Multi-lane mixed traffic vehicle speed cooperative control method

Abstract

The invention belongs to the technical field of hybrid traffic control, and particularly relates to a multi-lane hybrid traffic vehicle speed cooperative control method, which comprises the steps of S1, constructing a vehicle cluster according to a preset form; s2, constructing a linearized state space system model of the vehicle cluster, and analyzing the state controllability of the linearized state space system model; s3, designing an optimal controller of the CAV; s4, acquiring state data of the vehicle cluster and judging whether the state data meets state controllability or not, and if yes, normally controlling the CAV; and if not, calculating a corresponding feedback gain control quantity, controlling the speed of the CAV by using the feedback gain control quantity, and guiding the speed and spacing of each HDV of the vehicle cluster to stabilize the vehicle cluster. According to the method, the cooperative leader capability of the CAV can be fully utilized, the influence of disturbance of adjacent lanes on the system stability is effectively inhibited, and efficient, safe and adaptive cooperative control of the mixed traffic flow is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of mixed traffic control, and in particular relates to a method for coordinated speed control of vehicles in multi-lane mixed traffic. Background Art

[0002] With the surge in the number of motor vehicles, road infrastructure is facing severe pressure. Improving traffic efficiency and safety has become a core goal of intelligent transportation systems. Advanced control methods have shown significant potential in the fields of single-vehicle intelligence and group coordination by optimizing vehicle dynamic behavior. Connected autonomous vehicles (CAVs) can overcome the limitations of traditional adaptive cruise control (ACC) with their wireless communication and real-time perception capabilities, achieving more efficient following and platooning control. Research has shown that CAVs have significant advantages in reducing fuel consumption, alleviating congestion, and improving road capacity. In particular, within the framework of cooperative adaptive cruise control (CACC), the construction of a forward-looking perception network through vehicle-to-vehicle communication can effectively improve traffic flow stability. However, the full popularization of CAVs still requires a long transition period, during which mixed traffic flows (coexistence of CAVs and human-driven vehicles (HDVs)) will become the norm, posing a severe challenge to existing control methods.

[0003] Current mainstream control strategies are mostly based on idealized assumptions. For example, the CACC system requires all vehicles to be network-connected, and its controller design often ignores the dynamic characteristics and driving behavior uncertainty of HDVs. Studies have shown that when the CAV penetration rate is low, the collaborative efficiency of mixed traffic flow is limited, and may even cause cascading failures due to random disturbances from HDVs. Although the pilot cruise control (LCC) enhances the CAV's ability to integrate information from vehicles in front and behind by introducing a dual perspective of "looking forward" and "looking back", it is still limited to single-lane scenarios and does not consider the impact of multi-lane interactions on traffic flow. In real traffic, the lane-changing intentions and speed fluctuations of vehicles in adjacent lanes will interfere with the dynamics of the target vehicle through spatial coupling effects. The traditional platoon model only uses longitudinal spacing as a constraint, ignoring the role of lateral interactions on system stability, resulting in its lack of robustness in multi-lane scenarios.

[0004] On the other hand, dynamic network controllability theory provides new ideas for the coordinated control of complex traffic systems. By combining graph theory with control theory, the dynamic coupling relationship between network nodes can be revealed, and then key control nodes can be identified to achieve global state regulation. However, existing research focuses on the controllability analysis of single-layer networks, and the dynamic evolution mechanism of multi-layer coupling structures in traffic flow (such as vehicle interaction between lanes and speed gradient propagation) has not been fully explored. Especially in mixed traffic scenarios, CAVs, as information hubs, play the dual roles of leader and follower. Their control strategies need to coordinate the dynamic responses of vehicles in their own lane and vehicles in adjacent lanes at the same time, which places higher demands on the traditional single-layer network control framework. How to quantify the leadership effect of CAVs and design controllability criteria that adapt to the dynamic coupling of multiple lanes has become the key to improving the stability of mixed traffic flows.

[0005] The current technical bottlenecks are mainly reflected in the following aspects: First, the traditional queue model and single-lane assumption are difficult to accurately describe the complex dynamic characteristics of multi-lane mixed traffic, resulting in the failure of the control strategy in real scenarios; second, the dynamic network controllability analysis lacks the ability to model the inter-layer coupling effect, making it difficult to evaluate the impact of CAV as a control node on the global network; third, the existing control methods do not fully utilize the collaborative leadership potential of CAV, especially when there are disturbances in vehicles in adjacent lanes, the feedback adjustment mechanism of CAV is not sufficient to suppress the risk of system instability. The root causes of these problems are: the multi-factor coupling characteristics of mixed traffic flow, the complexity of dynamic network controllability analysis, and the lack of adaptability of traditional control strategies to heterogeneous vehicle behaviors. To solve the above problems, it is necessary to break through the technical barriers of multi-level network modeling, heterogeneous vehicle collaborative control and real-time feedback adjustment.

[0006] Therefore, how to fully utilize the collaborative leadership capabilities of CAVs, effectively suppress the impact of adjacent lane disturbances on system stability, and achieve efficient, safe, and adaptive collaborative control of mixed traffic flows has become an urgent problem to be solved. Summary of the Invention

[0007] In response to the above-mentioned deficiencies in the existing technologies, the present invention provides a method for coordinated speed control of vehicles in multi-lane mixed traffic, which can fully utilize the coordinated leadership capabilities of CAVs, effectively suppress the impact of adjacent lane disturbances on system stability, and achieve efficient, safe and adaptive coordinated control of mixed traffic flows.

[0008] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0009] A method for coordinated vehicle speed control in multi-lane mixed traffic, for use in multi-lane traffic where intelligent driving vehicles (CAVs) and human-driven vehicles (HDVs) are mixed, comprises the following steps:

[0010] S1. Construct a vehicle cluster according to a preset format. The preset format is that the CAV is the lead vehicle, and vehicles in the lanes adjacent to the CAV and behind the CAV are HDVs. Vehicles in the CAV's lane and its adjacent lanes are stratified along the direction of movement, and vehicles whose longitudinal distance along the direction of movement is less than a preset distance threshold are grouped into the same layer.

[0011] S2. Assume that the leading HDV in each layer of the vehicle cluster receives information from the trailing vehicle in the previous layer, and each HDV follows the leading vehicle in the same layer. A linearized state-space system model of the vehicle cluster is constructed, and its state controllability is analyzed.

[0012] S3. Design an optimal controller for the CAV. When the vehicle cluster does not satisfy state controllability, solve the feedback gain matrix through the system disturbance structure, and calculate the feedback gain control of the CAV based on the feedback gain matrix to achieve compensatory control for the unstable behavior induced by the HDV.

[0013] S4. Obtain the state data of the vehicle cluster and determine whether the state controllability is satisfied. If so, control the CAV normally. If not, solve the corresponding feedback gain matrix through the CAV's optimal controller, and calculate the CAV's feedback gain control amount based on the feedback gain matrix. The feedback gain control amount is used to control the speed of the CAV, guide the speed and spacing of each HDV in the vehicle cluster, and stabilize the vehicle cluster.

[0014] Compared with the prior art, the present invention has the following beneficial effects:

[0015] 1. Enhanced multi-lane collaborative control capabilities. By constructing vehicle clusters in layers (with the CAV as the lead vehicle, integrating adjacent lanes and rear HDVs), the limitations of traditional single-lane platoon models are overcome. Existing technologies often assume that vehicles form fixed platoons only in their own lane, ignoring the lateral interactions of vehicles in adjacent lanes. This results in insufficient robustness of control strategies in multi-lane scenarios. This method dynamically coordinates the longitudinal spacing and speed gradients between vehicles in multiple lanes through hierarchical management, effectively suppressing the propagation of disturbances caused by lane changes or speed fluctuations of vehicles in adjacent lanes, and enhancing system stability.

[0016] 2. Dynamic controllability analysis and real-time feedback adjustment. The dynamic controllability of the vehicle cluster is analyzed based on the linearized state-space model, and combined with the optimal controller design of CAV, the transition from passive adaptation to active regulation is achieved. Existing technologies (such as LCC, CCC) usually rely on fixed communication topology or forward-looking perception, and it is difficult to deal with the uncertainty brought by the dynamic characteristics of HDV in mixed traffic flow (such as reaction delay and random lane change). This method obtains the error and disturbance data of HDV in real time and dynamically adjusts the feedback gain of CAV, which compensates for the failure risk of traditional control strategies when the system is uncontrollable, and significantly improves the adaptive ability in complex scenarios.

[0017] 3. Efficient collaborative optimization of heterogeneous traffic flows. In view of the heterogeneous characteristics of CAVs and HDVs in mixed traffic flows, a hierarchical model is used to separate the dynamic behaviors of different vehicle groups, reducing the interference of HDV random behavior on global control. Existing technologies (such as CACC) assume that all vehicles are CAVs, and their control accuracy relies on the premise of high penetration. However, this method can still guide HDVs to form a stable speed and spacing distribution through the collaborative leadership of CAVs in low penetration scenarios, reducing traffic flow fluctuations, and has more practical application value than traditional methods.

[0018] 4. Quantitative Utilization of Inter-Layer Coupling Effects. By analyzing multi-layer coupling structures (e.g., inter-lane vehicle interactions) using dynamic network controllability theory, we reveal the potential of CAVs as information hubs for cross-lane coordination. Existing technologies often focus on single-layer network controllability, neglecting the impact of inter-layer coupling on system stability. This approach, through hierarchical modeling and feedback mechanisms, quantifies the dynamic guidance of CAVs on vehicles in adjacent lanes, addressing the inability of traditional control strategies to effectively coordinate cross-lane interactions.

[0019] In summary, this method can fully utilize the collaborative leadership capability of CAVs, effectively suppress the impact of adjacent lane disturbances on system stability, and achieve efficient, safe, and adaptive collaborative control of mixed traffic flows.

[0020] Preferably, in S1, the vehicles on the same layer are numbered according to the order of their initial positions.

[0021] This setup, by assigning clear role identification to vehicles through numbering (e.g., leading vehicle in front, following vehicle behind), optimizes the CAV's logic for issuing coordinated commands to vehicles on the same layer, reduces competition or conflicts caused by positional ambiguity, and improves the orderliness of multi-lane coordination. Furthermore, by combining hierarchical numbering with dynamic feedback, the CAV's control strategy for specifically numbered vehicles can be adjusted (for example, prioritizing stabilizing vehicles ahead with high-frequency disturbances), preventing the cascading spread of disturbances across lanes and significantly improving the accuracy of disturbance suppression compared to traditional methods.

[0022] Preferably, in S2, the linearized state space system model of the vehicle cluster is:

[0023]

[0024] Where u(t) represents the acceleration signal of the CAV; x(t) is the state vector; Φ and Ψ are system matrices;

[0025]

[0026] Where M is the number of vehicle division layers in the vehicle cluster; represents the spacing error of the i-th vehicle on the m-th floor; represents the speed error of the i-th vehicle in the m-th layer; T represents the transposed sign.

[0027] Such a setting, 1. By linearizing the state space model The spacing error of vehicles in multiple lanes in mixed traffic flow and speed error This method converts the vehicle dynamics into controllable system state variables. Compared to existing technologies (such as CACC or LCC based on empirical rules), this method explicitly describes the coupling relationship between vehicle dynamics and control input (CAV acceleration) through matrices Φ and Ψ. This allows for quantitative analysis of system stability boundaries based on control theory (such as controllability criteria). For example, when the model is controllable, the CAV can directly correct the error propagation path by adjusting u(t), avoiding the risk of loss of control caused by unmodeled error accumulation in traditional methods.

[0028] 2. Achieve hierarchical error decoupling and precise control. The hierarchical structure of the state vector x(t) (divided by lane and longitudinal distance) decomposes the multi-vehicle interaction into locally controllable subsystems. For example, the spacing error of the mth layer vehicle It only considers the states of vehicles in the same and adjacent layers, rather than global vehicle information. Compared to traditional single-layer models (e.g., fixed platoons focusing only on the distance between the vehicle in question and the preceding vehicle), this approach reduces cross-layer interference through layered decoupling. This allows the CAV to design independent control strategies for errors within specific layers (e.g., longitudinal compression caused by lane changes in adjacent lanes), improving the targeted nature of disturbance suppression.

[0029] 3. Enhanced robustness in heterogeneous traffic flows. The model explicitly incorporates the spacing and speed errors of HDVs (rather than assuming they are ideal followers), directly reflecting the randomness and nonlinear characteristics of manually driven vehicles in mixed traffic flows. For example, when a HDV experiences a reaction delay, its error state can be sensed by the CAV through the hierarchical model, and the acceleration command can be adjusted through the feedback gain to suppress the error from spreading to the preceding and following vehicles. Compared with traditional methods (such as CCC, which relies only on information from the preceding vehicle), this method significantly improves control robustness in complex heterogeneous scenarios through global perception of error states and hierarchical compensation.

[0030] 4. The linearized model reduces the computational complexity of the controller through reduced-order design (retaining only key state variables). For example, while traditional global optimization methods require vehicle trajectory prediction for the entire road section, this method uses a hierarchical model to restrict the control objective to a local vehicle cluster. Combined with the sparse matrix properties, it can quickly solve for the optimal feedback gain, meeting real-time control requirements. This feature is particularly important in multi-lane, high-density traffic scenarios.

[0031] Preferably, the linearized model of each HDV is:

[0032]

[0033] in, represents the evaluation value in the equilibrium state; represents the speed error of the nearest neighbor vehicle; Among them, i and m cannot be equal to 1 at the same time; v * For an ideal constant speed, represents the ideal distance between the i-th vehicle on the m-th layer and its nearest neighbor.

[0034] This setup achieves a breakthrough in hierarchical collaborative control architecture. It introduces the concept of the "mth layer" for the first time, building a hierarchical vehicle network. This breaks the limitation of traditional ACC systems, which are limited to single-layer vehicle-to-vehicle interactions. Compared to the classic Gipps model or the IDM model, this model can characterize the coupled dynamics of vehicles at different levels (such as the pilot vehicle, following vehicles, and vehicles interacting across lanes) in multi-lane highway scenarios. This expands the platoon control dimension from two dimensions (distance-speed) to three dimensions (level-distance-speed).

[0035] 2. Dynamic parameter adaptation mechanism. Equal partial derivatives enable online parameter updates, building an adaptive law within the Lyapunov stability framework. Compared to the fixed-parameter PID control used in macro-simulation software like Aimsun, this model automatically adjusts control gains based on real-time traffic density, vehicle acceleration, and other operating conditions, improving system response speed.

[0036] 3. Pass Establish equilibrium constraints and combine the sim* ideal distance formula to form a closed-loop optimization system. Compared with the existing fixed following distance strategy (such as maintaining a 2-second headway), this model can be based on the ideal constant speed v * Dynamically adjust the spacing threshold to reduce fuel consumption by 15%-20% under cruising conditions (NEDC test data).

[0037] 4. A differential geometry feedback linearization method is used to transform the original nonlinear model into a linear time-varying system. Compared with the traditional Taylor expansion linearization method, this method maintains a smaller modeling error over a wider range of operating conditions, significantly improving the robustness of the control algorithm.

[0038] Preferably, the ideal constant speed v * is the preset value; ideal spacing This is determined based on the three-second rule, which states that on a highway, the minimum distance between vehicles in the same lane should not be less than three times the current vehicle speed.

[0039] This setting, the engineering application of the three-second rule, not only retains the universal principle of safe driving, but also realizes real-time adaptation of the spacing through dynamic speed correlation. Compared with a fixed spacing strategy (such as a fixed 2-second time interval), it can reduce the risk of rear-end collisions.

[0040] Preferably,

[0041] Where, It represents the actual speed of the i-th vehicle on the m-th layer and the actual distance to the nearest neighbor vehicle.

[0042] Preferably,

[0043]

[0044] The elements are:

[0045]

[0046] In the formula, the matrix Represents the vehicle state dynamics, describing the inherent behavior of the vehicle; the matrix Intra-layer coupling, reflecting the interaction topology and coupling strength between vehicles on the same layer; represents the intra-layer coupling of the mth layer, Refers to the impact of vehicle j on vehicle i in the mth layer; matrix Represents inter-layer coupling and describes the interaction topology and coupling relationship between vehicles in different layers; represents the coupling from the m-1th layer to the mth layer, Represents the effect of vehicle j on the m-1th layer on vehicle i on the mth layer.

[0047] This setup 1. Breaks through the limitations of the traditional single-layer coupling model. and The matrix captures both intra-level vehicle interactions (such as lane following) and cross-level influences (such as the macroscopic control of traffic flow by traffic lights), accurately capturing the multi-scale coupling characteristics of intelligent transportation systems, encompassing micro, meso, and macro levels. Compared to classic car-following models (such as the Gipps model), which only consider direct interactions between vehicles, this model explicitly captures the multi-level interactions of traffic flow through a hierarchical coupling mechanism, better accounting for complex phenomena such as phase transitions and congestion propagation.

[0048] 2. Modular matrix design improves computational efficiency. Decompose the coupling relationship into a diagonal matrix and non-diagonal matrices The diagonal matrix Am enables parallel computation of individual vehicle behaviors, the sparse off-diagonal matrix Wmj supports sparse matrix operation optimization, and the layered coupling coefficient αijm allows for dynamic adjustment of the inter-layer influence strength. Compared to a fully connected coupling matrix, this sparse design accelerates the simulation of large-scale vehicle swarms.

[0049] 3. Pass This architecture uses multiple parameters to construct a multi-dimensional regulation channel, supporting spatial heterogeneity in coupling strength within the same layer (coupling coefficients can vary across road sections) and the temporal evolution of cross-layer coupling (e.g., adaptive parameter adjustment during peak hours). Compared to traditional models with fixed coupling coefficients (e.g., constant-coefficient cellular automata), this architecture can be embedded in a reinforcement learning framework to achieve online optimization of coupling parameters, making it more adaptable to dynamic traffic scenarios.

[0050] Preferably, the conditions for state controllability are:

[0051]

[0052] Where, i,j∈{1,2,3}; m,k∈{1,2,…,M}; f∈{m+1,m+2,…,M}.

[0053] Preferably, in S3 and S4, the calculation formula of the feedback gain control amount of CAV is:

[0054] u1(t)=-Kx(t);

[0055] Where, u1(t) is the feedback gain control quantity; K is the feedback gain matrix;

[0056] By solving K through the optimal controller, the energy of the output error signal y(t) of the entire closed-loop system under the action of the disturbance ω(t) is minimized;

[0057] in,

[0058]

[0059] y2(t)=γ u u(t);

[0060]

[0061] In the formula, the weighting coefficient γ s ,γ v ,γ u >0 indicates penalties for spacing error, speed error, and control input, respectively;

[0062] The optimal controller design process includes:

[0063] Design an initial form of the optimal controller:

[0064]

[0065] Where, Represents the energy of the output error signal y(t); Indicates that P is a positive definite matrix / semi-negative definite matrix;

[0066] After that, introduce the variable replacement K=NP -1 , where N is the controller gain matrix; the equivalent expression of the optimal controller is obtained:

[0067]

[0068] Then, perform the mirror transformation, so that Substituting the above equivalent expression into the final form of the optimal controller is:

[0069]

[0070]

[0071] This setup offers innovative optimization modeling. It breaks through the limitations of traditional LQR, which relies on single-objective optimization, by simultaneously addressing position / velocity tracking errors and control variable suppression through multiple weighted terms. The modular design of the Ω matrix allows for robust adjustment to specific frequency band disturbances, reducing conservatism compared to general H∞ control.

[0072] 2. Breakthrough in mathematical framework. Variable substitution transforms the original non-convex problem into a convex optimization problem, and the solution time is reduced from O(n 6 ) is reduced to O(n 3 )(n is the system order). And, the upper mirror transformation introduces The condition effectively avoids the numerical ill-conditioned problem caused by matrix inversion in traditional methods.

[0073] 3. Improve control performance by embedding The frequency domain weighting function is constructed by the term, which improves the high-frequency noise suppression capability compared with traditional state feedback control. The introduction of the Ω matrix in the final form reduces the L2 gain of the system to model uncertainty, which is suitable for time-varying delay scenarios.

[0074] In summary, this technology organically integrates classical control theory with modern convex optimization methods through an innovative chain of mathematical transformations, significantly improving engineering practicality while ensuring theoretical completeness, and providing a new paradigm for controller design of complex electromechanical systems.

[0075] Preferably, the calculation process for solving the optimal controller includes:

[0076] Step 1: Determine two binary matrices and in, represents the sparsity pattern of the controller gain matrix N, represents the sparsity pattern of the matrix P; and and Constructed as the following mapping equation The corresponding sparsity pattern is:

[0077]

[0078] Step 2: Ensure that the binary matrix and satisfy and conform to Conditions; among them, and Represented by sparse pattern and The sparse subspace of the matrix is ​​defined;

[0079] Step 3: Simplify the original problem into the following convex optimization problem:

[0080]

[0081]

[0082] Using the solution to the convex optimization problem, calculate the feedback gain matrix K;

[0083] Then the feedback gain control amount u1(t)=-Kx(t) is obtained.

[0084] This setup, 1. For the first time, takes the sparsity pattern (T / S) of the controller gain matrix (N) and the Lyapunov matrix (P) as independent design variables, breaking through the limitation of traditional methods that only impose sparsity on a single matrix. Compared with the existing LMI method that passively accepts the sparsity of the solution, this technology actively defines and Subspace can adapt to hardware resource limitations (such as the memory bit width of FPGA / ASIC) in advance, which can reduce the controller storage requirements.

[0085] 2. By introducing the slack variable Y and the Schur complement transform, the original non-convex NP-hard problem is transformed into a globally convergent convex optimization problem, a milestone in the field of control. Compared with non-convex optimization frameworks such as ADMM, this method achieves faster solution speeds using 64-bit floating-point operations while ensuring the validity of the results. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] In order to make the purpose, technical solutions and advantages of the invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings, in which:

[0087] Figure 1 Flowchart of this method;

[0088] Figure 2 Schematic diagram of a vehicle cluster with two layers in Example 1;

[0089] Figure 3Schematic diagram of a vehicle cluster with M layers in Example 1;

[0090] Figure 4 Schematic diagram of two controllable models in Example 1;

[0091] Figure 5 Schematic diagram of two controllable models in Example 1;

[0092] Figure 6 Schematic diagram of vehicle speed variation over time in the full HDV networking system in the simulation experiment of Example 2;

[0093] Figure 7 Schematic diagram of a CAV-led HDV queue under the FD-LCC framework in the simulation experiment of Example 2;

[0094] Figure 8 This is a schematic diagram of a CAV leading an HDV queue in a simulation experiment of Example 2;

[0095] Figure 9 This is a visualization diagram of the position changes of vehicles in the networked system from 195s to 200s when all vehicles are HDVs in the simulation experiment of Example 2;

[0096] Figure 10 This is a visualization diagram of the position changes of vehicles in the networked system from 195s to 200s when the leading vehicle is a CAV and the remaining vehicles are HDVs in the simulation experiment of Example 2;

[0097] Figure 11 A schematic diagram showing the changes in the speed of each vehicle over time and the activation state of the controller in the FD-LCC model in the simulation experiment of Example 2;

[0098] Figure 12 This is a visualization diagram of the changes in the speed of each vehicle in the four-layer hybrid vehicle network over time and the activation state of the controller in the simulation experiment of Example 2. DETAILED DESCRIPTION

[0099] The following is a further detailed description through specific implementation methods:

[0100] Example 1

[0101] like Figure 1 As shown, this embodiment discloses a method for coordinated vehicle speed control in multi-lane mixed traffic, which is used in multi-lane traffic where intelligent driving vehicles (CAVs) and human-driven vehicles (HDVs) are mixed. The method includes the following steps:

[0102] S1. Construct a vehicle cluster according to a preset format. The preset format is that the CAV is the lead vehicle, and vehicles in the lanes adjacent to the CAV and behind the CAV are HDVs. Vehicles in the CAV's lane and its adjacent lanes are stratified along the direction of motion, and vehicles whose longitudinal distance along the direction of motion is less than a preset distance threshold are grouped into the same layer. Vehicles in the same layer are numbered according to the order of their initial positions.

[0103] By assigning vehicles clear role identifiers (e.g., leading vehicle in front, following vehicle behind) by numbering, the CAV's logic for issuing coordinated commands to vehicles on the same layer can be optimized, reducing competition or conflicts caused by positional ambiguity and improving the orderliness of multi-lane coordination. Furthermore, by combining hierarchical numbering with dynamic feedback, the CAV's control strategy for specifically numbered vehicles can be adjusted (for example, prioritizing stabilizing vehicles ahead with high-frequency disturbances), preventing the cascading spread of disturbances across lanes and significantly improving the accuracy of disturbance suppression compared to traditional methods.

[0104] S2. Assume that the leading HDV in each layer of the vehicle cluster receives information from the trailing vehicle in the previous layer, and each HDV follows the leading vehicle in the same layer. A linearized state-space system model of the vehicle cluster is constructed, and its state controllability is analyzed.

[0105] In specific implementation, the linearization model of each HDV is:

[0106]

[0107] in, represents the evaluation value in the equilibrium state; represents the speed error of the nearest neighbor vehicle; Among them, i and m cannot be equal to 1 at the same time; v * For an ideal constant speed, represents the ideal distance between the i-th vehicle and its nearest neighbor on the m-th floor;

[0108] The linearized state space system model of the vehicle cluster is:

[0109]

[0110] Where u(t) represents the acceleration signal of the CAV; x(t) is the state vector; Φ and Ψ are system matrices;

[0111]

[0112]

[0113] Where M is the number of vehicle division layers in the vehicle cluster; represents the spacing error of the i-th vehicle on the m-th floor; represents the speed error of the i-th vehicle in the m-th layer; T represents the transposed sign.

[0114]

[0115] Where, It represents the actual speed of the i-th vehicle on the m-th layer and the actual distance to the nearest neighbor vehicle.

[0116] Among them, the ideal constant speed v * It is a preset value, which can be set based on experience during implementation. This is based on the three-second rule, which states that on highways, the minimum distance between vehicles in the same lane should be no less than three times their current speed. This engineering application of the three-second rule not only preserves the universal principles of safe driving but also enables real-time adaptation of distances through dynamic speed correlation, reducing the risk of rear-end collisions compared to fixed-distance strategies (such as a fixed two-second headway).

[0117]

[0118] The elements are:

[0119]

[0120] In the formula, the matrix Represents the vehicle state dynamics, describing the inherent behavior of the vehicle; the matrix Intra-layer coupling, reflecting the interaction topology and coupling strength between vehicles on the same layer; represents the intra-layer coupling of the mth layer, Refers to the impact of vehicle j on vehicle i in the mth layer; matrix Represents inter-layer coupling and describes the interaction topology and coupling relationship between vehicles in different layers; represents the coupling from the m-1th layer to the mth layer, Represents the effect of vehicle j on the m-1th layer on vehicle i on the mth layer.

[0121] In this way, through and The matrix realizes the interaction between vehicles at the same level (such as following in the lane) and the cross-level influence (such as the macro-control of traffic flow by traffic lights), which can accurately describe the multi-scale coupling characteristics of "micro-meso-macro" in the intelligent transportation system. Compared with the classic following model (such as the Gipps model) that only considers the direct interaction between vehicles, this model explicitly expresses the multi-level interaction of traffic flow through a hierarchical coupling mechanism, which can better explain complex phenomena such as phase change and congestion propagation. In addition, the coupling relationship is decomposed into a diagonal matrix and non-diagonal matrices The diagonal matrix Am can parallelize the calculation of individual vehicle behaviors, the sparse non-diagonal matrix Wmj supports sparse matrix operation optimization, and the layered coupling coefficient αijm allows dynamic adjustment of the inter-layer influence intensity. Compared with the fully connected coupling matrix, the sparse design speeds up the simulation of large-scale vehicle clusters. In addition, This architecture uses multiple parameters to construct a multi-dimensional regulation channel, supporting spatial heterogeneity in coupling strength within the same layer (coupling coefficients can vary across road sections) and the temporal evolution of cross-layer coupling (e.g., adaptive parameter adjustment during peak hours). Compared to traditional models with fixed coupling coefficients (e.g., constant-coefficient cellular automata), this architecture can be embedded in a reinforcement learning framework to achieve online optimization of coupling parameters, making it more adaptable to dynamic traffic scenarios.

[0122] By linearizing the state-space model The spacing error of vehicles in multiple lanes in mixed traffic flow and speed error is converted into controllable system state variables. Compared with existing technologies (such as CACC or LCC based on empirical rules), this method explicitly describes the coupling relationship between vehicle dynamics and control input (CAV acceleration) through matrices Φ and Ψ, and can quantitatively analyze the system stability boundary based on control theory (such as controllability criteria). For example, when the model is controllable, CAV can directly correct the error propagation path by adjusting u(t), avoiding the risk of loss of control caused by the accumulation of unmodeled errors in traditional methods. In addition, the hierarchical structure of the state vector x(t) (divided by lanes and longitudinal distances) decomposes multi-vehicle interactions into locally controllable subsystems. For example, the spacing error of the m-th layer vehicle is It only considers the states of vehicles in the same and adjacent layers, rather than global vehicle information. Compared to traditional single-layer models (e.g., fixed platoons focusing only on the distance between the vehicle in question and the preceding vehicle), this approach reduces cross-layer interference through layered decoupling. This allows the CAV to design independent control strategies for errors within specific layers (e.g., longitudinal compression caused by lane changes in adjacent lanes), improving the targeted nature of disturbance suppression.

[0123] The model explicitly incorporates the spacing and speed errors of HDVs (rather than assuming they are ideal followers), directly reflecting the stochastic and nonlinear characteristics of human-driven vehicles in mixed traffic flows. For example, when an HDV experiences a reaction delay, its error state is sensed by the CAV through the hierarchical model. The CAV then adjusts the acceleration command via feedback gains to suppress the propagation of the error to leading and following vehicles. Compared to traditional methods (such as CCC, which relies solely on information from the preceding vehicle), this method significantly improves control robustness in complex heterogeneous scenarios through global perception of error states and hierarchical compensation. Furthermore, the linearized model reduces the computational complexity of the controller through reduced-order design (retaining only key state variables). For example, while traditional global optimization methods require vehicle trajectory prediction for the entire road section, this method restricts the control objective to a local vehicle cluster through the hierarchical model. Combined with the sparse matrix properties, it can quickly solve for the optimal feedback gain, meeting real-time control requirements. This feature is particularly important in multi-lane, high-density traffic scenarios.

[0124] In specific implementation, the conditions for state controllability are:

[0125]

[0126] Where, i,j∈{1,2,3}; m,k∈{1,2,…,M}; f∈{m+1,m+2,…,M}.

[0127] To help those skilled in the art better understand the relevant contents of the vehicle cluster and its linearized state space system model, the following description is made.

[0128] In a multi-layer network with mixed vehicle dynamics, the hierarchical structure is defined based on the longitudinal distance between vehicles. Specifically, it is assumed that the distance between vehicles in the same layer is much smaller than that between vehicles in different layers.

[0129] like Figure 2 As shown, each layer contains three vehicles. Vehicles located in three adjacent lanes and whose longitudinal distance along the direction of motion is less than a preset distance threshold are classified into the same layer. The leading vehicle in each layer is assumed to receive information from the trailing vehicle in the previous layer. Furthermore, a CAV is designated as the leader of the overall network model to ensure effective control of the speed and spacing of following vehicles, thereby smoothing the overall traffic flow in each lane. This structure simplifies the modeling process while effectively capturing the characteristics of real-world traffic dynamics. Figure 2 In the figure, blue vehicles represent CAVs and green vehicles represent HDVs. The numbers indicate the initial position of the vehicles in the sorting sequence, and the x-axis represents the position coordinates. The blue line represents the distance within a layer, the purple line represents the distance between layers, and the green line indicates the required following distance for vehicles in the same lane according to the universal three-second rule.

[0130] Figure 3A network model with M layers (i.e., a cluster of vehicles) is presented, where m represents the mth layer (m = 1, …, M) and i represents the i-th vehicle in the current layer (i = 1, 2, 3). The equation s_i^m = p_nnv - p_i^m describes the distance between the i-th vehicle and its nearest neighbor (nnv). Here, p_i^m represents the position of the i-th vehicle in the m-th layer in the direction of motion, and its velocity is denoted by v_i^m. This model ignores vehicle length and assumes that the intra-layer spacing is significantly smaller than the inter-layer spacing. The lead vehicle in the first layer is a CAV, and subsequent HDVs follow their nearest neighbors in adjacent lanes or across lanes. Vehicle numbers are arranged according to their initial positions. Figure 3 In this figure, the green vehicles are HDVs, and the blue vehicles are CAVs. Solid blue lines represent intra-layer coupling of vehicle dynamics, while dashed blue lines represent inter-layer coupling. Numbers 1, 2, and 3 denote the initial sequential positions of the vehicles. Dashed green lines illustrate the inter-CAV communication topology. The x-axis represents the platoon's direction of motion and the position coordinates, which serve as the lane localization reference in the experimental setup.

[0131] The optimal velocity model (OVM) is a typical model that describes the dynamics of HDV car-following, and its expression is:

[0132]

[0133] in is the sensitivity coefficient of the i-th vehicle on the m-th floor, Indicates the desired speed of the vehicle, described as:

[0134]

[0135] In the formula Indicates the minimum spacing for generating velocity, Indicates the maximum distance allowed when the speed reaches the maximum value. The model establishes a steady-state condition under which all vehicles in the network system maintain a constant speed v * and predetermined relative spacing because Available Therefore, it is derived from formula (1)

[0136] In reality, the vehicle state cannot always be in equilibrium To reasonably characterize this situation, the formula for the error position and speed of the i-th vehicle in the m-th layer is defined as follows:

[0137]

[0138] Based on equation (1) and The linearized model of each HDV can be derived as:

[0139]

[0140] in Indicates the evaluation value in equilibrium state. Physically, In the above description, since the leader is CAV, i and m cannot be equal to 1 at the same time.

[0141] For CAV, its acceleration signal is used as the control input u(t). The following model of this CAV is described as:

[0142]

[0143] Here It represents the longitudinal position of CAV over time. Since there is no vehicle in front of CAV, its spacing error satisfies

[0144] The final linearized state space system model is:

[0145]

[0146] in The state vector x and system matrices Φ and Ψ are defined as follows:

[0147]

[0148]

[0149]

[0150] in

[0151]

[0152] The elements are

[0153]

[0154] In the above model, the matrix Characterize the vehicle state dynamics and describe the inherent behavior of the vehicle; matrix Indicates the coupling within the layer, reflecting the interaction topology and coupling strength between vehicles in the same layer. represents the intra-layer coupling of the mth layer, Refers to the impact of vehicle j on vehicle i in the mth layer; matrix Represents inter-layer coupling, that is, the interaction topology and coupling relationship between vehicles in different layers, where represents the coupling from the m-1th layer to the mth layer, Represents the effect of vehicle j on the m-1th layer on vehicle i on the mth layer.

[0155] In the subsequent controllability and stabilization analysis, Figure 3 As shown, each HDV follows the same-layer pilot vehicle. Therefore, the matrix in system (6) Given by the following formula:

[0156]

[0157] Figure 3 and Figure 4 (d) shows the actual traffic flow scene. Figure 4 Schematic diagrams of two controllable models, Figure 4 (a) shows the network topology of system (6) with M = 2 layers (each layer has three vehicles, i.e., i∈{1,2,3}). The blue solid line represents the intra-layer coupling, the blue dashed line represents the inter-layer coupling, and the black dashed line represents the intra-node dynamic coupling. Figure 4 (b) shows the degenerate FD-LCC system topology (one vehicle per layer, i = 1), where the blue dashed line represents the inter-node dynamic coupling and the black dashed line represents the intra-node dynamic coupling. Figure 4 (c) Network topology showing the intrinsic dynamic characteristics of the vehicle. Figure 4 (d) A top-down schematic diagram showing the actual application scenario.

[0158] In addition, in order to facilitate those skilled in the art to better understand the relevant content of the controllability of the model (ie, state controllability), the following detailed description is given.

[0159] The controllability and stabilization of a multi-layer mixed vehicle dynamics network are analyzed. The multi-layer mixed traffic flow consists of HDVs in the rear lane and in the left and right adjacent lanes.

[0160] A. Controllability

[0161] The movement of the CAV will affect the HDV behind it and the HDVs in the adjacent lanes on both sides. First, the controllability of system (6) is analyzed.

[0162] Definition 1 (Controllability): Consider a linear time-invariant (LTI) system Where x(t) is the state vector, u(t) is the input vector, A is the state matrix, and B is the input matrix. If there exists an input u(t) that can be f >t0 drives the system from any initial state x(t0)=x0 to any desired final state x(t f )=x f , then the system is said to be in the time interval [t0,t f ]The internal state is controllable.

[0163] Lemma 1 (PBH controllability criterion): The state of a system (A,B) is controllable if and only if for all eigenvalues ​​λ of A, the matrix [λI-A,B] has full row rank.

[0164] against Figure 3 For the model shown, the PBH criterion is first used to prove that its state is controllable.

[0165] Theorem 1 (State controllability of system (6)): For an m-layer networked system (6) with a leader CAV, the system state is controllable if the following conditions are met:

[0166]

[0167] This holds for all i,j∈{1,2,3},m,k∈{1,2,…,M},f∈{m+1,m+2,…,M}.

[0168] Proof: First, analyze the eigenvalues ​​of system (6). Assume [Φ-λI] = 0, then:

[0169]

[0170] According to formula (8), the system eigenvalue can be divided into two cases: λ = 0 and λ ≠ 0.

[0171] Case 1: λ=0.

[0172] When the eigenvalue is zero, we have:

[0173]

[0174] Where i and m are not 1 at the same time. This conclusion comes from the fact that the coefficients satisfy the condition and

[0175] Controllability is proved by contradiction. Assume that the mode corresponding to the zero eigenvalue is uncontrollable. According to Lemma 1, there exists one or more eigenvalues ​​λ = 0 of Φ such that [λI-Φ,Ψ] is rank-deficient. Therefore, there exists a non-zero vector ρ that satisfies Right now

[0176]

[0177] Let ρ be:

[0178]

[0179] in Since there are non-zero elements in Ψ, we can get from formula (10) Substituting Φ into formula (10) yields:

[0180]

[0181] Where g∈{1,2,…,M-1}. From formula (9), we can get Combined with formula (12b), it can be shown that By inductive deduction of formula (12a), we can get The expanded form is

[0182]

[0183] From formula (9) and formula (13), we can get So ρ = 0, which contradicts ρ ≠ 0. Therefore, the mode corresponding to the zero eigenvalue is controllable.

[0184] Case 2: λ≠0.

[0185] Analysis of formula (8) shows that for this non-zero λ, there exists at least one pair Make According to condition (7), we have:

[0186]

[0187] In this case, we also use the proof by contradiction to prove controllability. Suppose there is a non-zero vector ρ such that Then there is

[0188]

[0189] Expanding formula (15) yields:

[0190]

[0191] Expanding equation (16a), when m = 1, we obtain:

[0192]

[0193] Since λ≠0, From formula (17a), we can get According to formula (16b)-(16d), we can get:

[0194]

[0195] Where i and m are not 1 at the same time. Substituting equation (18) into equation (17b) yields:

[0196]

[0197] For the case of m=1, expanding equations (16b) and (16c) and substituting them into equation (19) yields:

[0198]

[0199] therefore, The value of Therefore, the following two situations need to be considered:

[0200] Scenario 2.1:

[0201] According to condition (7), when m=1, and From equation (16), we can see that ρ = 0, which contradicts ρ ≠ 0.

[0202] Scenario 2.2:

[0203] As mentioned at the beginning of Case 2, if the non-zero λ does not correspond to the second vehicle on the first floor, there is always a subsequent vehicle such that when m=1 If all layers satisfy That is, the second car on each floor should not correspond to a non-zero λ, and from equations (14), (16), (19) and (20) we can get According to equation (16b), we can get From equations (14) and (16a), we can see that no matter Is it zero? It is always true, that is, ρ=0, which contradicts ρ≠0.

[0204] If there exists an m-th layer satisfying m≠1 such that Then from equations (14), (16), (19) and (20) we can get According to condition (7), we can get and Substituting this into equation (16d) we can deduce From equation (16), we can see that ρ = 0, which contradicts ρ ≠ 0.

[0205] According to the above analysis of the multilayer network system (6) that satisfies condition (7), when λ≠0, there is no non-zero vector ρ such that Therefore, it can be concluded that the model is controllable under certain conditions (7).

[0206] Note 2: From condition (7), it can be seen that the inherent dynamic characteristics of the vehicle and the motion of the vehicles in the adjacent lanes play a key role in the controllability of the system, especially the vehicles marked as the second node in each layer (i.e., there is no upstream following vehicle in the network), such as Figure 4(a) is shown. It is worth noting that, according to condition (7), the inherent dynamic characteristics of these second-node vehicles are different from all the vehicles in front of them. Compared with the controllability conditions derived for homogeneous vehicle dynamics in LCC, this study explores the controllability of multi-lane mixed traffic flow with heterogeneous vehicle dynamics. In addition, when each layer contains only a single vehicle (i = 1), the proposed model will degenerate into the FD-LCC architecture, as shown in Figure 4 (b) shown.

[0207] B. Stability

[0208] Obviously, from Theorem 1, if system (6) is a homogeneous traffic system (i.e., all HDVs have the same and ), the system does not satisfy condition (7), indicating that the system is uncontrollable. In order to ensure that there is a controller that can stabilize the system in both homogeneous and heterogeneous networks, it is necessary to analyze the stabilization of the model under uncontrollable conditions.

[0209] Definition 2 (Stabilization of LTI Systems): Consider the LTI system described in Definition 1. If there exists a state feedback control law u(t) = Kx(t) (where K is the feedback gain matrix) such that the real parts of the closed-loop system eigenvalues ​​are all negative, then the system is said to be stabilizable.

[0210] In other words, the system can be stabilized to a state without instability by appropriate control input. In addition, if the uncontrollable modes of the system correspond to negative real eigenvalues, the system is considered to be stable.

[0211] against Figure 2 The uncontrollable model shown has the following conclusions:

[0212] Theorem 2: For an M-layer network system (6) led by a single CAV, the system can still be stabilized even if condition (7) is not satisfied.

[0213] Proof: The uncontrollable network system (6) has zero eigenvalues, and the modes corresponding to these zero eigenvalues ​​are all controllable. In addition, there are uncontrollable modes corresponding to non-zero eigenvalues. If all these uncontrollable modes are stable, the system is stabilized.

[0214] First, we analyze the stability of the uncontrollable mode. From Equation (8), we know that for non-zero λ, there is at least one pair of and Make (in and ). From this, it can be deduced that the real part of all non-zero eigenvalues ​​is negative, that is, λ<0 always holds. This shows that the dynamic modes associated with non-zero eigenvalues ​​in the model exhibit stable characteristics, and based on the system stability theory, the instability caused by positive real part eigenvalues ​​is eliminated. In the controllability analysis mentioned above, the controllability of the mode corresponding to the zero eigenvalue has been tested, and it has been proved that the mode corresponding to the zero eigenvalue of system (6) is always controllable. The theorem is now proved, indicating that the model is always stable.

[0215] These conclusions are crucial because they not only ensure that the system remains stable even in the presence of uncontrollable modes, but also provide a solid theoretical basis for subsequent optimization design.

[0216] S3. Design an optimal controller for the CAV, which is used to solve the feedback gain matrix through the system disturbance structure when the vehicle cluster does not meet the state controllability, and calculate the feedback gain control amount of the CAV based on the feedback gain matrix to achieve compensatory control for the unstable behavior induced by the HDV;

[0217] In specific implementation, the calculation formula of the feedback gain control amount of CAV is:

[0218] u1(t)=-Kx(t);

[0219] Where, u1(t) is the feedback gain control quantity; K is the feedback gain matrix;

[0220] By solving K through the optimal controller, the energy of the output error signal y(t) of the entire closed-loop system under the action of the disturbance ω(t) is minimized;

[0221] in,

[0222]

[0223]

[0224] y2(t)=γ u u(t);

[0225]

[0226] In the formula, the weighting coefficient γ s ,γ v ,γ u >0 indicates penalties for spacing error, speed error, and control input, respectively;

[0227] The optimal controller design process includes:

[0228] Design an initial form of the optimal controller:

[0229]

[0230] Where, Represents the energy of the output error signal y(t); Indicates that P is a positive definite matrix / semi-negative definite matrix;

[0231] After that, introduce the variable replacement K=NP -1 , where N is the controller gain matrix; the equivalent expression of the optimal controller is obtained:

[0232]

[0233] Then, perform the mirror transformation, so that Substituting the above equivalent expression into the final form of the optimal controller is:

[0234]

[0235]

[0236] In this way, the limitation of traditional LQR single-objective optimization is broken through, and position / velocity tracking error and control quantity suppression are processed synchronously through multiple weighted terms; the modular design of the Ω matrix allows robust adjustment for disturbances in specific frequency bands, which can reduce conservatism compared to general H∞ control. In addition, variable substitution transforms the original non-convex problem into a convex optimization problem, and the solution time is reduced from O(n 6 ) is reduced to O(n 3 )(n is the system order). And, the upper mirror transformation introduces The condition effectively avoids the numerical ill-conditioned problem caused by matrix inversion in traditional methods. The frequency domain weighting function is constructed by the term, which improves the high-frequency noise suppression capability compared with traditional state feedback control. The introduction of the Ω matrix in the final form reduces the L2 gain of the system to model uncertainty, which is suitable for time-varying delay scenarios.

[0237] To help those skilled in the art better understand the relevant technical content of the optimal controller of CAV, the following explanation is given.

[0238] The design and solution process for determining the optimal control inputs for CAVs to achieve traffic network stability, i.e., improve road safety and utilization, is first mathematically modeled as a non-convex optimal control problem, which is then converted into a convex optimization problem for solution.

[0239] First, consider the static state feedback controller:

[0240] u(t)=-Kx(t). (21)

[0241] Here Each block represent The feedback gain of the i-th vehicle on the m-th layer is as follows: Figure 5 As shown. It is required that K∈K, K has a decentralized structure under the block sparse mode:

[0242]

[0243] In particular, when the CAV does not receive the information of the i-th vehicle in the m-th layer,

[0244] Definition 3( Norm): For the system

[0245]

[0246] Its transfer function is

[0247] H=(A,B,C,D)=C(sI-A) -1 B+D, (24)

[0248] That The norm is defined as

[0249]

[0250] Lemma 2( Norm square calculation): For the transfer function H = (A, B, C, 0), if the system is stable, then H The squared norm can be calculated as

[0251]

[0252] where P is any positive definite solution to the Lyapunov inequality in equation (26). (or P≤0) means that P is a positive definite (or semi-negative definite) matrix.

[0253] To simulate the impact of disturbances on actual traffic flow, it is assumed that the acceleration of each vehicle is subjected to a finite energy disturbance signal The role of and represents the scalar disturbance signal of the i-th vehicle in the m-th layer. Therefore, the system model becomes

[0254]

[0255] in and

[0256] The state feedback control u=-Kx is introduced to control the system. By designing an appropriate controller gain K, the system dynamic characteristics can be changed to achieve stability. After applying the control law, the system dynamics becomes:

[0257]

[0258] definition

[0259]

[0260] y2(t)=γ u u(t), (30)

[0261] As the output error signal, the weighting coefficient γ s ,γ v ,γ u >0 indicates the penalty for spacing error, speed error and control input respectively. The output can be expressed as

[0262]

[0263] in and Since u=-Kx,y(t) can be written as

[0264]

[0265] Should The optimal control problem aims to find a conventional controller K that makes the closed-loop system internally stable while minimizing the transfer function H. Norm. Note that in the current model, the transfer function H represents the mapping from the disturbance ω to the output y, denoted by H yω When u = -Kx, a minor modification of Lemma 2 is as follows:

[0266]

[0267] Where Υ=(Φ-ΨK),H yω =(Υ,Ω,Θ,0).

[0268] This type of controller is called Optimal controller. To determine the most appropriate feedback gain matrix K, use Therefore, the system (6) The optimal controller is designed to be

[0269]

[0270] By introducing the variable replacement K=NP -1 (where N is the controller gain matrix), the controller design can be equivalently expressed as (35). Then, the upper mirror transformation is performed, and Substituting into the optimization problem (35) we obtain (36).

[0271] Due to hardware limitations, the network size composed of CAV and HDV in actual scenarios is constrained, making the constraint Therefore, problem (36) is transformed into a non-convex optimization problem. Therefore, we need to find a way to transform it into a convex optimization problem for approximate solution.

[0272] In specific implementation, the calculation process of solving the optimal controller includes:

[0273] Step 1: Determine two binary matrices and in, represents the sparsity pattern of the controller gain matrix N, represents the sparsity pattern of the matrix P; and and Constructed as the following mapping equation The corresponding sparsity pattern is:

[0274]

[0275] Step 2: Ensure that the binary matrix and satisfy and conform to Conditions; among them, and Represented by sparse pattern and The sparse subspace of the matrix is ​​defined;

[0276] Step 3: Simplify the original problem into the following convex optimization problem:

[0277]

[0278]

[0279] Using the solution to the convex optimization problem, calculate the feedback gain matrix K;

[0280] Then the feedback gain control amount u1(t)=-Kx(t) is obtained.

[0281] In this way, by taking the sparsity pattern (T / S) of the controller gain matrix (N) and the Lyapunov matrix (P) as independent design variables for the first time, we break through the limitation of traditional methods that only impose sparsity on a single matrix. Compared with the existing LMI method that passively accepts the sparsity of the solution, this technology actively defines and The subspace can be adapted to hardware resource constraints (such as FPGA / ASIC memory bit width) in advance, reducing controller memory requirements. Furthermore, by introducing the slack variable Y and the Schur complement transform, the original non-convex NP-hard problem is transformed into a globally convergent convex optimization problem, a milestone in the control field. Compared to non-convex optimization frameworks such as ADMM, this method achieves faster solutions using 64-bit floating-point operations while ensuring the validity of the results.

[0282] S4, S4, obtain the state data of the vehicle cluster and determine whether the state controllability is satisfied. If so, the CAV is controlled normally. If not, the corresponding feedback gain matrix is ​​solved by the optimal controller of the CAV, and the feedback gain control amount of the CAV is calculated based on the feedback gain matrix. The feedback gain control amount is used to control the speed of the CAV, guide the speed and spacing of each HDV in the vehicle cluster, and stabilize the vehicle cluster.

[0283] This method overcomes the limitations of traditional single-lane platooning models by constructing a hierarchical vehicle cluster (with a CAV as the lead vehicle and integrating adjacent lanes and rear HDVs). Existing technologies often assume that vehicles form fixed platoons within their own lane, ignoring the lateral interactions between vehicles in adjacent lanes. This results in insufficient robustness in control strategies for multi-lane scenarios. This method, through hierarchical management, dynamically coordinates the longitudinal spacing and velocity gradients between vehicles in multiple lanes, effectively suppressing the propagation of disturbances caused by lane changes or speed fluctuations in adjacent lanes and enhancing system stability. Furthermore, by analyzing the dynamic controllability of vehicle clusters based on a linearized state-space model and combining it with optimal controller design for CAVs, it achieves a transition from passive adaptation to active control. Existing technologies (such as LCC and CCC) typically rely on fixed communication topologies or forward-looking perception, making them difficult to address the uncertainties introduced by HDV dynamics (such as reaction delays and random lane changes) in mixed traffic flows. This method dynamically adjusts the CAV feedback gain by acquiring real-time HDV error and disturbance data, mitigating the risk of failure of traditional control strategies when the system is uncontrollable and significantly improving adaptive capabilities in complex scenarios.

[0284] Furthermore, this method addresses the heterogeneous characteristics of CAVs and HDVs in mixed traffic flows, separating the dynamic behaviors of different vehicle groups through a hierarchical model and reducing the interference of HDV random behavior on global control. Existing technologies (such as CACC) assume that all vehicles are CAVs, and their control accuracy relies on the premise of high penetration. However, this method can still guide HDVs to form a stable speed and spacing distribution through the collaborative leadership of CAVs in low penetration scenarios, reducing traffic flow fluctuations, and has more practical application value than traditional methods. In addition, the dynamic network controllability theory is used to analyze multi-layer coupling structures (such as vehicle interactions between lanes), revealing the regulatory potential of CAVs as information hubs for cross-lane coordination. Existing technologies mostly focus on the controllability of single-layer networks and ignore the impact of inter-layer coupling on system stability. This method quantifies the dynamic guidance of CAVs on vehicles in adjacent lanes through hierarchical modeling and feedback mechanisms, solving the problem that traditional control strategies cannot effectively coordinate cross-lane interactions.

[0285] In summary, this method can fully utilize the collaborative leadership capability of CAVs, effectively suppress the impact of adjacent lane disturbances on system stability, and achieve efficient, safe, and adaptive collaborative control of mixed traffic flows.

[0286] Example 2

[0287] In order to better illustrate the effect of this method, the following simulation experiment is carried out.

[0288] Three key aspects are verified through simulation experiments: stability of mixed vehicle networks, improved road utilization, and improved driving safety.

[0289] A. Simulation Data Preparation

[0290] Consider a four-layer mixed vehicle network consisting of 11 HDVs and 1 leading CAV, corresponding to the number of layers M = 4. Specifically, we study the scenario where a CAV is followed by three HDVs in its lane and in the adjacent lanes on both sides (i∈{1,2,3}, e.g. Figure 3 As shown in Figure 2, the anti-interference capability of CAV is significantly enhanced after implementing the “look back” and “look left and right” strategies. s =0.03,γ v =0.15 and γ u =1, and the above sparse inconvex approximation method is used to obtain the required linear feedback gain K.

[0291] To ensure the characteristics of heterogeneous heavy-duty vehicles (HDVs) and take into account the differences in inter-layer and intra-layer distances, the following parameters are set: and The value of is defined as

[0292]

[0293] The remaining parameters are set to and

[0294] To ensure highway driving safety, the three-second rule is used, recommending that the minimum distance between vehicles in the same lane should be no less than three times the current speed (m / s). In practice, a more relaxed requirement can be considered when determining the safety of vehicle spacing: a distance of no less than two to four times the current speed. Given the large distances and high speeds on highways, overtaking is not considered in this experiment. This setting avoids the simultaneous occurrence of extremely low and high speeds, more accurately reflecting road conditions and reducing accident risk.

[0295] B. Stable hybrid vehicle network

[0296] After completing the aforementioned data preparation, the linear feedback gain K is first calculated. Simulation experiments then compare the four-layer hybrid vehicle network with the FD-LCC model, demonstrating the potential of a connected autonomous vehicle (CAV) to guide an HDV in an adjacent lane.

[0297] In the four-layer hybrid vehicle network experiment, the initial vehicle positions were set according to the following rules: the longitudinal spacing within a layer was 11.67 meters, the longitudinal spacing between layers (i.e., the distance from the rear of the front layer vehicle to the front of the rear layer vehicle) was 100 meters to allow for speed adjustment, and the initial vehicle speed range was set between 23 and 27 m / s. The FD-LCC model used the same number of vehicles as the four-layer system: 11 HDVs and one leading CAV. The CAV also received feedback control information from the five vehicles behind it. Unlike the four-layer system, all vehicles in the FD-LCC model drove in the same lane. To ensure consistent experimental conditions, the FD-LCC parameters were aligned with the inter-layer parameters of the four-layer system.

[0298] When all four layers of hybrid vehicle networks are HDVs, the leading HDV applies [-5,2]m / s 2 Random acceleration within the range. Experiments show that under this configuration, the network system has multiple disturbances, causing the vehicle speed to deviate from the preset equilibrium speed by 25m / s ( Figure 6 ), causing system instability. Figure 6 The diagram of vehicle speed variation over time in the full HDV networking system. (a) shows the speed change curve within the first 160 seconds, and (b) focuses on the lowest point of the speed curve, reflecting the instantaneous lowest speed of the system.

[0299] Although the FD-LCC model is based on the leading CAV ( Figure 7 ) achieved single-lane stability, but at the expense of rationality: To adjust the distance between vehicles, the CAV and the multiple HDVs in the front row experienced rapid deceleration at the beginning of the simulation before gradually reaching a steady state. Such drastic speed changes lacked realism in highway scenarios. Figure 7Schematic diagram of a CAV-led HDV platoon under the FD-LCC framework. The system will first experience a brief speed drop and then stabilize at a steady-state speed of 25 m / s.

[0300] In contrast, the four-layer hybrid vehicle network ( Figure 8 By integrating HDV information from the same direction and adjacent lanes through CAV, its more compact network structure not only improves experimental performance, but also comprehensively considers real multi-lane interactions and lane-changing behaviors, with wider applicability and practical fit, providing a more reliable reference for the design and optimization of actual transportation systems. Figure 8 The figure shows how the vehicle speed in a networked system changes over time when a CAV leads a platoon of HDVs. The presence of the CAV enables the system speed to converge and stabilize at a set value of 25 m / s.

[0301] C. Improve road utilization

[0302] Figure 9 and Figure 10 Demonstrated the significant impact of CAVs on improving road utilization. Figure 9 The visualization of the position changes of vehicles in the networked system from 195s to 200s is shown when all vehicles are HDVs. Figure 10 The visualization of the position changes of vehicles in the networked system from 195s to 200s is shown when the leading vehicle is a CAV and the remaining vehicles are HDVs.

[0303] Figure 9 All vehicles in the are HDVs, and Figure 10 The leading vehicle in the middle traffic network is a CAV. Both figures show the average vehicle position distribution between 195s and 200s, with a time interval of 0.5s. Comparing road utilization in the two scenarios clearly demonstrates the impact of integrating CAVs into the networked system.

[0304] Figure 9 In the pure HDV scenario shown, the queue length is about 600m, and the maximum distance between vehicles in the same lane exceeds 200m. This indicates that the distance between vehicles is too large, which limits the road capacity and thus affects the overall network system performance. Figure 10 A traffic network with a CAV as the lead vehicle was demonstrated. In this mixed traffic environment, CAVs were able to more precisely control vehicle spacing, achieving more efficient acceleration and deceleration responses. As a result, the queue length was significantly reduced to 256 meters, with the maximum distance between vehicles in the same lane approximately 100 meters and the minimum distance approximately 60 meters. This not only ensured that vehicles in the same lane maintained a relatively safe following distance, but also allowed more vehicles to fit within the same road section, thereby improving road utilization. The experiment demonstrated that the introduction of CAV technology can improve road capacity while ensuring traffic flow efficiency and safety.

[0305] D. Improve driving safety

[0306] In this experiment, Figure 11 Corresponding to the FD-LCC single lane model, Figure 12 Represents a four-layer mixed vehicle network multi-lane model.

[0307] Figure 11 The visualization shows the speed evolution of each vehicle in the FD-LCC model over time and the controller activation state (the lead vehicle is a CAV, and the others are HDVs). It can be clearly seen that the system speed gradually converges to a steady-state value of 25 m / s between 300 and 450 seconds after controller activation. Figure 12 The paper visualizes the speed evolution of each vehicle in a four-layer mixed vehicle network over time and with the state of controller activation (the lead vehicle is a CAV, and the others are HDVs). Compared to the FD-LCC model, the multi-lane model exhibits more pronounced speed divergence after the control intervention is removed (t = 450-700s), but is able to achieve system stability under CAV intervention, maintaining the speed at a steady-state value of 25 m / s. This demonstrates the critical role of CAVs in complex multi-lane scenarios.

[0308] Introduce normal distribution random noise into the acceleration signal of each vehicle To simulate the small random disturbances that naturally exist in real traffic environments. Figure 11-12 As shown in the figure, when the controller fails during the time periods t = 0-300s and t = 450-700s, both models experience significant speed instability. However, after the controller is reactivated during the time period t = 300-450s, the system performance improves significantly—the controller intervention effectively suppresses speed fluctuations and guides the system back to a steady state.

[0309] Notably, when the controller intervention is removed, the four-layer hybrid vehicle network model exhibits more pronounced speed oscillation divergence. This phenomenon reveals the synergistic effect of CAV technology and multi-lane scenarios: on the one hand, the experimental results in multi-lane environments confirm the key role of the controller in stabilizing such complex systems; on the other hand, the multi-lane architecture better reflects real-world lateral interference (such as lane-changing behavior). Therefore, this study not only reveals the importance of CAVs in multi-lane scenarios but also demonstrates the guiding significance of multidimensional traffic modeling for the further development of intelligent transportation systems.

[0310] VI. Conclusion

[0311] This method proposes a multi-layer hybrid vehicle dynamics network model designed for multi-lane scenarios, which achieves improved performance compared to traditional single-lane models. By extending the cruise control model and introducing the three-second rule, the model can capture the interaction between vehicles in different lanes and layers, and more accurately characterize mixed traffic flows. System controllability and stabilization analysis show that the model is fully controllable and unconditionally stabilized under mild conditions. Numerical simulation verifies the effectiveness of the model in improving system stability, road utilization, and traffic safety. These results highlight the huge application potential of the hybrid vehicle dynamics multi-layer network model, expand the scope of mixed traffic flow research, and lay the foundation for subsequent research on intelligent traffic management and control in multi-lane environments.

[0312] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the technical solutions. Those skilled in the art should understand that modifications or equivalent replacements of the technical solutions of the present invention that do not depart from the purpose and scope of the technical solutions of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A method for coordinated speed control of vehicles in multi-lane mixed traffic, characterized by: For multi-lane traffic with mixed driving of intelligent driving vehicles (CAVs) and human-driven vehicles (HDVs), the method comprises the following steps: S1. Construct a vehicle cluster according to a preset format. The preset format is that the CAV is the lead vehicle, and vehicles in the lanes adjacent to the CAV and behind the CAV are HDVs. Vehicles in the CAV's lane and its adjacent lanes are stratified along the direction of movement, and vehicles whose longitudinal distance along the direction of movement is less than a preset distance threshold are grouped into the same layer. S2. Assume that the leading HDV in each layer of the vehicle cluster receives information from the trailing vehicle in the previous layer, and each HDV follows the leading vehicle in the same layer. A linearized state-space system model of the vehicle cluster is constructed, and its state controllability is analyzed. S3. Design an optimal controller for the CAV. When the vehicle cluster does not satisfy state controllability, solve the feedback gain matrix through the system disturbance structure, and calculate the feedback gain control of the CAV based on the feedback gain matrix to achieve compensatory control for the unstable behavior induced by the HDV. S4. Obtain the state data of the vehicle cluster and determine whether the state controllability is satisfied. If so, control the CAV normally. If not, solve the corresponding feedback gain matrix through the CAV's optimal controller, and calculate the CAV's feedback gain control amount based on the feedback gain matrix. The feedback gain control amount is used to control the speed of the CAV, guide the speed and spacing of each HDV in the vehicle cluster, and stabilize the vehicle cluster.

2. The method for coordinated vehicle speed control in multi-lane mixed traffic according to claim 1, wherein: In S1, the vehicles on the same layer are numbered according to the order of their initial positions.

3. The method for coordinated speed control of vehicles in multi-lane mixed traffic according to claim 2, wherein: In S2, the linearized state space system model of the vehicle cluster is: Where u(t) represents the acceleration signal of the CAV; x(t) is the state vector; Φ and Ψ are system matrices; Where M is the number of vehicle division layers in the vehicle cluster; represents the spacing error of the i-th vehicle on the m-th floor; represents the speed error of the i-th vehicle in the m-th layer; T represents the transposed sign.

4. The method for coordinated speed control of vehicles in multi-lane mixed traffic according to claim 3, wherein: The linearized model of each HDV is: in, represents the evaluation value in the equilibrium state; represents the speed error of the nearest neighbor vehicle; Among them, i and m cannot be equal to 1 at the same time; v * For an ideal constant speed, represents the ideal distance between the i-th vehicle on the m-th layer and its nearest neighbor.

5. The method for coordinated speed control of vehicles in multi-lane mixed traffic according to claim 4, wherein: Ideal constant speed v * is the preset value; ideal spacing This is determined based on the three-second rule, which states that on a highway, the minimum distance between vehicles in the same lane should not be less than three times the current vehicle speed.

6. The method for coordinated speed control of vehicles in multi-lane mixed traffic according to claim 5, wherein: Where, It represents the actual speed of the i-th vehicle on the m-th layer and the actual distance to the nearest neighbor vehicle.

7. The method for coordinated speed control of vehicles in multi-lane mixed traffic according to claim 6, wherein: The elements are: In the formula, the matrix Represents the vehicle state dynamics, describing the inherent behavior of the vehicle; the matrix Intra-layer coupling, reflecting the interaction topology and coupling strength between vehicles on the same layer; represents the intra-layer coupling of the mth layer, Refers to the impact of vehicle j on vehicle i in the mth layer; matrix Represents inter-layer coupling and describes the interaction topology and coupling relationship between vehicles in different layers; represents the coupling from the m-1th layer to the mth layer, Represents the effect of vehicle j on the m-1th layer on vehicle i on the mth layer.

8. The method for coordinated speed control of vehicles in multi-lane mixed traffic according to claim 7, wherein: The conditions for state controllability are: Where, i,j∈{1,2,3}; m,k∈{1,2,…,M}; f∈{m+1,m+2,…,M}.

9. The method for coordinated speed control of vehicles in multi-lane mixed traffic according to claim 8, wherein: In S3 and S4, the calculation formula of the CAV feedback gain control amount is: u1(t)=-Kx(t); Where, u1(t) is the feedback gain control quantity; K is the feedback gain matrix; By solving K through the optimal controller, the energy of the output error signal y(t) of the entire closed-loop system under the action of the disturbance ω(t) is minimized; in, y2(t)=γ u u(t); In the formula, the weighting coefficient γ s ,γ v ,γ u >0 indicates penalties for spacing error, speed error, and control input, respectively; The optimal controller design process includes: Design an initial form of the optimal controller: Where, Represents the energy of the output error signal y(t); P>0 / P≤0 indicates that P is a positive definite matrix / semi-negative definite matrix; After that, introduce the variable replacement K=NP -1 , where N is the controller gain matrix; the equivalent expression of the optimal controller is obtained: Then, perform the mirror transformation, so that Substituting the above equivalent expression into the final form of the optimal controller is:

10. The method for coordinated speed control of vehicles in multi-lane mixed traffic according to claim 9, wherein: The calculation process of solving the optimal controller includes: Step 1: Determine two binary matrices and in, represents the sparsity pattern of the controller gain matrix N, represents the sparsity pattern of the matrix P; and and Constructed as the following mapping equation The corresponding sparsity pattern is: Step 2: Ensure that the binary matrix and satisfy and conform to Conditions; among them, and Represented by sparse pattern and The sparse subspace of the matrix is ​​defined; Step 3: Simplify the original problem into the following convex optimization problem: Using the solution to the convex optimization problem, calculate the feedback gain matrix K; Then the feedback gain control amount u1(t)=-Kx(t) is obtained.

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