Vehicle formation MPC control method fusing asymmetric response model and delay compensation

Abstract

The invention relates to the technical field of intelligent traffic and automatic driving control, and discloses a vehicle formation MPC control method fusing an asymmetric response model and delay compensation, and the method comprises the steps: firstly building an asymmetric vehicle longitudinal dynamics model for distinguishing acceleration and deceleration characteristics; the longitudinal acceleration of the vehicle is monitored in real time, and if the acceleration working condition is judged, non-delay model parameters are adopted; and if the condition is judged to be a deceleration condition, model parameters containing pure time delay are adopted, a state augmentation technology is utilized to bring historical control input into a state vector, and a delay-free augmentation discrete state space model is constructed. On the basis, a quadratic programming problem containing multiple costs and soft constraint penalty is solved by combining acceleration disturbance information of the front vehicle and the head vehicle, and an optimal control instruction is obtained. In addition, a hierarchical security redundancy strategy when the solution fails is also designed. The method can accurately match the vehicle physical characteristic difference, effectively compensates the brake delay influence, and improves the tracking precision, stability and safety of formation control.

Description

Technical Field

[0001] This invention relates to the field of intelligent transportation and autonomous driving control technology, specifically to a vehicle platooning MPC control method that integrates asymmetric response model and delay compensation. Background Technology

[0002] Vehicle platooning, as a crucial component of intelligent transportation systems, can reduce wind resistance and improve road efficiency by shortening the distance between vehicles. In platooning control algorithms, Model Predictive Control (MPC) is widely used for longitudinal vehicle following control due to its ability to explicitly handle multi-objective optimization and system constraints. The performance of the MPC controller is highly dependent on the accuracy of the predictive model, i.e., whether the model can accurately reflect the dynamic response characteristics of the vehicle during actual driving.

[0003] However, existing studies on vehicle longitudinal control mostly employ a uniform linear model to describe vehicle dynamics, assuming that the vehicle's response characteristics are consistent during acceleration and deceleration. In reality, vehicle longitudinal dynamics are asymmetric. The acceleration process is mainly driven by the powertrain, including the engine, motor, and transmission, and its response characteristics are primarily influenced by mechanical inertia. The deceleration process, on the other hand, relies on hydraulic or pneumatic braking systems, and in addition to inertial lag, there is also a pure time delay due to pipeline transmission and pressure build-up. Traditional single models struggle to simultaneously account for these two distinct physical characteristics, resulting in model parameters typically only being calibrated for a specific operating condition.

[0004] Furthermore, when dealing with the pure time delay of the braking system, conventional linear MPC methods typically ignore or simplify it to a first-order inertial element. When the vehicle is decelerating, this simplification can cause the controller to mistakenly believe that the vehicle can respond to braking commands immediately, resulting in prediction bias. This mismatch between the model and the actual physical object can lead to overshoot oscillations in real-world applications. Particularly in platooning scenarios with small vehicle spacing, uncompensated braking delays reduce the system's phase margin, causing lag in the reaction of following vehicles, leading to increased tracking errors, decreased ride comfort, and in severe cases, even platoon instability or rear-end collisions. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a vehicle platooning MPC control method that integrates an asymmetric response model and delay compensation. This method solves the problems in existing vehicle platooning control, such as the inability of a single linear model to accurately describe the asymmetric characteristics of vehicle acceleration and deceleration dynamics, and the large model prediction bias, control command oscillation, and poor platooning stability caused by ignoring the pure time delay of the braking system.

[0006] To achieve the above objectives, this invention provides a vehicle platooning MPC control method that integrates an asymmetric response model and delay compensation, comprising: firstly, establishing a longitudinal dynamics model of the vehicle. Based on the differences in physical characteristics between the vehicle powertrain and braking system, this model adopts an asymmetric structure, including an acceleration longitudinal dynamics model describing acceleration characteristics and a deceleration longitudinal dynamics model describing deceleration characteristics. The acceleration longitudinal dynamics model is constructed as a first-order inertial system without pure time delay, and its characteristic parameters include the acceleration time constant. The deceleration longitudinal dynamics model is constructed as a first-order inertial system with pure time delay to characterize the hysteresis characteristics during the braking pressure build-up process, and its characteristic parameters include the deceleration time constant and the pure time delay, wherein the value of the deceleration time constant is greater than that of the acceleration time constant.

[0007] Based on the established dynamic model, this invention constructs a formation control state-space model. This model integrates the longitudinal dynamic model of the vehicles into the system state evolution equation, characterizing the dynamic correlation between formation error state variables and control inputs. The formation error state variables are selected as spacing error, relative velocity, relative velocity of the lead vehicle, and actual acceleration of the vehicle itself; wherein, spacing error is the difference between the actual distance between the vehicle and the vehicle in front and the expected distance calculated based on a constant time spacing strategy.

[0008] This invention employs a threshold-based model switching strategy. Within a control cycle, real-time driving state data, including at least the vehicle's longitudinal acceleration, is acquired. This longitudinal acceleration is compared with a preset threshold to determine the appropriate discretization base model for the current moment. If the vehicle's longitudinal acceleration is greater than or equal to the preset threshold, it is determined to be an acceleration condition, and the parameter matrix corresponding to the acceleration longitudinal dynamics model is directly selected as the discretization base model, which does not contain input delay terms. If the vehicle's longitudinal acceleration is less than the preset threshold, it is determined to be a deceleration condition, and the parameter matrix corresponding to the deceleration longitudinal dynamics model is selected as the discretization base model, which includes input delay terms.

[0009] To address the delay issue under deceleration conditions, this invention performs delay processing on the discretized basic model. Using state augmentation techniques, the pure time delay in the deceleration longitudinal dynamics model is quantized into an integer multiple of the sampling period, representing a delay step. Subsequently, an augmented state vector is defined, consisting of the original formation error state variables and historical control inputs from several past control cycles, with the number of historical control inputs corresponding to the delay step. By reconstructing the system evolution matrix, the historical control inputs are introduced into the state update equation, establishing a delay-free evolution relationship based on the augmented state vector, transforming the time-delayed system into an equivalent delay-free system. Under acceleration conditions, the discretized basic model remains unchanged.

[0010] Subsequently, the processed model is substituted into the model predictive control solver. A quadratic programming problem containing an objective function and constraints is constructed and solved. The objective function takes the form of a weighted cost term, which includes: state tracking cost penalizing the deviation between the predicted state and the reference state; control quantity cost penalizing the control input magnitude; control increment cost penalizing the rate of change of control input in adjacent control cycles; and soft constraint penalty cost penalizing the magnitude of slack variables.

[0011] When constructing the quadratic programming problem, the prediction equation represents the future state sequence as a linear combination of the free response of the current state, the forced response to future control inputs, and the forced response to measurable disturbances. The measurable disturbances include the accelerations of the preceding and lead vehicles obtained through inter-vehicle communication, which participate in the calculation as known inputs in the prediction time domain. For the constraints, this invention introduces a soft constraint on vehicle spacing, that is, assigning non-negative relaxation variables to the prediction steps in the prediction time domain, allowing the vehicle spacing to be less than the lower bound of the safe distance within a limited range, and penalizing the relaxation variables with high weights in the objective function to minimize the degree of violation while ensuring the feasibility of the solution.

[0012] Furthermore, this invention also establishes a layered safety redundancy mechanism to improve system robustness. The first layer is a degradation rollback strategy: when the quadratic programming problem fails to be solved in the current control cycle and the number of consecutive failures has not reached a preset upper limit, the optimal control sequence obtained from the successful solution in the previous control cycle is obtained, and the second element in the sequence is selected as the current instruction and sent to the actuator. The second layer is an emergency stop and reset strategy: when the number of consecutive solution failures reaches or exceeds a preset upper limit, the controller is determined to have failed, a preset emergency braking instruction is generated and sent to the actuator, and the internal state of the model predictive control solver is forcibly reset so that the calculation can be re-initialized in the next control cycle.

[0013] Through the above technical solution, the present invention can dynamically switch the prediction model according to the real-time operating conditions of the vehicle and actively compensate for the inherent delay in the braking process, effectively improving the tracking accuracy, smoothness and safety of vehicle formation control.

[0014] This invention provides a vehicle platooning MPC control method that integrates an asymmetric response model and delay compensation. It has the following advantages: 1. This invention solves the problem of inconsistent physical characteristics of vehicles at different dynamic response stages by constructing an asymmetric longitudinal dynamic model for acceleration and deceleration. Existing technologies typically use a single linear model, which is difficult to balance the rapid response of the powertrain with the braking system's build-up delay. In contrast, this invention switches applicable model parameters online based on the comparison between real-time acceleration and preset thresholds, accurately matching the inertial characteristics of the vehicle during acceleration and the braking hysteresis characteristics during deceleration, thereby improving the prediction accuracy and tracking performance of model predictive control under all operating conditions.

[0015] 2. This invention proposes a delay compensation strategy based on state augmentation technology, effectively overcoming the control oscillation risk caused by pure time delay in the braking system. For deceleration conditions, by quantizing historical control inputs and incorporating them into the augmented state vector, the system containing input delays is transformed into a formally delay-free high-dimensional linear system, enabling the model predictive controller to accurately account for the lag time of the braking command. Without altering the standard quadratic programming structure of the solver, the closed-loop stability of the vehicle in deceleration following and emergency braking scenarios is significantly improved.

[0016] 3. The multi-objective optimization function designed in this invention, combined with a hierarchical safety redundancy mechanism, enhances the robustness of the platoon control system and its feasibility for real-vehicle application. By introducing the accelerations of the preceding and lead vehicles as known disturbances for feedforward compensation, and using relaxation variables to transform hard constraints into soft constraints, the solver's solvability under strong disturbance conditions is guaranteed. Simultaneously, by combining a command rollback strategy based on the previous cycle's optimal solution and emergency braking logic, controller failure due to computation timeouts or solution failures is effectively prevented, ensuring the continuity and safety of the platooning process. Attached Figure Description

[0017] Figure 1 This is the overall flow of the method in an embodiment of the present invention; Figure 2 The process for establishing the vehicle longitudinal dynamics model of this invention; Figure 3 This is the process for constructing the state space model for formation control in this invention; Figure 4 This is the logic flow for determining the working condition and switching the model in this invention; Figure 5 This is the delay compensation and state augmentation process of the present invention. Detailed Implementation

[0018] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] See attached document Figure 1 This invention provides a vehicle formation MPC control method that integrates asymmetric response model and delay compensation, comprising the following steps: S10, Establish a longitudinal dynamics model for the vehicle, which includes an acceleration longitudinal dynamics model describing the vehicle's acceleration characteristics and a deceleration longitudinal dynamics model describing the vehicle's deceleration characteristics. S20. Construct a formation control state space model that integrates the above vehicle longitudinal dynamics model to characterize the dynamic relationship between formation error state variables and control input. S30, acquire real-time driving status data including at least the longitudinal acceleration of the vehicle; S40, compare the longitudinal acceleration of this vehicle with the preset threshold, determine the discretized basic model based on the formation control state space model, if it is determined to be an acceleration condition, select the corresponding parameters of the acceleration longitudinal dynamics model, if it is determined to be a deceleration condition, select the corresponding parameters of the deceleration longitudinal dynamics model. S50, the discretized basic model is delayed. If it corresponds to the deceleration condition, the historical control input is introduced using the state augmentation technique to construct a delay-free augmented discrete state space model. If it corresponds to the acceleration condition, the discretized basic model remains unchanged. S60 substitutes the augmented discrete state-space model or the discretized basic model into the model predictive control solver to solve the quadratic programming problem containing the objective function and constraints, and sends the first element of the resulting optimal control sequence to the actuator.

[0020] The technical implementation details of each of the above steps will be explained in detail below, combining mathematical formulas and specific implementation examples.

[0021] See attached document Figure 2 The process of establishing the vehicle's longitudinal dynamics model in step S10 aims to capture the differences in the vehicle's physical characteristics at different dynamic response stages. Given the physical asymmetry between the vehicle's powertrain drive mechanism and braking system deceleration mechanism, a single model cannot accurately cover all operating conditions. Therefore, this embodiment constructs an asymmetric structure model, including the following sub-steps: Step S11: Establish the acceleration longitudinal dynamics model. This model describes the response characteristics of the powertrain system, including the engine, motor, and transmission, to the desired acceleration command under vehicle acceleration conditions. During acceleration, the powertrain response is mainly affected by inertia, and the pure time delay is negligible. Therefore, a first-order inertial system without input delay is used to construct the acceleration longitudinal dynamics model. .

[0022] Should The transfer function is expressed as: ; In the formula, The Laplace transform representing the actual longitudinal acceleration of the vehicle; The Laplace transform of the desired acceleration command (i.e., control input) output by the controller; This is the system gain, which is approximately 1 in the idealized linear model; The acceleration time constant characterizes how fast the powertrain response is.

[0023] The corresponding time-domain differential equation is described as follows (assuming system gain). ): ; In the formula, for The derivative of the vehicle's actual longitudinal acceleration with respect to time at any given moment; for The actual longitudinal acceleration of the vehicle at any given moment; for The desired longitudinal acceleration command output by the time controller.

[0024] Step S12: Establish the longitudinal dynamics model for deceleration. This model describes the response characteristics of the hydraulic or pneumatic braking system to deceleration commands under vehicle deceleration conditions. During the process of establishing effective braking pressure, the braking system experiences hysteresis due to physical pipeline transmission and mechanical action, manifesting as a non-negligible pure time delay. Therefore, a first-order inertial system (First-Order Plus Dead-Time, FOPDT) with pure time delay is used to construct the longitudinal dynamics model for deceleration.

[0025] The deceleration model The transfer function is expressed as: ; In the formula, For pure time delay, it represents the time interval from when the controller issues a braking command to when the braking system begins to produce actual deceleration; The deceleration time constant characterizes the inertial characteristics of the braking force build-up process.

[0026] The corresponding time-domain differential equation is described as follows (assuming system gain). ): ; This equation shows that the acceleration response at the current moment depends not only on the current state, but also on... Control input before time .

[0027] Step S13: Determine key parameters of the model. These parameters are obtained by collecting response data from the actual vehicle under different throttle openings and braking intensities, using an offline system identification method. Regarding the numerical relationships of the parameters, since the braking system involves a fluid pressure build-up process, its response inertia is typically greater than the electronic control response of the powertrain; therefore, a deceleration time constant is set. The value is greater than the acceleration time constant. This asymmetric setting of parameters can more realistically reflect the vehicle's physical properties, thereby supporting the accuracy of subsequent control algorithms. The specific algorithm for system identification is well-known to those skilled in the art and will not be elaborated upon here.

[0028] See attached document Figure 3 In step S20, a formation control state-space model integrating the vehicle's longitudinal dynamics model is constructed, aiming to establish a mathematical mapping relationship between the vehicle's control input, external disturbances, and formation error state variables. This process includes the following sub-steps: Step S21: Define the platooning error state variables and control strategy. To ensure the safety and traffic efficiency of vehicles during platooning, this embodiment adopts a constant time headway (CTH) strategy as the spacing control benchmark.

[0029] Define the system state vector The vector below comprehensively describes the core error variables of formation control: ; In the formula: This refers to the distance error between this vehicle and the vehicle immediately in front of it. for At any given moment, the actual arc length distance between the front end of this vehicle and the rear end of the vehicle immediately preceding it, measured along the driving path; This is the relative speed between this vehicle and the vehicle immediately in front of it; This is the relative speed between this vehicle and the lead vehicle in the convoy, used to improve the overall stability of the convoy; Let this be the actual acceleration of the vehicle. Treating it as a state variable allows for the constraint and optimization of the acceleration and its rate of change. Indicates in At any given moment, the ideal safe distance that the vehicle should maintain is calculated based on the preset following strategy; This is the longitudinal speed of the vehicle; The longitudinal speed of the vehicle immediately preceding it; The longitudinal speed of the lead vehicle in the formation.

[0030] Based on this constant time interval strategy, the expected vehicle spacing is... Defined as: ; In the formula, The desired time interval; This is the vehicle's real-time speed; This is the minimum safe distance when stationary (including fixed factors such as vehicle length).

[0031] Step S22: Derive the continuous-time state differential equation of the system. For the state vector... Differentiating each component yields the continuous-time state-space equation of the system: For spacing error Its differential equation is: ; For relative velocity Its differential equation is: ; relative speed of the lead car Its differential equation is: ; Regarding the acceleration of this vehicle Its differential equation is: ; in, This represents the effective control input, and its value is determined based on the operating condition judgment result in step S40: For acceleration operating conditions, For deceleration conditions, .

[0032] acceleration of the vehicle in front and the acceleration of the lead car In the model, these are considered as two independent, measurable disturbances within the system. This vehicle can obtain the desired acceleration sequence calculated in real-time by the preceding and lead vehicles via V2V inter-vehicle communication. A disturbance vector is defined. By rewriting the above system of equations in standard matrix form, we obtain a continuous-time state-space model.

[0033] Regarding the acceleration of this vehicle Based on the first-order inertial system differential equations established in steps S11 and S12 ( By rearranging terms, we can obtain the derivative relationship as follows: ; In the formula, To accelerate the vehicle in front, To accelerate the lead car, The time constant under the corresponding operating condition (i.e.) or ), To control the input, the mathematical expression of the delay term will not be elaborated here; the effect of the delay will be handled uniformly in the subsequent discretization and augmentation steps.

[0034] Step S23: Establish the continuous-time state-space matrix equations. Rearrange the system of differential equations from step S22 into standard linear state-space form: ; in, The state matrix; The input matrix; Here is the perturbation matrix; The external disturbance vector; Represents the system state vector Regarding time The first derivative of the state is the rate of change of the state.

[0035] In this embodiment, the acceleration information of the preceding vehicle and the lead vehicle is obtained in real time through V2V vehicle-to-vehicle communication technology as a known disturbance input system.

[0036] System state matrix Input matrix and perturbation matrix The specific structure is as follows: ; ; ; This state-space model fully characterizes the dynamic evolution of the vehicle during longitudinal following and establishes the control input. Driven state variables Changes, and external disturbances The mathematical framework of the influence provides a basic model for subsequent model predictive control solutions. The fundamental theories of matrix operations and state spaces are well-known to those skilled in the art and will not be elaborated upon here.

[0037] Step S30, which involves acquiring real-time driving state data, provides the model predictive control with the current system initial state and known disturbance inputs in the prediction time domain. This process utilizes the onboard perception system and the vehicle-to-vehicle communication system, and specifically includes the following sub-steps: Step S31: Collect vehicle kinematic parameters and environmental perception data. Utilize onboard sensors to acquire the vehicle's dynamic response and surrounding environment information. Measure the vehicle's longitudinal acceleration in real time using an onboard inertial measurement unit (IMU) or a longitudinal acceleration sensor. This parameter serves as a state vector component and as the basis for condition determination and model switching in step S40. The vehicle's real-time speed is obtained via wheel speed sensors or a Global Navigation Satellite System (GNSS). Using a sensor fusion system comprised of onboard millimeter-wave radar, lidar, or vision cameras, the actual physical distance between the vehicle and the vehicle in front is measured. and relative speed The acquisition frequency of the aforementioned sensor data must meet the controller's operation cycle requirements, such as 10Hz to 100Hz, to ensure real-time data transmission.

[0038] Step S32: Obtain external traffic information for the convoy. Using the V2X inter-vehicle communication module, establish a low-latency data link between this vehicle and the preceding and lead vehicles. Receive real-time calculated or measured acceleration data from the preceding vehicles through this link. and speed And the acceleration of the lead car. and speed In this embodiment, the acceleration of the vehicle in front is... and the acceleration of the lead car These are set as measurable disturbances. Within the prediction time domain of model predictive control, these disturbances are considered to remain constant or vary according to the received prediction sequence, thus being treated as known input quantities. Substituting the values ​​into the prediction equation, feedforward compensation for the disturbance is achieved.

[0039] Step S33: Construct the real-time state vector and disturbance vector. Perform timestamp alignment and filtering on the raw data obtained in steps S31 and S32 to remove high-frequency measurement noise. Based on the processed data, calculate the spacing error according to the definition in step S21. Relative speed with the lead car And combine to generate the current control cycle. System state vector at time t And the perturbation vector. This completes the conversion from physical sensor signals to the mathematical vectors required by the control algorithm. The data filtering algorithm and V2X workshop communication module are well-known technologies to those skilled in the art and will not be elaborated upon here.

[0040] See attached document Figure 4 Step S40, which involves threshold-based condition determination and model switching, aims to address the model mismatch issue in the acceleration / deceleration transition region. This process establishes a Piecewise Affine (PWA) mechanism to select the best-matching discretized base model online based on real-time operating conditions. Specifically, it includes the following sub-steps: Step S41, model discretization. First, we discretize the two continuous-time models. The sampling period is used. The discrete-time state-space model can be obtained using the zero-order hold (ZOH) method: ; in, This refers to the discrete time step number; Indicates the first The controller outputs a constant control input at each sampling time and is held constant by a zero-order hold; Indicates the first External disturbance values ​​observed at each sampling time; Let be a discrete state matrix, mathematically defined as ; For a discrete input matrix, the mathematical definition is... ; The discrete perturbation matrix is ​​mathematically defined as follows: .

[0041] According to the use With different values, we will obtain two different sets of discrete matrices: Acceleration Model Using time constant It accurately describes the dynamic response under acceleration conditions. Its state-space matrix is ​​obtained through discretization. This model has no input delay.

[0042] Braking model Using time constant This model accurately describes the dynamic response under braking conditions. However, it also includes pure delay. It needs to be processed using the state augmentation technique described in step S50, and its state space matrix is ​​obtained through discretization. .

[0043] Step S42, online model switching logic. In each control cycle... The system is based on the actual acceleration of the vehicle. Compared with the preset braking judgment threshold The system makes a judgment and selects the model for MPC prediction in the current period online. This switching logic can be expressed as: ; in, This is the set of model parameters used for MPC prediction in the current control cycle, along with the initial values ​​of the current state. This represents the actual acceleration of the vehicle at the current moment. The braking determination threshold; This represents the original system state vector; Augmented state vector.

[0044] This logic indicates that when an acceleration condition is identified, the original state should be used directly. And acceleration model parameters; when the condition is determined to be deceleration, switch to braking model parameters and use augmented state. To compensate for the impact of the delay.

[0045] Step S43, Online operating condition determination. In each control cycle... Read the longitudinal acceleration of the vehicle obtained in step S31. Set a preset threshold to distinguish between acceleration and deceleration behavior. , usually take Or a small negative value (such as -0.1 m / s²) to accommodate sensor noise and road resistance.

[0046] The decision logic is as follows: If If the vehicle is in acceleration mode, then the vehicle dynamics are determined to be under acceleration conditions. In this state, vehicle dynamics are governed by powertrain characteristics, and model parameters without delay are applied. If... If the vehicle is in a deceleration state, it is determined that the braking system is engaged. At this time, the braking system intervenes, and its delay characteristics affect the vehicle response. Therefore, model parameters that include delay characteristics are applicable.

[0047] Step S44: Discretize the basic model. Based on the determination result of step S43, select the basic model parameters for prediction in the current cycle. When the condition is determined to be accelerated, select... As the basic model matrix, let This model form is directly used for subsequent calculations. When the condition is determined to be deceleration, select... As the basic model matrix, let It should be clarified that although the model selected at this time is a standard discrete matrix in mathematical form, its physical essence corresponds to a continuous system with delay. Therefore, it must undergo the delay compensation process in step S50 before being input into the solver.

[0048] Through the above logic, the control system achieves switching between different dynamic characteristics, reducing the prediction bias of a single model under asymmetric responses. Numerical discretization methods such as matrix exponent calculation are well-known techniques to those skilled in the art and will not be elaborated upon here.

[0049] See attached document Figure 5 The implementation of delay compensation and state augmentation techniques in step S50 addresses the pure time delay characteristics under deceleration conditions. When step S40 determines that a deceleration condition has occurred, the physical model upon which the system is based includes control input delay, and directly using the standard state equations would result in a response lag in the prediction time domain. This embodiment employs state augmentation techniques to incorporate historical control inputs into the state vector, reconstructing a delay-free discrete state-space model. This process includes the following sub-steps: Step S51, discretization of the delay time. The braking system not only has a slow response (due to large...) (This is reflected in the text), and is often accompanied by a significant pure time delay. This means that in Control commands issued at all times , will It only begins to have an effect on the system at a certain moment, in which It is the discrete step count after the delay is quantized.

[0050] The braking model with input delay can be represented as: ; This is a typical time-delay system, whose future state depends not only on the current state but also on historical inputs, thus violating the Markov property and making it unsuitable for direct handling by standard MPC. To address this issue, we employ the classic state augmentation technique from control theory. Its core idea is to internalize the system's memory (i.e., historical inputs) as part of the state, thereby transforming a non-Markov problem into an equivalent, delay-free, high-dimensional Markov problem.

[0051] Step S52: Construct the augmented state vector. To eliminate the input delay term, a new augmented state vector is defined. It is from the original state and the past The control input for each cycle consists of: ; in, It is the dimension of the original state vector.

[0052] Step S53: Reconstruct the delay-free augmented state space model. This is achieved through derivation. and and Based on this relationship, we can construct a standard augmented linear system: The structure of the augmented matrix is ​​as follows: in, The original system state vector The dimension; This is the delay step number; This is the augmented state matrix, with dimensions of . ; The input matrix is ​​augmented, and its dimension is... ; This is the augmented perturbation matrix, with dimensions of . .

[0053] The first row of the matrix cleverly... With historical input stored in augmented states The multiplication correctly simulates the delay effect. The shift matrix structure below it implements the first-in-first-out update of historical control inputs.

[0054] Through this transformation, we obtain a standard, delay-free augmented linear system. When the system is in braking condition, MPC will make predictions and optimizations based on this augmented model, thereby being able to anticipate and proactively compensate for braking delay.

[0055] Step S54, output equation adjustment. Because model predictive control requires adjustments to the original physical state... Perform constraints and optimizations, and define the output matrix. Extract the original state: In the formula, for 3D identity matrix; It is a matrix consisting entirely of zeros.

[0056] Through the above steps, the system with input delay is transformed into a high-dimensional linear system that is formally delay-free. For the acceleration condition, since there is no delay (i.e.,...) (Use the original matrix directly) The predictive model can be constructed without state augmentation. This approach allows the subsequent model predictive control solver to employ a unified standard quadratic programming algorithm. Matrix block construction and state augmentation theory are well-known techniques to those skilled in the art and will not be elaborated upon here.

[0057] In step S60, the model predictive controller is designed and solved. Using the discretized model determined in steps S40 and S50, the optimal longitudinal control command is calculated while satisfying vehicle physical constraints and safety constraints. This process includes the following sub-steps: Step S61: Construct a multi-step prediction equation. Based on the current time... Given a discrete system model (which may be an acceleration model or a braking augmented model depending on the operating conditions), derive the evolution law of the future state. Let the prediction time domain be... Control time domain is (This is a simplified design) The optimization variable is the future control sequence. If soft constraints are introduced, the optimization variables are expanded to... .

[0058] All future states can be represented as current states. Future control sequence and currently measurable disturbances Linear combination: ; The above formula represents the future state sequence It is fully represented. The handling of disturbances is based on the assumption that disturbances... The matrix is ​​known (and is assumed to remain constant within the prediction time domain) and obtained through workshop communication. The system's free response to the state, its forced response to control inputs, and its forced response to measurable disturbances are described respectively.

[0059] Step S62: Design a multi-objective optimization function. The core of MPC is to solve an open-loop optimization problem in a finite time domain at each control cycle, based on the latest state of the current system, in order to find the optimal sequence of future control inputs.

[0060] The objective function of this method The aim is to systematically balance multiple performance metrics: tracking accuracy, control energy consumption, actuator smoothness, and constraint flexibility, especially the key performance of MPC.

[0061] The objective function is defined as follows: ; in: and They represent in Always The state at any given time and the predicted value of the control input; As a state tracking cost, this penalty applies to the predicted state and the reference state. The deviation, weight matrix It is a diagonal matrix, where the diagonal elements correspond to the penalty weights of each state variable (e.g., ...). (etc.), used to adjust the importance of different error components; To control energy consumption, this limit controls the magnitude of the input to prevent excessive input. As a trade-off for smoothness, this penalty control variable changes rate to ensure smooth actuator operation; For soft constraint penalties, among which As slack variables, This represents the corresponding penalty weight, used to handle situations where hard constraints might lead to no solution.

[0062] Step S63: Construct a set of constraints. The controller solution must satisfy the vehicle's physical limitations and safety requirements; therefore, we need to uniformly convert all constraints into linear inequalities. In the form of.

[0063] Control input constraints: This is the most direct constraint, directly affecting the optimization variables. Its matrix form is: ; Control Incremental Constraints: This constraint, which relates to the control input at adjacent time points, is crucial for ensuring control smoothness. Specifically, the first control increment... It is the actual control quantity relative to the previous cycle. Calculated, i.e. .

[0064] To transform it into the standard QP constraint form, we first define a difference matrix. : ; Using this matrix, the control increment vector throughout the entire prediction time domain It can be represented as: ; in, This is the known control quantity from the previous time step. Therefore, the complete control increment constraint... This can be summarized as follows regarding optimization variables. The standard form of the linear inequality: ; State constraints: such as acceleration constraints Actual acceleration It is a state vector The fourth component. We can define a selection matrix. , making Substituting the prediction equation, the constraints become: ; in, These are matrices describing future states. The Each block of lines.

[0065] exist Time, Current State and current disturbance All of these are known quantities. Therefore, we can rearrange the inequality to reflect the optimization variables. Standard linear inequalities: ; ; For all prediction steps Combining these inequalities yields a portion of the QP constraint matrix. The derivation of other state constraints, such as velocity, follows the same process.

[0066] Soft constraints on vehicle spacing: In certain emergency avoidance or strong disturbance scenarios, it may be unavoidable for the distance between vehicles to briefly exceed a certain safety upper bound. Applying hard constraints could lead to an unsolvable QP problem and controller failure. Therefore, we introduce soft constraints, assigning an independent slack variable to each prediction time step. : ; in, It is the first component of the state vector, and the selection matrix is ​​defined. .

[0067] This constraint is in the first The QP form of the step is: ; By integrating the constraints of all time steps into matrix form, it can be written as: ; At the same time, it is necessary to add nonnegativity constraints to the slack variables. In this way, we transform the original problem into one that includes... and For larger-scale QP problems, the stability of the solver and the continuous availability of the controller are achieved at the expense of minor, temporary constraint violations.

[0068] Step S64, Rolling Optimization Solution and Safety Redundancy. After transforming the objective function of step S62 and the constraints of S63 into a standard quadratic programming (QP) problem, perform the following operations: Optimization Solution: Use an efficient online QP solver (such as OSQP or qpOASES) to solve the optimization problem and obtain the optimal control sequence. and optimal relaxation amount .

[0069] Rolling time-domain implementation: This is the core idea of ​​MPC. Although we plan a series of future actions, we only execute the first one: the first element of the optimal control sequence. Applied to vehicle actuators.

[0070] Time-domain forward push: in the next cycle The system evolves to a new state, and the entire process repeats from step S1 (i.e., data acquisition and state update).

[0071] In addition, to further improve system reliability, this embodiment also establishes a layered security redundancy mechanism: To ensure the system's reliability under solver malfunctions or extreme conditions, this method incorporates a hierarchical safety redundancy mechanism, which significantly enhances the system's robustness and fault tolerance. Specifically, this includes: Level 1 redundancy (rollback strategy): If the solver fails to find a feasible solution in the current cycle (e.g., iteration timeout), it reads the optimal control sequence calculated in the previous control cycle. Move it one step back as the current backup instruction.

[0072] Secondary redundancy (fail-safe): If there is no solution for several consecutive cycles, the fail-safe strategy is triggered, and a preset emergency braking deceleration is output to ensure vehicle safety.

Claims

1. A vehicle platooning MPC control method integrating asymmetric response model and delay compensation, characterized in that, Includes the following steps: S1. Establish a longitudinal dynamics model for the vehicle, which includes an acceleration longitudinal dynamics model describing acceleration characteristics and a deceleration longitudinal dynamics model describing deceleration characteristics. S2. Construct a formation control state space model that integrates the longitudinal dynamics model of the vehicle, and characterize the dynamic relationship between the formation error state variables and the control input; S3. Obtain real-time driving status data, including at least the longitudinal acceleration of the vehicle. S4. Compare the longitudinal acceleration of the vehicle with a preset threshold, and determine the discretized basic model based on the formation control state space model. If it is determined to be an acceleration condition, select the corresponding parameters of the acceleration longitudinal dynamics model; if it is determined to be a deceleration condition, select the corresponding parameters of the deceleration longitudinal dynamics model. S5. Delay processing is applied to the discretized basic model. If it corresponds to deceleration, historical control inputs are introduced using state augmentation techniques to construct a delay-free augmented discrete state space model. If it corresponds to acceleration, the discretized basic model remains unchanged. S6. Substitute the augmented discrete state space model or the discretized basic model into the model predictive control solver to solve the quadratic programming problem containing the objective function and constraints, and send the first element of the obtained optimal control sequence to the actuator.

2. The vehicle platooning MPC control method integrating asymmetric response model and delay compensation according to claim 1, characterized in that, In step S1: The acceleration longitudinal dynamics model is constructed as a first-order inertial system without input delay. Its characteristic parameters include the acceleration time constant; The deceleration longitudinal dynamics model is constructed as a first-order inertial system with pure time delay. Its characteristic parameters include deceleration time constant and pure time delay; The value of the deceleration time constant is greater than the acceleration time constant.

3. The vehicle platooning MPC control method integrating asymmetric response model and delay compensation according to claim 1, characterized in that, The formation error state quantities represented by the formation control state space model in step S2 include: Spacing error, which is the difference between the actual distance between the vehicle and the vehicle in front and the expected distance, wherein the expected distance is calculated based on a constant time spacing strategy; Relative speed, which is the speed difference between the vehicle and the vehicle in front; The relative speed of the lead vehicle is the speed difference between this vehicle and the lead vehicle. And the actual acceleration of the vehicle.

4. The vehicle platooning MPC control method integrating asymmetric response model and delay compensation according to claim 1, characterized in that, The determination logic in step S4 is as follows: If the longitudinal acceleration of the vehicle is greater than or equal to the preset threshold, it is determined to be an acceleration condition, and the discretized basic model does not contain an input delay term; If the longitudinal acceleration of the vehicle is less than the preset threshold, it is determined to be a deceleration condition. The discretized basic model includes input delay terms that need to be processed.

5. The vehicle platooning MPC control method integrating asymmetric response model and delay compensation according to claim 1, characterized in that, The state augmentation technique used in step S5 specifically includes: The pure time delay in the deceleration longitudinal dynamics model is quantized into an integer multiple of the sampling period, which is the number of delay steps. Define an augmented state vector, which is composed of the formation error state quantity and the historical control inputs of the past several control cycles, wherein the number of historical control inputs corresponds to the number of delay steps; The system evolution matrix is ​​reconstructed, and the historical control input is introduced into the state update equation to establish a delay-free evolution relationship based on the augmented state vector.

6. The vehicle platooning MPC control method integrating asymmetric response model and delay compensation according to claim 1, characterized in that, The objective function in step S6 includes the following weighted cost term: State tracking cost is used to penalize the deviation between the predicted state and the reference state; Control cost, used to penalize the magnitude of the control input; Control increment cost is used to penalize the rate of change of control input between adjacent control cycles; The soft constraint penalty cost is used to penalize the magnitude of the slack variable, which is used to handle situations where hard constraints are not feasible.

7. The vehicle platooning MPC control method integrating asymmetric response model and delay compensation according to claim 6, characterized in that, The constraints include soft constraints on vehicle spacing, which are constructed as follows: Non-negative slack variables are assigned to the prediction steps in the prediction time domain. The extent to which the vehicle spacing is allowed to be less than the lower bound of the safe distance is limited by the slack variables. The slack variables are penalized in the objective function through the soft constraint penalty cost, thereby minimizing the degree of violation while ensuring the feasibility of the solution.

8. The vehicle platooning MPC control method integrating asymmetric response model and delay compensation according to claim 1, characterized in that, It also includes a first-level security redundancy strategy: When the quadratic programming problem fails to be solved in the current control cycle and the number of consecutive failures does not reach the preset upper limit, the optimal control sequence obtained from the successful solution in the previous control cycle is obtained. The second element of the optimal control sequence of the previous control cycle is selected and sent to the actuator as the instruction for the current control cycle.

9. The vehicle platooning MPC control method integrating asymmetric response model and delay compensation according to claim 1, characterized in that: Including a second-level security redundancy strategy: When the number of consecutive failures in solving the quadratic programming problem reaches or exceeds the preset upper limit, the controller is deemed to have failed. A preset emergency braking command is generated and sent to the actuator, and the internal state of the model predictive control solver is forcibly reset, thereby re-initializing the calculation in the next control cycle.

10. The vehicle platooning MPC control method integrating asymmetric response model and delay compensation according to claim 1, characterized in that, The prediction equation used to construct the quadratic programming problem in step S6 includes a disturbance response term: The prediction equation represents the future state sequence as a linear combination of the free response of the current state, the forced response of the future control input, and the forced response of the measurable disturbance. The measurable disturbances include the acceleration of the lead vehicle and the acceleration of the first vehicle obtained through workshop communication, and within the prediction time domain of model predictive control, the measurable disturbances are treated as known input quantities for computation.

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