents the search direction vector for all vehicles (i.e., the entire fleet), used to iteratively update the solution until it converges to the optimal solution. >0 indicates that the variable is updated along the current gradient descent direction, meaning that the acceleration / control quantity needs to be increased. <0 indicates that the variable is updated along the opposite direction, meaning that the acceleration / control quantity needs to be decreased. The acceleration vector representing all vehicles (i.e., the entire convoy) is a decision variable. These are the weights of the constraints, i.e., Lagrange multipliers. These are the weights of the equality constraints, and also the Lagrange multipliers. T denotes transpose. Represents the gradient operator. This represents the Hessian matrix (the matrix of second derivatives).

[0115] Because the KKT matrix K contains coupling terms, Newton's method requires a central solver, where... The control inputs of adjacent CAVs are closely related to the vehicle fleet control dynamics, which are related to the objective function J. It is the gradient of the safety distance constraint, coupled with the states of two adjacent CAVs, but centralized calculation is difficult to meet the computational requirements of real-time control. Therefore, The KKT matrix K in the equation is approximately equal to CAV. i matrix blocks To improve computational efficiency and adapt to distributed optimization frameworks, the following measures are taken:

[0116] ;

[0117] ;

[0118] ;

[0119] in, Indicates CAV i The search direction vector, Indicates CAV i The residual vector includes the gradient term of the Lagrange function, uncoupled constraints, and coupled constraints. Indicates CAV i The corresponding submatrix block, where N represents the Nth vehicle, This indicates a structural approximation operation.

[0120] S34, Synchronization and Global Update: Each CAV communicates across vehicles via the vehicle network, sharing its operational status information (such as position, speed, and control input) in real time and aligning all relevant constraints to ensure that the local solution obtained from distributed optimization meets global consistency requirements. Adjacent vehicles exchange optimized control inputs and status data to correct their respective boundary conditions, thereby generating a globally consistent control input sequence that satisfies all coupled constraints.

[0121] S35, Convergence Check and Termination: During the iteration process, the algorithm checks whether the objective function value tends to stabilize and evaluates whether all key constraints (such as safe following distance and speed limits) are satisfied. If the optimization result meets the preset convergence criteria (the objective function converges to the minimum value and all constraints are satisfied), the algorithm terminates; otherwise, it returns to step S32 to continue updating the activity set and performing optimization iterations.

[0122] S36, Optimal Control Input Execution. After the optimization process is complete, the output optimal control input sequence will be distributed to each vehicle in the sub-platform, enabling them to adjust their speed and spacing according to the planning results, ensuring the smoothness and consistency of platoon operation. In a real traffic environment, this means that vehicles can eliminate traffic ripples in a distributed and coordinated manner, avoid amplifying local disturbances, and improve traffic efficiency and safety.

[0123] This invention decomposes the problem of absorbing shock waves from a large-scale vehicle fleet into a distributed collaborative optimization problem of multiple sub-vehicle fleets through a collaborative mechanism of dynamic decomposition and distributed multi-objective trajectory optimization. Ultimately, it achieves smooth suppression of traffic shock waves on urban expressways, improving road traffic efficiency and driving safety.

[0124] Experimental verification

[0125] To verify the effectiveness of the proposed distributed vehicle fleet cooperative oscillation absorption strategy based on multi-objective optimization, a simulation experiment was designed using the traffic simulation software SUMO to study the generation, propagation, and controlled dissipation of oscillations in bottleneck areas. The simulation was set in an intelligent connected environment where vehicle and surrounding environment information could be perceived in real time and vehicle driving behavior could be precisely controlled. A 1.5 km long urban expressway segment was constructed in the simulation scenario. HDV and CAV adopted the IDM and CACC car-following models, respectively, with mixed traffic flow traveling on the road at an initial speed of 20 m / s. In the simulation, the first vehicle was designated to complete deceleration, stopping, and acceleration at t=75 s, forming a traffic bottleneck area and oscillations. The stopping time lasted for 20 s. Subsequent vehicles followed according to the car-following model, sequentially performing deceleration, stopping, and acceleration. Upstream vehicles successively decelerated and entered the bottleneck area, forming oscillations originating from that location and propagating upstream. After the oscillation wave is formed, the control effects of the proposed strategy on absorbing the oscillation wave, reducing traffic flow instability and the risk of vehicle collision are compared and analyzed, based on the Jam-absorption Driving (JAD) strategy based on wavelet transform, the JAD strategy that completely eliminates traffic oscillation, and the strategy proposed in this section.

[0126] Figure 3 The spatiotemporal trajectory diagrams of the vehicle under different control methods are shown. Figure 3 (a) is the spatiotemporal trajectory of vehicles under uncontrolled conditions. The speed of vehicles downstream of the oscillation zone is limited, resulting in a decrease in speed and the formation of a fixed bottleneck oscillation wave, which exacerbates traffic flow fluctuations and traffic delays. Figure 3 (b) is the trajectory diagram under the full JAD strategy without considering the bottleneck speed limit (full JAD strategy). Due to the imbalance in the coordination of speed and spacing between "slow in" and "fast out", the "fast out" phase accelerates to form a dissipation wave, but decelerates again at the bottleneck speed limit, resulting in the generation of a secondary wave. Fixing the "fast out" acceleration position at the bottleneck and executing speed limit is the key to avoiding the spread of the secondary wave and absorbing the bottleneck oscillation wave. Figure 3 (c) and Figure 3 (d) shows the trajectories of the WT-JAD strategy (a JAD strategy based on wavelet transform) and the WT-WOA oscillation absorption strategy (an oscillation absorption strategy that combines wavelet transform and whale optimization algorithm). Although the WT-WOA-based oscillation absorption strategy is better than the WT-JAD strategy in identifying and predicting the start and end times of the oscillation, it still forms a secondary wave due to the limitations of the fleet length and the controlled vehicles. Therefore, fleet cooperative control becomes the key to reduce the propagation of the oscillation and enhance the stability of the fleet by localizing the disturbance. Figure 3(e) illustrates the trajectory under this strategy, where the convoy is divided into two sub-convoys to effectively absorb shock waves. Although the first sub-convoy still generates secondary waves, the second sub-convoy absorbs them in time, preventing their upstream propagation and achieving localized elimination of the shock waves. Therefore, this strategy reduces shock wave propagation and improves convoy stability through convoy coordination.

[0127] Figure 4 This demonstrates the changes in vehicle speed under different control strategies. For example... Figure 4 As shown in (a), in an uncontrolled scenario, vehicles exhibit significant speed fluctuations when passing through traffic bottlenecks, even dropping to 0 m / s and remaining there for a period of time, reflecting queuing phenomena at the oscillation points, leading to traffic flow instability and delays; Figure 4 As shown in (b), the oscillation wave absorption strategy based on WT-WOA effectively reduces the speed fluctuation of the following vehicle fleet by adjusting the speed of the absorbing vehicle, but it is limited to single vehicle control and the overall cooperative stability of the fleet is still limited. Figure 4 (c) demonstrates the effectiveness of the fleet cooperative control strategy. By splitting the fleet and achieving speed coordination between sub-fleets, the overall speed fluctuation of the fleet is significantly reduced, improving traffic flow stability and efficiency. Compared with single-vehicle control, fleet cooperative control effectively improves fleet stability through the reduction of local disturbances and global coordination.

[0128] Figure 5 The effects of different control strategies on vehicle acceleration fluctuations were demonstrated, among which... Figure 5 (a) is a no-control policy. Figure 5 (b) is the WT-JAD strategy. Figure 5 (c) is a platoon-coordinated oscillation absorption strategy. Without a control strategy, vehicle acceleration fluctuations are significant, especially in the middle of the platoon, leading to traffic flow instability and potential safety issues. The WT-WOA-based oscillation absorption strategy reduces acceleration fluctuations by optimizing the control scheme, improving platoon stability and coordination, and reducing the propagation of oscillations caused by speed differences. This strategy further reduces platoon acceleration fluctuations, particularly affecting upstream platoons, effectively absorbing oscillations through coordinated control, enhancing overall stability and coordination, and ensuring safe and smooth traffic flow. Therefore, this strategy has significant advantages in reducing acceleration fluctuations and improving platoon stability.

[0129] Depend on Figure 6 It is evident that different oscillation absorption strategies exhibit significant differences in their effectiveness in controlling speed fluctuations during the acceleration and deceleration of vehicle convoys. From a time-dimensional perspective, such as... Figure 6 As shown in (a), compared to other control methods, the strategy of this invention reduces the speed standard deviation by approximately 17.45% and exhibits the smallest standard deviation fluctuation, demonstrating its advantages in limiting vehicle speed fluctuations and improving driving stability. In the spatial dimension, as... Figure 6 As shown in (b), the strategy of this invention is particularly effective in controlling the speed standard deviation of vehicles in the middle and later stages (numbered 8-20), reducing it by approximately 34.73%, effectively minimizing speed fluctuations in subsequent vehicles. The multi-vehicle coordination mechanism, by splitting the vehicle fleet into sub-vehicle fleets, localizes disturbances and enhances cooperative suppression, suppressing the accumulation of oscillations in upstream vehicles. Further analysis shows that when the fleet size exceeds 12 vehicles, structural decoupling effectively slows down the rate of increase in standard deviation, indicating that this strategy can maintain stability and control effectiveness even in large-scale fleets. In summary, this strategy demonstrates excellent performance in the initial stage of oscillation absorption and in the control of large-scale fleets, possessing strong adaptability and providing an effective solution for fleet stability control.

[0130] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0131] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A multi-objective optimization based distributed platoon coordinated shockwave absorption method, characterized by the steps of The application relates to a method for controlling a mixed flow vehicle team to pass through a traffic shock zone. The method comprises the following steps: S1, acquiring a scene in which a mixed flow vehicle team passes through a traffic shock zone, dividing the vehicle team, and determining key parameters; S2, constructing an optimal control model to solve an optimal vehicle team splitting point, and splitting the mixed vehicle team; S3, based on an improved AS-OCD distributed trajectory optimization algorithm, synchronously controlling each sub-vehicle team to completely absorb a traffic shock wave; The specific steps of S3 are as follows: ； ； wherein is the acceleration of the vehicle , is the acceleration of the vehicle , denotes a constraint term involving two or more vehicles, upon activation of which an equation is formed, denotes a hard constraint for a single vehicle; S31, based on the running state of the head vehicle of the vehicle team, initializing the AS-OCD algorithm, incorporating the constraints meeting the boundary into the active set, and solving the initial optimization problem through the Lagrange multiplier, outputting an initial solution and the Lagrange multiplier corresponding to each constraint, and clearly defining the equation constraints that are activated under the current running state and that truly affect the safety and stability of the vehicle, as shown in the following formula: S32, active set iteration, traversing all constraint dynamic filters of the networked automatic driving vehicle, identifying and marking the constraints triggered under the current running state as candidate activated items, and adding the candidate constraints into the active set and executing them in the form of equations; if the corresponding Lagrange multiplier in the active set becomes negative, the constraint is removed and restored to an inactive constraint; ； ； ； ； ； wherein is a Lagrangian function derived from the objective function J; and is a Lagrangian multiplier, denotes a search direction vector for all vehicles, denotes an acceleration vector for all vehicles, is a decision variable, is a weight of a constraint condition, is a weight of an equality constraint, T denotes a transpose, denotes a gradient operator, denotes a Hessian matrix; The KKT matrix K is approximated as a matrix block of CAV i , as follows:​ ； ； ； wherein denotes the search direction vector of the CAV i , denotes the residual vector of the CAV i , denotes the corresponding submatrix block of the CAV i , N denotes the Nth vehicle, denotes the structure approximation operation; S33, optimal condition decomposition solution, constructing a KKT condition and a matrix approximation thereof, and solving the condition by using a distributed Newton iteration method, optimizing the distributed control input of the networked automatic driving vehicle and the Lagrange multiplier through iteration, so that the constraint conditions in step S23 are met, and the objective function value is minimized, as shown in the following formula: S34, synchronization and global update, each networked automatic driving vehicle communicates across vehicles through vehicle networking, shares the running state information of each vehicle in real time, aligns all the constraint conditions involved, exchanges the optimized control input and state data between adjacent vehicles, and uses the data to correct the boundary conditions of each vehicle, so that the control input sequence consistent in the global range and meeting all coupled constraints is generated; S35, convergence check and termination, checking whether the objective function value tends to be stable in the iteration process, and evaluating whether all key constraints are met, if the optimization result reaches the preset convergence standard, the algorithm is terminated, otherwise, returning to step S32 to continue the active set update and optimization iteration; 2. The method of claim 1, wherein, S36, optimal control input execution, after the optimization process is completed, the optimal control input sequence output is issued to each sub-vehicle team, so that the speed and distance of each vehicle are adjusted according to the planning result, and the stability and consistency of the queue running are ensured. The specific steps of S1 are as follows: For networked autonomous vehicles, maximum number of following vehicles Directly determined by the number of information transfer layers in the vehicle topology The expected distance between two adjacent vehicles in the sub-platoon The sum of the distance traveled by the vehicle within the maximum delay and the expected safety distance ​ For manually driven vehicles, maximum number of following vehicles Decided by the communication effective distance of the vehicle The total length of the sub-platoon ≤ the communication effective distance ; maximum number of vehicles of the sub-platoon , wherein denotes taking the minimum value; S12, determine the distance between the sub-platoon, the head vehicle of adjacent sub-platoon must be within the communication effective distance , and the expected following distance D between the sub-platoon is greater than the length of the front sub-platoon; S13, determining the number of sub-platoons, in a multi-platoon system, the maximum number of sub-platoons is limited by the number of sub-platoons affected by the topology and the number of sub-platoons affected by the controller stability jointly, where n p,max is the maximum number of sub-platoons, denotes taking the minimum value.

3. The method of claim 1, wherein, S11, determining the distance between the vehicles in the sub-vehicle team and the number of vehicles following the sub-vehicle team; S21, introducing binary variables to describe the location of the platoon split, i = 1 indicates that the platoon splits before the 1st vehicle, i = N indicates that the platoon splits between the N-1st and Nth vehicles, i = N+1 indicates that the platoon splits after the Nth vehicle, imposing a unique split point constraint, an earliest pass constraint for the front sub-platoon, and an earliest pass constraint for the rear sub-platoon; The specific steps of S2 are as follows: S22, determining the safety time interval, the speed difference between the last vehicle of the front sub-vehicle team and the first vehicle of the rear sub-vehicle team, as shown in the following formula: ； wherein L i represents the length of the CAV i plus the minimum following distance, CAV i represents vehicle i and vehicle i is a connected and automated vehicle, τ is the baseline safety time gap, δ1 is a time gap conservatism factor, δ2τ(v i (t) - v i-1 (t)) is the speed difference, δ2 is a speed difference coefficient, represents the position of the CAV i-1 at time t, CAV i-1 represents vehicle i-1 and vehicle i-1 is a connected and automated vehicle, represents the position of the CAV i at time t, represents the speed of the CAV i at time t, represents the speed of the CAV i-1 at time t. S23, based on S21-S22, construct the objective function of the vehicle fleet splitting algorithm The formula is as follows: ； In the formula, denotes the minimum value, is the energy consumption objective function, is the risk objective function, and α1 and α2 respectively represent the weight coefficients of the objective functions , , is the speed of vehicle i at time t; is the acceleration of vehicle i at time t.

4. The method of claim 3, wherein, The unique split point constraint: requires that there must be and only one split point in the mixed flow fleet, all binary variables have a value of 1 and the rest have a value of 0; The front sub-platoon is constrained to arrive at the split point i with the last vehicle CAV of the front sub-platoon at the latest at the split time i-1 must pass its corresponding oscillation end position before its oscillation end time ; The latest through constraint: split point is i, the last vehicle of the rear sub-platoon CAV i At the end of its oscillation , it must not pass its corresponding oscillation end position .

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