Safety constraint vehicle formation distributed sliding mode control method based on preset performance function

Abstract

The invention relates to a safety constraint vehicle formation distributed sliding mode control method based on a preset performance function. Compared with the prior art, the defect that vehicle formation control is difficult to meet safety constraint, preset performance and distributed cooperative control at the same time is overcome. The method comprises the following steps: establishing a vehicle formation three-order state space model; generating a following vehicle smooth reference trajectory; a preset performance constraint of the following vehicle is designed; calculating the expected speed of the following vehicle; calculating the expected torque of the following vehicle; a following vehicle driving system is controlled; and formation cooperative control is realized. According to the invention, through a reference generation mechanism of constraint perception, a preset performance function with a self-adaptive boundary and a topological structured reaching law, high-performance tracking of the track of the pilot vehicle is realized on the premise of ensuring that all following vehicles meet the time-varying safety boundary.

Description

Technical Field

[0001] This invention relates to the field of multi-agent system control technology, specifically a distributed sliding mode control method for vehicle platooning based on a preset performance function and safety constraints. Background Technology

[0002] Currently, research on vehicle platooning system control has many branches, including consensus control, platooning control, and swarm control, among which consensus control is the foundation and core of other research branches. Consensus control in vehicle platooning systems refers to designing appropriate control protocols for each agent, enabling them to interact only with their neighbors, ultimately leading all agents to the same target state. After nearly two decades of development, consensus research in vehicle platooning systems has gradually matured, giving rise to important directions such as average consensus and finite-time consensus.

[0003] In actual vehicle platooning operations, due to the complexity of road environments, the constraints of traffic regulations, and the limitations of vehicle physical performance, each vehicle needs to meet time-varying safety constraints. For example, vehicles need to stay within lane boundaries, avoid collisions, and meet space restrictions. These safety constraints typically change dynamically with road conditions, weather conditions, and traffic flow. Traditional platooning control methods often ignore these safety constraints, which may lead to traffic violations or safety accidents.

[0004] Meanwhile, the control performance requirements for vehicle platooning systems are becoming increasingly stringent. Besides requiring the system to achieve the desired platooning configuration, constraints must also be placed on transient performance indicators such as overshoot, convergence speed, and steady-state error. Pre-defined performance control methods can specify the transient and steady-state performance boundaries of the system in advance by designing performance functions. However, traditional pre-defined performance functions use fixed boundaries, making it difficult to adapt to sudden changes in the reference signal, which may lead to transient error peaks exceeding expectations.

[0005] Furthermore, vehicle platooning systems are typical distributed multi-agent systems, where each vehicle can only obtain limited information about its own status and that of its neighbors through onboard sensors and communication equipment. Centralized control methods require global information, increasing the communication burden and reducing system reliability and scalability. Therefore, designing a distributed controller that enables each vehicle to achieve collaborative control using only local information has significant theoretical and practical value.

[0006] Therefore, there is an urgent need to implement a distributed sliding mode control method for vehicle platooning based on a preset performance function with safety constraints in order to solve the above-mentioned technical problems. Summary of the Invention

[0007] The purpose of this invention is to address the shortcomings of existing vehicle platooning control technologies that struggle to simultaneously satisfy safety constraints, preset performance, and distributed collaborative control. This invention provides a safety-constrained distributed sliding mode control method for vehicle platooning based on preset performance functions to solve these problems.

[0008] To achieve the above objectives, the technical solution of the present invention is as follows:

[0009] A distributed sliding mode control method for vehicle platooning based on a preset performance function with safety constraints includes the following steps:

[0010] Establish a third-order state-space model for vehicle platooning;

[0011] Generate a smooth reference trajectory for following the vehicle;

[0012] Design follows the vehicle's preset performance constraints;

[0013] Calculate the expected speed of the following vehicle;

[0014] Calculate the expected torque of the following vehicle;

[0015] Control the following vehicle's drive system;

[0016] Achieve coordinated control of the formation.

[0017] The establishment of the third-order state-space model for vehicle platooning includes the following steps:

[0018] Constructing vehicle platoon communication topology: A directed graph is used to describe the platoon communication structure containing 1 lead vehicle and N follower vehicles. The adjacency matrix, Laplace matrix and lead vehicle connection matrix are defined to characterize the communication relationships and topological characteristics between vehicles.

[0019] Establish the longitudinal dynamics model of the following vehicle: Establish the first A third-order dynamic model of the longitudinal position, velocity, and driving torque of the following vehicle is used to describe the longitudinal motion characteristics of the vehicle.

[0020] Transform into a relative deviation state-space model: Define the first The positional deviation, speed deviation, and torque deviation of each following vehicle relative to the lead vehicle are used to transform the absolute dynamics of the vehicle into a third-order deviation state-space model relative to the lead vehicle. Using the lead vehicle as a reference benchmark, it is convenient to design distributed cooperative control laws.

[0021] The generation of the smooth reference trajectory for the following vehicle involves: based on the position of the lead vehicle and the desired inter-vehicle spacing in the platoon, designing a constraint-aware reference generation mechanism with time-varying safety margins, and generating a smooth reference signal that satisfies the time-varying safety boundaries through dynamic adjustment of the safety margin and trajectory smoothing processing; including the following steps:

[0022] Setting the formation configuration and designing time-varying safety margins: Defining the desired vehicle spacing and time-varying safety constraint boundaries, for the first... Vehicle following vehicle design with variable safety margin:

[0023] ,

[0024] in: For the first The time-varying safety margin of a vehicle describes the buffer distance between the reference trajectory and the safety boundary; This serves as the initial safety margin, providing a significant safety safety tolerance during the formation startup phase. This is the final safety margin value, the minimum safety margin maintained after the formation stabilizes; This is the margin gain coefficient, which controls the magnitude of margin decay; This is the margin decay coefficient, which controls the rate at which the margin decays from its initial value to its final value. Runtime; As an exponential decay function, this margin design allows the safety buffer distance to gradually tighten from an initial conservative value to a steady-state compact value as the formation status changes, balancing startup safety and steady-state tracking accuracy.

[0025] Generate constraint-aware reference signals: Generate reference signals that satisfy boundary constraints based on time-varying safety margins.

[0026] ,

[0027] in: For the first Vehicle constraint reference signals; Used as an initial position reference; , These are the time-varying lower and upper boundaries, respectively; when the initial reference is lower than the lower boundary plus margin, the reference signal is set to the lower boundary plus margin; when the initial reference is within the safe range, the original value is maintained; when the initial reference is higher than the upper boundary minus margin, the reference signal is set to the upper boundary minus margin.

[0028] Smoothing and defining tracking error: Hermite interpolation is used to smooth the discontinuous moments of the constraint reference signal to generate the final smooth safety reference trajectory. and define the first Position tracking error of the following vehicle , Let i be the actual position of the i-th following vehicle, which will be the control object for the subsequent control law design.

[0029] The design of the following vehicle is subject to the following preset performance constraints: A preset performance function with adaptive boundaries is constructed for each following vehicle; a singularity-free error transformation is used to map the bounded position tracking error to an unbounded space, ensuring that control singularities are avoided and transient error peaks are suppressed during the control process; including the following steps:

[0030] Design a preset performance boundary function: Design a preset performance function with adaptive boundaries. , ,in Based on the fundamental performance boundary, For adaptive boundary components; basic performance boundaries Designed as follows:

[0031] ,

[0032] in: As the initial performance boundary, satisfying A larger tracking error is allowed during the formation start-up phase; The final performance boundary is the required tracking accuracy after the formation has stabilized. The preset convergence time controls the time scale from the initial boundary to the final boundary; This is the current running time;

[0033] Designing adaptive boundary dynamics: Adaptive boundary components are generated by differential equations:

[0034] ,

[0035] in: The time derivative of the adaptive boundary component; This is the adaptive boundary attenuation coefficient, which controls the attenuation rate of the adaptive boundary. The adaptive gain coefficient controls the intensity of the influence of the control error on the boundary. This is the sensitivity exponent parameter, which controls the sensitivity of the adaptive boundary to changes in error. This refers to the time-delay position tracking error; This is a time delay parameter used to avoid high-frequency oscillations;

[0036] Apply performance constraints and implement error transformation: require the position tracking error to meet performance constraints.

[0037] ,

[0038] Initial conditions are met:

[0039] ,

[0040] Define normalization error:

[0041] ,

[0042] Employing a singularity-free transformation:

[0043] ,

[0044] in: For the first Position tracking error of the following vehicle To preset performance constraints, This means that the condition holds true for all non-negative moments, ensuring that the position tracking error remains within the specified range. The initial conditions ensure that the initial error meets performance requirements and does not violate safety constraints. , These represent the time-varying upper and lower boundaries at the initial moment; The normalization error is dimensionless and has a range of values. This normalizes the bounded error; It is dimensionless and has no singular transformation error, with a range of values. ,in For the natural logarithm function, the transformation ensures that when hour This maps the bounded normalization error to an unbounded space.

[0045] The calculation of the desired speed of the following vehicle involves: based on a singular error-free transformation, designing a virtual control law for the position tracking layer, and deriving the desired speed command for each following vehicle using the Lyapunov method; including the following steps:

[0046] Construct a dynamic equation for position error: differentiate the non-singular error transformation of the following vehicle to obtain the relationship between the time derivative of the transformation error, the derivative of the position tracking error, and the rate of change of the preset performance boundary;

[0047] Design the position tracking control law: Based on Lyapunov stability theory, for the first... Vehicle following vehicle design position layer expected dynamics :

[0048] ,

[0049] in: Position layer control gain; To eliminate singular transformation errors, this control law ensures that the transformation error decays to zero at an exponential rate, thereby guaranteeing that the original position tracking error converges to within the preset performance boundary.

[0050] Generate the desired speed command: This is achieved by inversely calculating the speed using the position tracking control law. The vehicle following the vehicle generates the desired speed command, which includes a reference trajectory feedforward term, a position error feedback term, a performance boundary compensation term, and a transformation error compensation term.

[0051] The calculation of the desired torque for the following vehicle involves: designing a virtual control law for the speed tracking layer based on the desired speed command and the actual speed deviation, and deriving the desired drive torque for each following vehicle using the Lyapunov method; including the following steps:

[0052] Define speed tracking error: Define the first The difference between the actual speed deviation of the following vehicle and the desired speed command is the speed tracking error. ;

[0053] Design the speed tracking control law: Based on Lyapunov stability theory, for the first... Vehicle following vehicle design speed layer expected dynamics :

[0054] ,

[0055] in: Control the gain for the velocity layer; For speed tracking error; this control law ensures that the speed tracking error converges to zero at an exponential rate;

[0056] Generate desired drive torque command: Combining the longitudinal dynamics model of the following vehicle, the desired drive torque deviation is generated for the i-th following vehicle by inverse calculation using the speed tracking control law. It includes the expected acceleration feedforward term, the speed error feedback term, the air resistance compensation term, and the navigator acceleration compensation term.

[0057] The controlled following vehicle drive system comprises: constructing a distributed sliding mode surface based on torque error weighted by vehicle communication topology; designing a distributed sliding mode controller using a topology-structured reaching law; and generating drive system control inputs for each following vehicle; including the following steps:

[0058] Define torque tracking error: Define the first The difference between the actual driving torque deviation and the expected driving torque deviation of the following vehicle is the torque tracking error. ;

[0059] Constructing a distributed sliding surface: Based on the vehicle formation communication topology, for the first Vehicles follow each other to construct a distributed sliding surface:

[0060] ,

[0061] in: For the first The individual sliding surface of the following vehicle reflects the torque tracking status of the vehicle and its communication neighbors; The total number of following vehicles; These are adjacency matrix elements, describing the communication connections between vehicles; For the first Torque tracking error of the following vehicle; The connection coefficient of the lead vehicle;

[0062] The collective sliding surface of all following vehicles is represented in vector form. ,

[0063] in For the collective sliding surface vector, For Laplace matrix, Connect the matrix for the lead vehicle. This is the torque error vector;

[0064] Design a topology-structured reaching law: To suppress sliding mode control chattering and ensure finite-time arrival, a topology-structured reaching law is designed.

[0065] ,

[0066] in: For the first The time derivative of the sliding surface of the vehicle; The proportional gain of the approach law controls the speed at which the sliding surface approaches. For the reaching law switching gain; This is a boundary layer function used to suppress high-frequency chattering; This refers to the boundary layer thickness parameter;

[0067] Generate distributed control inputs: using the reaching law and torque error dynamics, for the first... Vehicle following vehicle generates drive system control input It includes a feedback control term based on the sliding surface and a feedforward compensation term for the desired torque, ensuring that the system reaches the sliding surface in a finite time and converges asymptotically and stably along the sliding surface.

[0068] The formation cooperative control is achieved by: verifying the finite-time reachability of the sliding surface and the asymptotic stability of the tracking error based on Lyapunov theory; issuing control commands through the onboard controller to enable all following vehicles to cooperatively follow the trajectory of the lead vehicle while meeting safety constraints and preset performance requirements; including the following steps:

[0069] Verifying the finite-time reachability of the sliding surface: drive system control input Based on Lyapunov theory, the arrival phase performance of the distributed sliding mode control system is verified, proving that the upper bound of the sliding surface arrival time is:

[0070] ,

[0071] in: This is the upper bound of the arrival time of the sliding surface; Let be the 2-norm of the initial collective sliding surface; For the reaching law switching gain; For matrix The smallest eigenvalue represents the connectivity strength of the communication topology;

[0072] Verifying the asymptotic stability of the tracking error: Based on Lyapunov theory, it is proved that when the control gain satisfies and At that time, the position and speed tracking errors of all following vehicles asymptotically converge to zero:

[0073] ,

[0074] in: For the first Position tracking error of the following vehicle For speed tracking error; , The gain is controlled at the position and velocity levels, respectively; this condition ensures that the following vehicle ultimately and accurately tracks the desired trajectory.

[0075] Achieving coordinated following across multiple performance constraints: Control commands are issued by the onboard controller to ensure that all following vehicles simultaneously meet the following three performance constraints:

[0076] (1) Preset performance constraints: The position tracking error always meets the following requirements. , To ensure that the transient and steady-state performance of the tracking error meets the preset targets, For the first The preset performance boundaries of the following vehicle;

[0077] (2) Safety boundary constraints: The position of the following vehicle always meets the following conditions. , To ensure safe vehicle operation, The time-varying lower boundary, Let i be the actual position of the following vehicle. For time-varying upper boundary, For time;

[0078] (3) Asymptotic convergence performance: The position and speed tracking errors of all following vehicles asymptotically converge to zero, ensuring the final stability of the formation.

[0079] A computer-readable storage medium storing a computer program, which, when executed by a processor, enables a distributed sliding mode control method for vehicle platooning based on a preset performance function and safety constraints.

[0080] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it can realize a distributed sliding mode control method for vehicle platooning based on a preset performance function with safety constraints.

[0081] Beneficial effects

[0082] The distributed sliding mode control method for vehicle platooning based on a preset performance function, as described in this invention, compared with the prior art, ensures that all following vehicles can achieve high-performance tracking of the navigator's trajectory while meeting time-varying safety boundaries through a constraint-aware reference generation mechanism, a preset performance function with adaptive boundaries, and a topology-structured approach law.

[0083] The present invention also has the following advantages:

[0084] (1) For vehicle platooning systems with time-varying safety constraints, existing control methods often neglect safety boundary requirements, which may lead to vehicle violations of traffic rules or collisions. While traditional obstacle Lyapunov function methods can handle constraints, they require fixed or slowly changing constraint boundaries, making them difficult to cope with rapidly changing obstacles, lane-changing scenarios, and traffic regulations in real-world road environments. This invention designs a constraint-aware reference generation mechanism, combining safety margin design with Hermite interpolation smoothing, to transform discontinuous and potentially safety-constraint-violation expected trajectories into C¹ continuously differentiable smooth reference signals that satisfy time-varying safety boundaries, fundamentally ensuring that vehicle positions always meet the requirements. The safety constraints break through the strict assumptions of traditional methods regarding constraint conditions.

[0085] (2) Existing vehicle formation control methods mostly employ preset performance control with fixed performance boundaries. While these methods can constrain the transient and steady-state performance of tracking errors, when the reference signal undergoes abrupt changes (such as emergency lane changes or obstacle avoidance maneuvers), the fixed boundaries cannot adapt to the rapid changes in the reference trajectory, potentially leading to transient error peaks exceeding expectations or even violating performance constraints. This invention designs a two-layer preset performance function with adaptive boundaries, where the basic performance boundary... Guarantee convergence characteristics within a preset time period, adaptive boundary Through differential equations Automatically adjusted based on the rate of change of the reference signal, the boundary is temporarily relaxed during sudden changes in the reference signal to absorb transient shocks, and tightened during steady-state conditions to improve tracking accuracy. This is combined with a singularity-free error transformation. Bounded error space Mapping to unbounded space avoids the numerical singularity problem near the boundary of traditional tan and log transformations, ensuring the continuity and realizability of the control law.

[0086] (3) Traditional sliding mode control methods employ centralized design or coordination strategies based on global information, which not only increases the communication burden but also reduces the system's reliability and scalability. While existing distributed sliding mode control utilizes neighbor information, its approach law design does not fully consider the communication topology, resulting in slow convergence and significant chattering. This invention introduces a topology-structured approach law. By utilizing the algebraic properties of the Laplace matrix L and the navigator connection matrix P, the collective sliding surface is ensured. In a limited time Reaching zero point, among which It is the smallest eigenvalue of L+P. Simultaneously, the boundary layer function BL(s,δ) is designed in... The linear function s / δ is used to replace the symbolic function sgn(s), effectively suppressing high-frequency chattering and ensuring continuous and bounded control input. This distributed control law relies only on the vehicle's state, neighbor vehicle information, and the lead vehicle's signal, requiring no global information, thus significantly reducing communication complexity and improving the system's scalability and fault tolerance.

[0087] (4) This invention constructs a complete three-layer control architecture (position layer, velocity layer, torque layer) that matches a third-order vehicle dynamics model (position, velocity, torque). Virtual control laws are designed layer by layer using the backstepping method, ultimately achieving seamless integration from high-level trajectory planning to low-level actuator control. Based on Lyapunov stability theory, it is rigorously proven that the closed-loop system simultaneously satisfies: preset performance and tracking error. Satisfy preset boundary constraints across the entire time domain; ensure safety, vehicle position. Always within the safe zone; asymptotic convergence, position and velocity tracking errors. and It converges asymptotically to zero; it is achievable in a finite time, and the sliding surface reaches zero in a finite time.

[0088] Theoretical analysis and simulation verification show that the method proposed in this invention can achieve high-performance trajectory tracking in a formation system of 1 lead vehicle + 5 follower vehicles, after experiencing 4 different communication topology switching, while ensuring safety constraints. The position error of all follower vehicles converges to within ±0.5m within a preset time, and the speed error converges to within ±0.2m / s, verifying the effectiveness and robustness of the control method. Attached Figure Description

[0089] Figure 1 This is a sequence diagram of the method of the present invention;

[0090] Figure 2 This is a schematic diagram of the vehicle platooning distributed control system architecture of the present invention;

[0091] Figure 3 This is a flowchart of the distributed sliding mode control method for vehicle platooning based on a preset performance function according to the present invention.

[0092] Figure 4 The following are schematic diagrams of four communication topologies in embodiments of the present invention, wherein: (a) is a bidirectional topology, in which following vehicles communicate bidirectionally; (b) is a bidirectional-leader vehicle topology, in which the leader vehicle broadcasts information to all following vehicles based on the bidirectional topology; (c) is a symmetrical dual-neighbor topology, in which each following vehicle communicates bidirectionally with the two vehicles adjacent to it in front and behind; and (d) is a symmetrical dual-neighbor-leader vehicle topology, in which the leader vehicle broadcasts information to all following vehicles based on the symmetrical dual-neighbor topology.

[0093] Figure 5 This is a schematic diagram illustrating the effect of the constraint perception reference generation mechanism of vehicle 1 in this embodiment of the invention, showing the original reference trajectory. Constrained reference trajectory Smoothed reference trajectory With system output The contrast relationship;

[0094] Figure 6 The figures shown are simulation results of position tracking error, velocity tracking curves, and control input under the bidirectional topology in this embodiment of the invention.

[0095] Figure 7 The figures shown are simulation results of position tracking error, velocity tracking curves, and control input under a symmetrical dual-neighbor topology in this embodiment of the invention.

[0096] Figure 8 The figures shown are simulation results of position tracking error, speed tracking curves, and control input under the bidirectional-navigator topology in this embodiment of the invention.

[0097] Figure 9 The figures shown are simulation results of position tracking error, velocity tracking curves, and control input under the symmetrical dual-neighbor-leader vehicle topology in this embodiment of the invention. Detailed Implementation

[0098] To provide a better understanding of the structural features and effects achieved by the present invention, a detailed description is provided below, accompanied by preferred embodiments and accompanying drawings:

[0099] Example 1

[0100] For vehicle platooning systems with time-varying safety constraints, this invention proposes a distributed sliding mode control method based on a preset performance function. This method transforms discontinuous desired trajectories into smooth signals that satisfy safety boundaries through a constraint-aware reference generation mechanism, suppresses transient error peaks using a preset performance function with adaptive boundaries, and achieves high-performance trajectory tracking using a three-layer distributed sliding mode controller. Theoretical analysis and simulation verification show that the proposed method can ensure that vehicle positions always meet the safety constraints. Under the premise of safety constraints, minimize tracking error It satisfies the preset performance and eventually converges asymptotically to zero.

[0101] like Figure 1 and Figure 2 As shown, the distributed control system architecture for vehicle platooning consists of six main parts: communication topology, vehicle dynamics model, constraint-aware reference generation, preset performance function design, three-layer controller, and stability proof. The communication topology uses graph theory to describe the information interaction relationships between vehicles; the vehicle dynamics model establishes a third-order state-space model (position-velocity-torque); the constraint-aware reference generation module generates smooth safety references based on time-varying safety boundaries; the preset performance function design module handles position errors through adaptive boundaries and singular transformations; the three-layer controller designs virtual control laws layer by layer, ultimately outputting distributed sliding mode control inputs; and the stability proof, based on Lyapunov theory, ensures finite-time reachability and asymptotic stability, forming a complete closed loop of "topology construction - reference generation - performance constraints - hierarchical control - stability analysis".

[0102] like Figure 3 As shown, the distributed sliding mode control method for vehicle platooning based on a preset performance function includes seven main steps: S1 constructing the communication topology and dynamics model, S2 designing the constraint-aware reference generation mechanism, S3 constructing the preset performance function, S4 designing the position tracking layer control law, S5 designing the speed tracking layer control law, S6 designing the distributed sliding mode controller, and S7 proving stability. There is a clear progressive relationship between each step; the output of the previous step serves as the input for the subsequent step, ultimately achieving a complete mapping from the desired trajectory to the actual control input.

[0103] S1. Constructing a communication topology and dynamics model

[0104] We use graph theory to construct the communication topology of the vehicle platooning system and establish a longitudinal dynamics model of the vehicles, transforming the vehicle dynamics model into a third-order state-space model.

[0105] S11. Construct a communication topology based on graph theory: ,in The set of nodes contains one lead vehicle (node ​​0) and Follow-up vehicles (node ​​1 to ); A set of directed edges, representing communication links between vehicles; a communication graph. It contains a directed spanning tree rooted at the navigator, and the information exchange between following nodes is undirected.

[0106] like Figure 4 As shown, this embodiment considers four typical communication topologies: Figure 4 (a) is a two-way topology, where following vehicles communicate with each other in both directions, but do not communicate directly with the lead vehicle; Figure 4 (b) is a symmetric two-neighbor topology, in which each following vehicle communicates bidirectionally with the two vehicles adjacent to it in front and behind; Figure 4 (c) is a two-way lead vehicle topology. Based on the two-way topology, the lead vehicle broadcasts information to all following vehicles, which enhances the global coordination capability. Figure 4 (d) is a symmetrical dual-neighbor-leader vehicle topology. Based on the symmetrical dual-neighbor topology, the leader vehicle broadcasts information to all following vehicles, combining the advantages of dual-neighbor communication and direct connection of the leader vehicle.

[0107] S12. Define the matrix representation of the communication topology: adjacency matrix. If node From the node Receive information ,otherwise Laplace matrix ,in when , ; Navigator vehicle connection matrix If node If it can directly receive information from the navigator vehicle, then ,otherwise .

[0108] S13, Establish the first Longitudinal dynamics model of the following vehicle:

[0109] ,

[0110] in, , , The first Vehicle position, speed, and drive torque; For virtual control input; For vehicle quality; For transmission efficiency; The radius of the wheel; This is the aerodynamic drag coefficient; It is the acceleration due to gravity; This is the rolling resistance coefficient; This is the actuator time constant.

[0111] S14. Define the deviation variable , , The position of the lead car Balance speed Balance torque .

[0112] S15. Transform into a deviation state-space model:

[0113] ,

[0114] S2, Design Constraint-Aware Reference Generation Mechanism

[0115] Based on the state model described in S1, the discontinuous desired trajectory is transformed into a smooth reference signal that satisfies the time-varying safety boundary through safety margin design and Hermite interpolation, and the position tracking error is defined.

[0116] S21, Set the desired vehicle spacing as Traditional location reference is However, this reference may violate security constraints. ,in and For time-varying lower / upper boundaries.

[0117] S22, for the first Vehicle design safety margin:

[0118] ,

[0119] in, For safety margin; For adaptive boundary initial values; , These are the gain coefficient and the attenuation coefficient, respectively. This is the final boundary.

[0120] S23. Generate a constrained reference signal based on the safety margin:

[0121]

[0122] S24, Regarding discontinuous moments In the interval Apply Hermite interpolation, where , The interpolation function is:

[0123]

[0124] in Hermite basis functions are:

[0125] .

[0126] S25. Construction of final smooth safety reference:

[0127] ,

[0128] S26. Define position tracking error .

[0129] S3. Construct a preset performance function

[0130] A preset performance function with adaptive boundaries is constructed, and a singularity-free error transformation is used to map the bounded position tracking error to an unbounded space, thereby avoiding control singularity and suppressing transient error peaks.

[0131] S31. Design a preset performance function with adaptive boundaries. ,in Based on the fundamental performance boundary, For adaptive boundary components.

[0132] S32, the basic performance boundary design is as follows:

[0133]

[0134] in, These are the initial and final performance boundaries, respectively. This is the preset convergence time.

[0135] S33. Adaptive boundaries are generated by differential equations:

[0136]

[0137] in, The attenuation coefficient; This is the gain coefficient; For sensitivity parameters; This is the time delay parameter.

[0138] S34. Error must always be limited: , The initial conditions must be met. .

[0139] S35. Define normalization error Normalize the position tracking error to Interval.

[0140] S36. Introduce a saturation protection mechanism:

[0141]

[0142] in, To prevent numerical singularity.

[0143] S37. Employ a singularity-free transformation:

[0144]

[0145] This transformation will have bounded error. Mapped to unbounded space.

[0146] S4. Design the control law for the position tracking layer.

[0147] Based on the singular error-free transformation in S3, a virtual control law for the position tracking layer is designed, and the desired velocity is derived using the Lyapunov method.

[0148] S41. Differentiate the transform with no singular error:

[0149] ,

[0150] in, .

[0151] S42, Design Expectations Dynamics ,in To adjust the parameters.

[0152] S43. Derivation of the expected velocity:

[0153]

[0154] in, This is a compensation item.

[0155] S44. Define speed deviation and desired speed deviation .

[0156] S5, Design of speed tracking layer control law

[0157] Based on the desired speed in S4, a virtual control law for the speed tracking layer is designed, and the desired torque is derived using the Lyapunov method.

[0158] S51, Define speed tracking error .

[0159] S52. Based on deviation dynamics, differentiate the velocity error:

[0160]

[0161] in, .

[0162] S53, Design Expectations Dynamics ,in To adjust the parameters.

[0163] S54. Deriving the expected torque deviation:

[0164] ,

[0165] S6. Design a distributed sliding mode controller

[0166] A distributed sliding mode surface is constructed based on topology-weighted torque error. A distributed sliding mode controller is designed using topology-structured reaching law and boundary layer function to achieve chattering suppression and bounded control input.

[0167] S61, Define torque tracking error .

[0168] S62. Define individual sliding surfaces:

[0169] ,

[0170] in, These are elements of the adjacency matrix; Indicates car Can it directly receive information from the navigator vehicle?

[0171] S63, collective sliding surface is represented as ,in It is a Laplace matrix; Connect the matrix for the navigator vehicle; This is the torque error vector.

[0172] S64. Design the boundary layer function:

[0173]

[0174] in, This represents the boundary layer thickness.

[0175] S65, Designing Topology Structuring Approach Laws ,in and To adjust the parameters.

[0176] S66, due to Reversible, thus obtaining .

[0177] S67. Solving the simultaneous approach law and deviation dynamics, we obtain the distributed control input:

[0178]

[0179] The control law is distributed across each node, using only the states of the self node, neighbor nodes, and the navigator.

[0180] S7, Prove Stability

[0181] Based on Lyapunov theory, we prove the finite-time reachability of the sliding surface and the asymptotic stability of the tracking error.

[0182] S71. Selecting Lyapunov candidate functions for the arrival phase. .

[0183] S72. Differentiate the Lyapunov function and apply the inequality. ,get:

[0184] +1

[0185] in, yes The smallest eigenvalue.

[0186] S73, the upper limit of the sliding surface arrival time is... This proves that finite-time accessibility is possible.

[0187] S74, During the sliding phase When selecting Lyapunov candidate functions If you choose , ,but Negative definiteness proves asymptotic stability: .

[0188] S75, The comprehensive proof closed-loop system simultaneously meets: preset performance , Safety constraints , asymptotic convergence and It can be achieved in a limited time, and the sliding surface is in The time has reached midnight.

[0189] Simulation parameter settings

[0190] In this embodiment, a vehicle platooning system consisting of one lead vehicle and five follower vehicles is considered. The simulation parameters are set as follows:

[0191] Vehicle parameters: mass kg, expected vehicle spacing m, transmission efficiency Wheel radius m, aerodynamic drag coefficient gravitational acceleration m / s², rolling resistance coefficient Actuator time constant s.

[0192] Controller parameters: Position layer gain Velocity layer gain Arrival Law Parameters and Boundary layer thickness .

[0193] Preset performance function parameters: initial boundary m, final boundary m, convergence time s; Adaptive boundary parameter: attenuation coefficient Gain coefficient Sensitivity parameters Time delay parameter s.

[0194] Error transformation parameters: detection threshold Safety Limit .

[0195] Safety margin is based on the formula Calculation, approximately m.

[0196] The speed trajectory of the navigator is set as follows: Maintaining a constant speed of 20 m / s at time s, Smoothly decelerate to 16 m / s at time s, Accelerating to 21 m / s at s, and It maintains a constant speed of 21 m / s for s.

[0197] The initial values ​​of the system state variables are: vehicle position. Based on the desired vehicle spacing m setting, i.e. m, where m; initial velocity m / s; initial drive torque .

[0198] Simulation Results and Analysis

[0199] A simulation model was built in the MATLAB / Simulink environment to simulate and verify the state evolution process of a vehicle platooning system under four different communication topologies. The simulation results are as follows: Figures 5 to 9 As shown.

[0200] like Figure 5The figure illustrates the effect of the constraint-aware reference generation mechanism for vehicle 1. The figure contains four curves: the original reference trajectory... (Blue solid line) Constrained reference trajectory (Red solid line) Smoothed reference trajectory (Green dashed line) and system output (Orange dotted lines). As can be seen from the diagram, in... s and At two points in time, the original reference undergoes abrupt changes. After constraint, the reference is kept within the safety boundary through safety margin design. After smoothing, the discontinuity of the reference is eliminated through Hermite interpolation. Finally, the system output closely follows the smoothed reference. Two magnified views ( s and s) clearly demonstrates the smoothing effect of the interpolation process, verifying the effectiveness of the constraint-aware reference generation mechanism.

[0201] like Figure 6 As shown, the simulation results for the bidirectional topology are presented. Figure 6 It contains three sub-plots: the top plot shows the position tracking error. [m], where the gray shaded area represents the preset performance boundary. The five colored curves represent the positional errors of following vehicles 1-5; the middle graph shows speed tracking. [m / s] displays the speed changes of the lead car and the five following cars; the following figure shows the control input. [m / s²], displays the acceleration control signals of the five following vehicles. From Figure 6 It can be seen that the position tracking error converges rapidly into the preset performance boundary in the initial stage and stabilizes within ±0.5 m after about 5 seconds. The speed tracking curve shows that all following vehicles can closely follow the speed changes of the lead vehicle (20→16→21 m / s), and the speed error is less than ±0.2 m / s in steady state. The control input fluctuates significantly in the initial stage and at the moment of speed change (about ±2-3 m / s²), and then tends to stabilize without obvious chattering, verifying the anti-chattering effect of the boundary layer function.

[0202] like Figure 7 As shown, the simulation results for a symmetric two-neighbor topology are presented. Figure 7 Subgraph layout and Figure 6 Similarly, it also includes three sub-graphs: position tracking error, velocity tracking, and control input. From Figure 7As can be seen, due to the increased bidirectional communication between the front and rear vehicles in the topology, the convergence speed of the position tracking error is slightly improved compared to the bidirectional topology, and the steady-state error is slightly smaller. Speed ​​tracking performance is comparable to the bidirectional topology, with all following vehicles closely following the speed changes of the lead vehicle. The peak value of the control input is slightly reduced, indicating that the symmetrical two-neighbor topology has better disturbance suppression capabilities.

[0203] like Figure 8 As shown, the simulation results for the bidirectional-navigator topology are presented. Figure 8 The subgraph structure remains consistent with the previous two graphs. From Figure 8 As can be seen, due to the addition of the direct connection of the lead car, the convergence speed of the position tracking error is significantly faster, reaching steady state in about 3 seconds, which is significantly better than the topology without a direct connection of the lead car. The transient response of speed tracking is faster, the overshoot is smaller, and all following cars can respond more quickly to the speed changes of the lead car. The initial peak value of the control input is larger than that of the bidirectional topology, but the convergence speed is faster, indicating that the direct connection of the lead car provides stronger global coordination capabilities.

[0204] like Figure 9 As shown, the simulation results for a symmetric two-neighbor-leader topology are presented. Figure 9 It also includes three sub-graphs: position tracking error, velocity tracking, and control input. From Figure 9 As can be seen, this topology combines the advantages of dual-neighbor communication and navigator vehicle connectivity, exhibiting optimal overall performance: the position tracking error converges fastest and has the smallest steady-state error, reaching steady state in approximately 2 seconds and remaining within ±0.3 m; speed tracking is the smoothest, with a more natural transition process; the control input has a moderate peak value and converges rapidly, fluctuating by approximately ±2 m / s² in the initial stage before quickly stabilizing, with no significant jitter throughout the process. All performance indicators reach optimal levels, verifying the superiority of this topology in practical applications.

[0205] Comprehensive comparative analysis

[0206] Comparing the simulation results of the four topologies, the following conclusions can be drawn:

[0207] (1) Preset performance guarantee: All topologies can guarantee that the position tracking error is always within the preset performance boundary, which verifies the effectiveness of the preset performance function design.

[0208] (2) Impact of pilot vehicle connection: The topology of pilot vehicle connection ( Figure 8 , Figure 9 Compared to a topology without a navigator connection ( Figure 6 , Figure 7 It exhibits faster convergence speed and smaller steady-state error, with convergence time reduced by approximately 40%, which proves... The significant impact of positive definiteness on system performance.

[0209] (3) Advantages of symmetric two-neighbor topology: symmetric two-neighbor topology ( Figure 7 , Figure 9 Compared to bidirectional topology ( Figure 6 , Figure 8 It has better robustness and smaller control input ripple, with control input peak reduced by about 15%.

[0210] (4) Optimal topology recommendation: Symmetric dual-neighbor-navigator topology ( Figure 9 It has the best overall performance and is the recommended choice for practical applications.

[0211] (5) Chattering suppression: The boundary layer function effectively suppresses chattering in sliding mode control, and the control inputs of all topologies remain bounded and smooth.

[0212] (6) Reference generation effect: The constraint-aware reference generation mechanism successfully transforms discontinuous references into smooth signals, avoiding abrupt changes in control input.

[0213] (7) Adaptive boundary effect: The adaptive boundary at the reference abrupt change time ( s and s) Temporarily relaxing the performance boundary effectively suppresses the peak value of transient error.

[0214] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention. The scope of protection claimed by the appended claims and their equivalents is defined.

Claims

1. A distributed sliding mode control method for vehicle platooning based on a preset performance function with safety constraints, characterized in that, Includes the following steps: 11) Establish a third-order state-space model for vehicle platooning; 12) Generate a smooth reference trajectory for the following vehicle; 13) Design the following vehicle's preset performance constraints; 14) Calculate the desired speed of the following vehicle; 15) Calculate the expected torque of the following vehicle; 16) Control the following vehicle's drive system; 17) Achieve coordinated control of formations.

2. The distributed sliding mode control method for vehicle platooning based on a preset performance function according to claim 1, characterized in that, The establishment of the third-order state-space model for vehicle platooning includes the following steps: 21) Construct vehicle platoon communication topology: Use a directed graph to describe the platoon communication structure containing 1 lead vehicle and N follower vehicles, define the adjacency matrix, Laplace matrix and lead vehicle connection matrix to characterize the communication relationship and topological characteristics between vehicles; 22) Establish the longitudinal dynamics model of the following vehicle: Establish the first... A third-order dynamic model of the longitudinal position, velocity, and driving torque of the following vehicle is used to describe the longitudinal motion characteristics of the vehicle. 23) Transform into a relative deviation state-space model: Define the first The positional deviation, speed deviation, and torque deviation of each following vehicle relative to the lead vehicle are used to transform the absolute dynamics of the vehicle into a third-order deviation state-space model relative to the lead vehicle. Using the lead vehicle as a reference benchmark, it is convenient to design distributed cooperative control laws.

3. The distributed sliding mode control method for vehicle platooning based on a preset performance function according to claim 1, characterized in that, The generated smooth reference trajectory for the following vehicle is as follows: based on the position of the lead vehicle and the expected spacing between vehicles in the formation, a constraint-aware reference generation mechanism with time-varying safety margin is designed, and a smooth reference signal that meets the time-varying safety boundary is generated through dynamic adjustment of the safety margin and trajectory smoothing. Includes the following steps: 31) Set formation configuration and design time-varying safety margin: Set the desired vehicle spacing and time-varying safety constraint boundaries, for the first Vehicle following vehicle design with variable safety margin: ， in: For the first The time-varying safety margin of a vehicle describes the buffer distance between the reference trajectory and the safety boundary; This serves as the initial safety margin, providing a significant safety safety tolerance during the formation startup phase. This is the final safety margin value, the minimum safety margin maintained after the formation stabilizes; This is the margin gain coefficient, which controls the magnitude of margin decay; This is the margin decay coefficient, which controls the rate at which the margin decays from its initial value to its final value. Runtime; As an exponential decay function, this margin design allows the safety buffer distance to gradually tighten from an initial conservative value to a steady-state compact value as the formation status changes, balancing startup safety and steady-state tracking accuracy. 32) Generate constraint-aware reference signals: Generate reference signals that satisfy boundary constraints based on time-varying safety margins. ， in: For the first Vehicle constraint reference signals; Used as an initial position reference; , These are the time-varying lower and upper boundaries, respectively; when the initial reference is lower than the lower boundary plus margin, the reference signal is set to the lower boundary plus margin; when the initial reference is within the safe range, the original value is maintained; when the initial reference is higher than the upper boundary minus margin, the reference signal is set to the upper boundary minus margin. 33) Smoothing and defining tracking error: Hermite interpolation is used to smooth the discontinuous moments of the constraint reference signal to generate the final smooth safety reference trajectory. and define the first Position tracking error of the following vehicle , Let i be the actual position of the i-th following vehicle, which will be the control object for the subsequent control law design.

4. The distributed sliding mode control method for vehicle platooning based on a preset performance function according to claim 1, characterized in that, The design of the following vehicle is subject to the following preset performance constraints: A preset performance function with adaptive boundaries is constructed for each following vehicle; a singularity-free error transformation is used to map the bounded position tracking error to an unbounded space, ensuring that control singularities are avoided and transient error peaks are suppressed during the control process; including the following steps: 41) Design a preset performance boundary function: Design a preset performance function with adaptive boundaries. , ,in Based on the fundamental performance boundary, For adaptive boundary components; basic performance boundaries Designed as follows: ， in: As the initial performance boundary, satisfying A larger tracking error is allowed during the formation start-up phase; The final performance boundary is the required tracking accuracy after the formation has stabilized. The preset convergence time controls the time scale from the initial boundary to the final boundary; This is the current running time; 42) Designing adaptive boundary dynamics: Adaptive boundary components are generated by differential equations: ， in: The time derivative of the adaptive boundary component; This is the adaptive boundary attenuation coefficient, which controls the attenuation rate of the adaptive boundary. The adaptive gain coefficient controls the intensity of the influence of the control error on the boundary. This is the sensitivity exponent parameter, which controls the sensitivity of the adaptive boundary to changes in error. This refers to the time-delay position tracking error; This is a time delay parameter used to avoid high-frequency oscillations; 43) Apply performance constraints and implement error transformation: require the position tracking error to meet performance constraints: ， Initial conditions are met: ， Define normalization error: ， Employ singularity-free transformation: ， in: For the first Position tracking error of the following vehicle To preset performance constraints, This means that the condition holds true for all non-negative moments, ensuring that the position tracking error remains within the specified range. The initial conditions ensure that the initial error meets performance requirements and does not violate safety constraints. , These represent the time-varying upper and lower boundaries at the initial moment; The normalization error is dimensionless and has a range of values. This normalizes the bounded error; It is dimensionless and has no singular transformation error, with a range of values. ,in For the natural logarithm function, the transformation ensures that when hour This maps the bounded normalization error to an unbounded space.

5. The distributed sliding mode control method for vehicle platooning based on a preset performance function according to claim 1, characterized in that, The calculation of the desired speed of the following vehicle involves: based on a singular error-free transformation, designing a virtual control law for the position tracking layer, and deriving the desired speed command for each following vehicle using the Lyapunov method; including the following steps: 51) Construct the dynamic equation of position error: Take the derivative of the singular error transformation of the following vehicle to obtain the relationship between the time derivative of the transformation error, the derivative of the position tracking error, and the rate of change of the preset performance boundary; 52) Design the position tracking control law: Based on Lyapunov stability theory, for the first... Vehicle following vehicle design position layer expected dynamics : ， in: Position layer control gain; To eliminate singular transformation errors, this control law ensures that the transformation error decays to zero at an exponential rate, thereby guaranteeing that the original position tracking error converges to within the preset performance boundary. 53) Generate the desired speed command: This is achieved by reverse engineering the position tracking control law to generate the first... The vehicle following the vehicle generates the desired speed command, which includes a reference trajectory feedforward term, a position error feedback term, a performance boundary compensation term, and a transformation error compensation term.

6. The distributed sliding mode control method for vehicle platooning based on a preset performance function according to claim 1, characterized in that, The calculation of the desired torque for the following vehicle involves: designing a virtual control law for the speed tracking layer based on the desired speed command and the actual speed deviation, and deriving the desired drive torque for each following vehicle using the Lyapunov method; including the following steps: 61) Define speed tracking error: Define the first The difference between the actual speed deviation of the following vehicle and the desired speed command is the speed tracking error. ; 62) Design of speed tracking control law: Based on Lyapunov stability theory, for the first... Vehicle following vehicle design speed layer expected dynamics : ， in: Control the gain for the velocity layer; For speed tracking error; this control law ensures that the speed tracking error converges to zero at an exponential rate; 63) Generate desired drive torque command: Combining the longitudinal dynamics model of the following vehicle, the desired drive torque deviation is generated for the i-th following vehicle by back-calculating through the speed tracking control law. It includes the expected acceleration feedforward term, the speed error feedback term, the air resistance compensation term, and the navigator acceleration compensation term.

7. The distributed sliding mode control method for vehicle platooning based on a preset performance function according to claim 1, characterized in that, The controlled following vehicle drive system comprises: constructing a distributed sliding mode surface based on torque error weighted by vehicle communication topology; designing a distributed sliding mode controller using a topology-structured reaching law; and generating drive system control inputs for each following vehicle; including the following steps: 71) Define torque tracking error: Define the first The difference between the actual driving torque deviation and the expected driving torque deviation of the following vehicle is the torque tracking error. ; 72) Constructing a distributed sliding surface: Based on the vehicle formation communication topology, for the first... Vehicles follow each other to construct a distributed sliding surface: ， in: For the first The individual sliding surface of the following vehicle reflects the torque tracking status of the vehicle and its communication neighbors; The total number of following vehicles; These are adjacency matrix elements, describing the communication connections between vehicles; For the first Torque tracking error of the following vehicle; The connection coefficient of the lead vehicle; The collective sliding surface of all following vehicles is represented in vector form. , in For the collective sliding surface vector, For Laplace matrix, Connect the matrix for the lead vehicle. This is the torque error vector; 73) Design of a topology-structured reaching law: To suppress sliding mode control chattering and ensure finite-time arrival, a topology-structured reaching law is designed: ， in: For the first The time derivative of the sliding surface of the vehicle; The proportional gain of the approach law controls the speed at which the sliding surface approaches. For the reaching law switching gain; This is a boundary layer function used to suppress high-frequency chattering; This refers to the boundary layer thickness parameter; 74) Generate distributed control input: Through the reaching law and torque error dynamics, for the first... Vehicle following vehicle generates drive system control input It includes a feedback control term based on the sliding surface and a feedforward compensation term for the desired torque, ensuring that the system reaches the sliding surface in a finite time and converges asymptotically and stably along the sliding surface.

8. The distributed sliding mode control method for vehicle platooning based on a preset performance function according to claim 1, characterized in that, The formation cooperative control is achieved by: verifying the finite-time reachability of the sliding surface and the asymptotic stability of the tracking error based on Lyapunov theory; issuing control commands through the onboard controller to enable all following vehicles to cooperatively follow the trajectory of the lead vehicle while meeting safety constraints and preset performance requirements; including the following steps: 81) Verify the finite-time reachability of the sliding surface: drive system control input Based on Lyapunov theory, the arrival phase performance of the distributed sliding mode control system is verified, proving that the upper bound of the sliding surface arrival time is: ， in: This is the upper bound of the arrival time of the sliding surface; Let be the 2-norm of the initial collective sliding surface; For the reaching law switching gain; For matrix The smallest eigenvalue represents the connectivity strength of the communication topology; 82) Verify the asymptotic stability of the tracking error: Based on Lyapunov theory, prove that when the control gain satisfies and At that time, the position and speed tracking errors of all following vehicles asymptotically converge to zero: ， in: For the first Position tracking error of the following vehicle For speed tracking error; , The gain is controlled at the position and velocity levels, respectively; this condition ensures that the following vehicle ultimately and accurately tracks the desired trajectory. 83) Achieve multi-performance constraint cooperative following: Control commands are issued by the onboard controller to ensure that all following vehicles simultaneously meet the following three performance constraints: (1) Preset performance constraints: The position tracking error always meets the following requirements. , To ensure that the transient and steady-state performance of the tracking error meets the preset targets, For the first The preset performance boundaries of the following vehicle; (2) Safety boundary constraints: The position of the following vehicle always meets the following conditions. , To ensure safe vehicle operation, The time-varying lower boundary, Let i be the actual position of the following vehicle. For time-varying upper boundary, For time; (3) Asymptotic convergence performance: The position and speed tracking errors of all following vehicles asymptotically converge to zero, ensuring the final stability of the formation.

9. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the safety-constrained vehicle platooning distributed sliding mode control method based on a preset performance function as described in any one of claims 1-8.

10. A computer device, characterized in that, The system includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it can implement the distributed sliding mode control method for safety-constrained vehicle platooning based on a preset performance function as described in any one of claims 1-8.

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