A hierarchical robust control method and system for connected autonomous vehicle platooning against FDI attacks

Abstract

This invention provides a hierarchical robust control method and system for connected autonomous vehicle platoons against FDI attacks. The invention constructs a longitudinal dynamics model of the vehicles and, combined with input time delays, builds a discrete-state longitudinal dynamics model of the attacked state affected by time delays. Then, through multi-channel redundant communication and residual consistency verification, reliable communication links are selected, and highly reliable preceding vehicle state information is reconstructed. Subsequently, the random time delays are transformed into bounded additive perturbations, constructing a perturbation set including extreme, nominal, and internal sampling scenarios. A minimalist-maximum robust optimization problem is then constructed, and auxiliary variables are introduced to transform it into a standard quadratic programming form. The optimal control input is then solved using KKT conditions. This invention achieves decoupling of attack isolation and time delay suppression, simultaneously resisting two types of coupled perturbations, exhibiting high optimization efficiency, and effectively improving the stability and safety of vehicle platoon driving.

Description

Technical Field

[0001] This invention relates to the field of autonomous driving technology, and in particular to a hierarchical robust control method and system for connected autonomous vehicle platoons against FDI attacks. Background Technology

[0002] With the development of connected autonomous vehicle (CAV) technology, vehicle platoon control (VPC) has become an important means to improve road safety, fuel economy, and traffic efficiency. The main goal of VPC is to coordinate multiple vehicles to form a stable platoon and maintain precise distances between them. Unlike traditional adaptive cruise control, which relies solely on onboard radar to measure the distance and relative speed of the vehicle ahead, VPC utilizes vehicle-to-everything (V2X) technology to exchange comprehensive vehicle status information through vehicle-to-vehicle (V2V) communication.

[0003] However, in practical applications, achieving the aforementioned coordinated control remains a significant challenge due to the time delay of control inputs. Vehicle braking, drive, and other actuators all exhibit input time delays; even small delays can significantly reduce system dynamic performance and disrupt queue stability, especially under conditions of close vehicle spacing. In addition to these inherent technical limitations, cybersecurity threats further reduce the reliability of the queue system. False data injection (FDI) attacks, by injecting misleading information into the communication network, can distort the state perception of adjacent vehicles and disrupt queue synchronization. When input time delays and FDI attacks coexist, their adverse effects are compounded, easily leading to queue instability.

[0004] Therefore, there is an urgent need to provide a robust hierarchical control scheme for connected autonomous vehicle platoons against FDI attacks. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a hierarchical robust control method and system for connected autonomous vehicle queues against FDI attacks, achieving attack isolation, time delay suppression, and safe collaborative control. This invention adopts a hierarchical architecture, with the upper layer using multi-channel redundancy fusion to achieve attack data detection and state reconstruction; the lower layer uses scenario-based minimum-maximum robust MPC to process random input time delays, ensuring the stability and security of the queue under complex disturbances.

[0006] In a first aspect, the technical solution provided by this invention is: a hierarchical robust control method for connected autonomous vehicle platoons against FDI attacks, comprising:

[0007] Construct a longitudinal convoy consisting of one lead vehicle and multiple follower vehicles;

[0008] A longitudinal dynamics model is established for the current following vehicle in the longitudinal platoon, and then discretized to obtain a discrete-state longitudinal dynamics model;

[0009] Introducing input time delay into the discrete-state longitudinal dynamics model, we construct an attack-affected discrete-state longitudinal dynamics model influenced by time delay, and also construct a state information receiving model subject to FDI attacks.

[0010] From all communication links, obtain the unattacked available communication links, divide the unattacked available communication links into multiple candidate available communication link subsets, and select the optimal trusted communication link subset based on the consistency index of the candidate available communication link subsets;

[0011] The difference between the random input time delay and the maximum allowable time delay is transformed into a time delay mismatch, and the time delay mismatch is transformed into an additive bounded perturbation to construct a discretized vehicle state prediction model that considers the random input time delay.

[0012] Construct a multi-scenario perturbation set, and with the goal of minimizing the worst-case cost, construct a scenario mini-maximum optimization problem, and transform the scenario mini-maximum optimization problem into a standard quadratic programming problem;

[0013] The Karush-Kuhn-Tucker conditions are used to solve the reconstructed standard quadratic programming problem to obtain the optimal control input for the current following vehicle.

[0014] Preferably, a longitudinal dynamics model is established for the current following vehicle in the longitudinal platoon, and after discretization, a discrete-state longitudinal dynamics model is obtained, including:

[0015] Based on the position, velocity, and acceleration state of the following vehicle, a longitudinal dynamics model of the following vehicle is established;

[0016] The control input of the following vehicle is calculated based on its own state information and the received reference state information of the preceding vehicle.

[0017] The longitudinal dynamics model of the following vehicle is discretized according to the sampling period to obtain the discrete-state longitudinal dynamics model.

[0018] Preferably, an input time delay is introduced into the discrete-state longitudinal dynamics model to construct an attacked discrete-state longitudinal dynamics model affected by the time delay, and a state information receiving model under FDI attack is constructed, including:

[0019] Based on the real reference state information of the preceding vehicle received by the following vehicle, the false data injected by the attacker, and communication noise or measurement disturbances, the reference state information of the attacked preceding vehicle received by the following vehicle for future prediction step size is obtained.

[0020] The control input of the attacked following vehicle is constructed based on the following vehicle's own state information and the reference state information of the attacked preceding vehicle. The control input time delay is introduced to construct a longitudinal dynamic model of the attacked discrete state affected by the time delay.

[0021] The system configures the preceding vehicle to broadcast its reference status information to the following vehicle via multiple independent and insecure communication links. Received at discrete time k Group redundancy information is represented as:

[0022] ;

[0023] In the formula, Indicates following vehicle At discrete time from The stacking matrix of redundant status information of the preceding vehicle received by the communication link; To follow the car At discrete time Through the first The reference status information of the attacked preceding vehicle received by the communication link;

[0024] Each communication link Received reference status information of the attacked vehicle ahead satisfy:

[0025] ;

[0026] In the formula, To follow the car At discrete time Through the first Communication noise received by the communication link; To follow the car At discrete time Through the first The communication link received false data injected by the attacker; Indicates at discrete time Following vehicle Obtained reference status information of the vehicle ahead;

[0027] Ultimately, it was found that an FDI attack existed. The state information reception model under the influence is as follows:

[0028] ;

[0029] In the formula, Indicates following vehicle At discrete time from The stacking matrix of redundant status information of the preceding vehicle received by the communication link; express A matrix consisting entirely of 1s; To follow the car At discrete time Data on the attacks received; Indicates following vehicle The number of communication links; Indicates following vehicle At discrete time Received communication noise; Indicates following vehicle At discrete time Received reference status information of the vehicle ahead; For Kronecker product.

[0030] Preferably, unattacked available communication links are obtained from all communication links, and these unattacked available communication links are divided into multiple candidate available communication link subsets. The optimal trusted communication link subset is selected based on a consistency index of the candidate available communication link subsets, including:

[0031] Assuming at most The communication link was attacked by a fake data injection attack, and From all communication links The system identifies unattacked available communication links and divides these links into multiple candidate subsets.

[0032] Based on the preceding vehicle reference state information received by each candidate available communication link subset, calculate the average preceding vehicle state estimate for the candidate available communication link subset;

[0033] The residuals of each available communication link in the candidate subset of available communication links are calculated at future prediction times based on the mean state estimation of the preceding vehicle.

[0034] Based on the residuals at future prediction times, a standardized residual index is constructed using the covariance matrix and Mahalanobis distance.

[0035] Calculate the multi-step consistency index of candidate available communication link subsets based on standardized residual index;

[0036] The candidate available communication link subset with the smallest multi-step consistency index is selected as the optimal trusted communication link subset, and the state information of the optimal trusted communication link subset is used as the robust reference state.

[0037] Preferably, the difference between the random input time delay and the maximum permissible time delay is converted into a time delay mismatch, and the time delay mismatch is converted into an additive bounded perturbation to construct a discretized vehicle state prediction model that considers the random input time delay, including:

[0038] Set the maximum allowable input delay and construct an input buffer with a length equal to the maximum allowable delay to store historical control instructions, thus converting the random input delay into a delay mismatch between the fixed maximum delay and the actual delay;

[0039] By converting the time delay mismatch into an additive bounded perturbation, the complex stochastic time delay problem is simplified into a deterministic bounded perturbation problem, resulting in a discretized vehicle state prediction model that considers the random input time delay.

[0040] As a preferred approach, a multi-scenario perturbation set is constructed, and a scenario mini-maximum optimization problem is built with the objective of minimizing the worst-case cost. This scenario mini-maximum optimization problem is then transformed into a standard quadratic programming problem, including:

[0041] Construct a multi-scenario perturbation set that includes extreme scenarios, nominal scenarios, and internal sampling scenarios;

[0042] A total prediction cost function is constructed under the disturbance scenario s based on the tracking error between the vehicle state and the reference state for all future prediction steps.

[0043] Transform the prediction of the total cost function into a mini-maximum optimization problem;

[0044] By introducing an auxiliary variable as a common upper bound for the total cost function in all scenarios, the mini-max optimization problem is transformed into a standard quadratic programming problem. By minimizing the auxiliary variable, the cost in all scenarios is forced not to exceed the auxiliary variable, and the optimal control input of the auxiliary variable is achieved at the optimum point.

[0045] The reconstructed standard quadratic programming problem is solved using the Karush-Kuhn-Tucker conditions to obtain the optimal control input for the following vehicle, including:

[0046] Construct a Lagrangian function based on the auxiliary variable z and the total prediction cost function under the perturbation scenario s;

[0047] Transform the total cost function into a standard quadratic form;

[0048] At each sampling time, an optimal control input sequence is obtained by solving based on the current vehicle state information, robust reference state, scene disturbance set, and historical information of the input buffer.

[0049] The first optimal control input is added to the actuator of the vehicle currently being followed, and the remaining control inputs are re-optimized at the next sampling time.

[0050] Secondly, the technical solution provided by this invention is: a hierarchical robust control system for connected autonomous vehicle platoons against FDI attacks, comprising:

[0051] The fleet building module is used to build a longitudinal fleet consisting of one lead vehicle and multiple follower vehicles;

[0052] The first module is used to establish a longitudinal dynamics model for the current following vehicle in the longitudinal convoy, and the discrete state longitudinal dynamics model is obtained by discretization.

[0053] The second module is used to introduce input time delay into the discrete state longitudinal dynamics model to construct the attacked discrete state longitudinal dynamics model affected by time delay, and to construct the state information receiving model under FDI attack.

[0054] The link filtering module is used to obtain unattacked available communication links from all communication links, divide the unattacked available communication links into multiple candidate available communication link subsets, and filter the optimal trusted communication link subset based on the consistency index of the candidate available communication link subsets.

[0055] The third module is used to convert the difference between the random input time delay and the maximum allowable time delay into a time delay mismatch, and to convert the time delay mismatch into an additive bounded perturbation to construct a discretized vehicle state prediction model that considers the random input time delay.

[0056] The optimization module is used to construct a multi-scenario perturbation set, and to construct a scenario mini-maximum optimization problem with the goal of minimizing the worst-case cost, and then transform the scenario mini-maximum optimization problem into a standard quadratic programming problem.

[0057] The solution module uses the Karush-Kuhn-Tucker conditions to solve the reconstructed standard quadratic programming problem and obtain the optimal control input for the current following vehicle.

[0058] Thirdly, the present invention provides an electronic device, comprising:

[0059] At least one processor;

[0060] and memory that is communicatively connected to at least one processor;

[0061] The memory stores a computer program that can be executed by at least one processor. When the computer program is executed by at least one processor, it implements the hierarchical robust control method for connected autonomous vehicle queues against FDI attacks.

[0062] The beneficial effects of this invention are as follows:

[0063] 1. The present invention adopts a layered architecture, which can resist FDI attacks and random input delays at the same time. The upper layer can isolate the tampered data link channel, and the lower layer minimax optimization problem can cover the worst-case deviation caused by delay. Under the harsh working conditions where FDI attacks and delays coexist, the vehicle spacing error of the present invention is significantly lower than that of the prior art.

[0064] 2. This invention transforms random time delays into bounded perturbations through an input buffer and introduces auxiliary variables to transform complex minimax optimization problems into standard quadratic programming (QP) problems, avoiding multi-level nested optimization and high-dimensional traversal solutions. Under limited on-board computing resources, it can achieve millisecond-level fast solutions, meeting the real-time control cycle requirements of autonomous vehicles. Attached Figure Description

[0065] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention;

[0066] Figure 2 This is a schematic diagram of the system framework of Embodiment 2 of the present invention;

[0067] In the diagram, 10 is the fleet construction module; 20 is the first module; 30 is the second module; 40 is the link filtering module; 50 is the third module; 60 is the optimization module; and 70 is the solution module. Detailed Implementation

[0068] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings:

[0069] like Figure 1 As shown, this embodiment provides a hierarchical robust control method for connected autonomous vehicle platoons against FDI attacks, including:

[0070] S1: Construct a longitudinal convoy consisting of one lead vehicle and multiple follower vehicles;

[0071] S2: Establish a longitudinal dynamics model for the current following vehicle in the longitudinal platoon, and obtain a discrete-state longitudinal dynamics model after discretization;

[0072] S3: Introduce input time delay into the discrete state longitudinal dynamics model to construct an attacked discrete state longitudinal dynamics model affected by time delay, and construct a state information receiving model under FDI attack.

[0073] S4: Obtain unattacked available communication links from all communication links, divide the unattacked available communication links into multiple candidate available communication link subsets, and select the optimal trusted communication link subset based on the consistency index of the candidate available communication link subsets;

[0074] S5: Transform the difference between the random input time delay and the maximum allowable time delay into a time delay mismatch, and then transform the time delay mismatch into an additive bounded perturbation to construct a discretized vehicle state prediction model that considers the random input time delay.

[0075] S6: Construct a multi-scenario perturbation set, and with the goal of minimizing the worst-case scenario cost, construct a scenario minimum-maximum optimization problem, and transform the scenario minimum-maximum optimization problem into a standard quadratic programming problem;

[0076] S7: Solve the reconstructed standard quadratic programming problem using the Karush-Kuhn-Tucker conditions to obtain the optimal control input for the current following vehicle.

[0077] In this embodiment, in step S2, a longitudinal dynamics model is established for the current following vehicle in the longitudinal platoon, and a discrete-state longitudinal dynamics model is obtained by discretization, including:

[0078] S21. Based on the position, velocity, and acceleration state of the following vehicle, establish a longitudinal dynamics model of the following vehicle, namely:

[0079] ;

[0080] In the formula, To follow the car Position status obtained from the vehicle in front; To follow the car The first derivative of the position state obtained from the vehicle in front; To follow the car Speed ​​status obtained from the vehicle in front; To follow the car Acceleration status obtained from the vehicle in front; To follow the car Control input; The vehicle's inertial time constant;

[0081] In this embodiment, the kinematic model of the navigator vehicle is as follows:

[0082]

[0083] In the formula, , , They are respectively The position, speed, and acceleration status of the navigator vehicle are constantly monitored.

[0084] S22, based on following vehicle The following vehicle is calculated by combining its own state information with the received reference state information of the preceding vehicle. The control input, namely:

[0085] ;

[0086] In the formula, Represents the optimal control law function; Discrete time Following vehicle The obtained reference status information of the preceding vehicle, with the superscript B indicating that it comes from the preceding vehicle's broadcast or reference information;

[0087] S23. Discretize the longitudinal dynamics model of the following vehicle according to the sampling period to obtain the discrete-state longitudinal dynamics model, namely:

[0088] ;

[0089] , ;

[0090] In the formula, Discrete time Following vehicle Its own state information, Discrete time points Following vehicle Position, velocity, and acceleration; For the sampling period and vehicle inertial time constant A defined state transition matrix; Represents the control input matrix; Discrete time Following vehicle Control input.

[0091] In this embodiment, step S3 involves introducing an input time delay into the discrete-state longitudinal dynamics model to construct an attacked discrete-state longitudinal dynamics model affected by the time delay, and constructing a state information receiving model subject to FDI attacks, including:

[0092] S31, based on following vehicle The received real preceding vehicle reference state information, spoofed data injected by the attacker, and communication noise or measurement disturbances are used to obtain the attacked preceding vehicle reference state information received by the future prediction step-following vehicle, i.e.:

[0093] ;

[0094] In the formula, Indicates following vehicle The reference state information of the attacked vehicle ahead received at discrete time k for the h-th prediction step in the future; Indicates following vehicle At discrete time k, the real reference state information of the vehicle ahead is received for the h-th prediction step in the future. To follow the car The received data is fake data injected by the attacker; This could be communication noise or measurement disturbance. To predict the step size.

[0095] S32. Construct the control input for the attacked following vehicle based on its own state information and the reference state information of the attacked preceding vehicle, and introduce a control input time delay. Construct a longitudinal dynamic model of the attacked discrete state under time delay, namely:

[0096] ;

[0097] ;

[0098] In the formula, To follow the car At discrete time k, the control input is attacked; To follow the car At discrete time Received reference status information of the attacked vehicle ahead;

[0099] Furthermore, even under conditions of communication attacks and input delays, the vehicle formation still meets the requirements for safe spacing, tracking accuracy, and string stability, namely:

[0100] ;

[0101] In the formula, To follow the car With following vehicle Target spacing; Each following vehicle gradually approaches and tracks the speed of the lead vehicle. This indicates that the acceleration of each following vehicle asymptotically tracks the acceleration of the navigating vehicle.

[0102] S33, Setting the Leading Vehicle To the following car pass Independent and insecure communication links broadcast the preceding train Reference status information, following vehicle Received at discrete time k Group redundancy information is represented as:

[0103] ;

[0104] In the formula, Indicates following vehicle At discrete time from The stacking matrix of redundant status information of the preceding vehicle received by the communication link; To follow the car At discrete time Through the first The reference status information of the attacked preceding vehicle received by the communication link;

[0105] Each communication link Received reference status information of the attacked vehicle ahead satisfy:

[0106] ;

[0107] In the formula, To follow the car At discrete time Through the first Communication noise received by the communication link; To follow the car At discrete time Through the first The communication link received false data injected by the attacker;

[0108] S34, ultimately revealing the existence of an FDI attack. The state information reception model under the influence, namely:

[0109] ;

[0110] In the formula, Indicates following vehicle At discrete time from The stacking matrix of redundant status information of the preceding vehicle received by the communication link; express A matrix consisting entirely of 1s; To follow the car At discrete time Data on the attacks received; Indicates following vehicle The number of communication links; Indicates following vehicle At discrete time Received communication noise; Indicates following vehicle At discrete time Received reference status information of the vehicle ahead; For Kronecker product.

[0111] In this embodiment, step S4 involves obtaining unattacked available communication links from all communication links, dividing these unattacked available communication links into multiple candidate available communication link subsets, and selecting the optimal trusted communication link subset based on the consistency index of the candidate available communication link subsets, including:

[0112] S41. Assume that at most there are The communication link was attacked by a fake data injection attack, and From all communication links The process involves identifying unattacked, usable communication links and dividing these links into multiple candidate subsets of usable communication links. ;

[0113] S42, Based on each candidate subset of available communication links Receive the reference state information of the preceding vehicle and calculate a subset of candidate available communication links. The mean state estimate of the preceding vehicle, i.e.:

[0114] ;

[0115] In the formula, Indicates a subset of candidate available communication links The obtained mean state estimate of the preceding vehicle; Indicates following vehicle At discrete time Through the first The preceding vehicle's reference status information received via the communication link;

[0116] S43. Calculate a subset of candidate available communication links based on the average state estimation of the preceding vehicle. Each available communication link in the future The residuals at each prediction time, i.e.:

[0117] ;

[0118] In the formula, Indicates following vehicle Through the first The residual of an available communication link at discrete time k for the next h-th prediction step relative to the average estimate of the candidate subset; Indicates accompanying the vehicle At discrete pre-processing time Through the first The preceding vehicle's reference status information received via the communication link; Indicates following vehicle Through the first The average state of the vehicle ahead is estimated at discrete time k for the h-th predicted step in the future using available communication links;

[0119] S44, Based on the future The residuals at each prediction time are used to introduce the covariance matrix. The standardized residual index is constructed using Mahalanobis distance, namely:

[0120] ;

[0121] In the formula, Indicates following vehicle Through the first The standardized residual index of an available communication link at discrete time k for the next h-th prediction step; Indicates the transpose operation;

[0122] Wherein, the covariance matrix Represented as:

[0123] ; ;

[0124] In the formula, This is the state transition matrix; This is the initial covariance matrix; A function for generating diagonal matrices; These represent the variances of the vehicle's position, velocity, and acceleration errors, respectively.

[0125] S45. Calculate candidate available communication link subsets based on standardized residual indices. The multi-step consistency metric, namely:

[0126] ;

[0127] In the formula, Indicates a subset of candidate available communication links A multi-step consistency index at discrete time k.

[0128] S46. Select the candidate available communication link subset with the smallest multi-step consistency index as the optimal trusted communication link subset, and use the state information of the optimal trusted communication link subset as the robust reference state. .

[0129] In this embodiment, step S5 involves converting the difference between the random input time delay and the maximum permissible time delay into a time delay mismatch, and then converting the time delay mismatch into an additive bounded perturbation to construct a discretized vehicle state prediction model that considers the random input time delay. This includes:

[0130] S51. Set the maximum allowable input delay. And construct a time delay of the maximum allowable length. The input buffer stores historical control instructions and delays random input. This is converted into the time delay mismatch between the fixed maximum time delay and the actual time delay, i.e.:

[0131] ; ;

[0132] In the formula, This is the time-delay mismatch; This refers to the historical control input applied to the vehicle under actual random time delay. This refers to the historical control input retrieved according to the maximum time-delay input buffer; To control the upper limit of the input amplitude;

[0133] S52. The time-delay mismatch is converted into an additive bounded perturbation, simplifying the complex stochastic time-delay problem into a deterministic bounded perturbation problem, resulting in a discretized vehicle state prediction model considering stochastic input time delays, i.e.:

[0134] ;

[0135] , ;

[0136] In the formula, This is the additional disturbance term caused by input time delay mismatch; This is the upper bound for the additional perturbation.

[0137] In this embodiment, step S6 involves constructing a multi-scenario perturbation set, and building a scenario mini-maximum optimization problem with the objective of minimizing the worst-case scenario cost. This scenario mini-maximum optimization problem is then transformed into a standard quadratic programming problem. This includes:

[0138] S61. Construct a multi-scenario perturbation set including extreme scenarios, nominal scenarios, and internal sampling scenarios, as detailed below:

[0139] Explicitly select perturbation boundary values and As an extreme scenario; and within the range of disturbance Generate using the Latin hypercube sampling method The first internal sample is used as the internal sampling scenario. Internal scene sample Represented as:

[0140] ;

[0141] In the formula, It is a random arrangement; Let be a uniformly distributed random variable in the range [0,1]. This represents the number of internal samples. Indicates an internal sampling scenario;

[0142] Using the zero-disturbance scenario as the nominal scenario, that is: .

[0143] S62, in the prediction time domain The goal is to minimize the cost of the worst-case scenario, thus constructing a scenario-based minimum-maximum optimization problem, namely:

[0144] For any scenario The predicted state, safety constraints, and control input constraints are as follows:

[0145] ;

[0146] ;

[0147] ;

[0148] In the formula, For scenario s, predict the vehicle state within the time domain with prediction step size j; This represents the control input to be optimized; Represents the perturbation input matrix; Let represent the bounded perturbation at step j in scenario s; This represents the predicted position at step j+1 in scenario s; This represents the reference position at step j+1 in scenario s; Indicates the safety distance constraint margin; These represent the lower and upper bounds of the control input, respectively.

[0149] A prediction total cost function is constructed based on the tracking error between the vehicle state and the reference state for all future prediction steps under the disturbance scenario s. ,Right now:

[0150] ;

[0151] in, This provides the actual state information of the following vehicle at discrete time k; The control input for the following vehicle at discrete time k; To predict the length of the time domain; Indicates the prediction step size Predicted vehicle state and reference state in scenario s Tracking error between; Represents the weighted L2 norm; Indicates the stage state tracking error weights, Indicates the terminal error weight. Control input weights; To predict step size Follow vehicle control input; To predict the tracking error in the final step of the time domain;

[0152] Predict the total cost function Transformed into a minimum-maximum optimization problem:

[0153] ;

[0154] in, This represents the set of control inputs for the following vehicle; For multi-scenario perturbation sets.

[0155] S63. Introducing an auxiliary variable z as a common upper bound for the cost function in all scenarios transforms the mini-max optimization problem into a standard quadratic programming problem. By minimizing the auxiliary variable z, the cost in all scenarios is forced not to exceed the auxiliary variable z, and the optimal control input of the auxiliary variable z is achieved at the optimum point.

[0156] ;

[0157] in, The optimal solution for the auxiliary variable z represents the comprehensive control cost under the worst-case scenario; This is the optimal control input.

[0158] The constraints are as follows:

[0159] ;

[0160] ;

[0161] ;

[0162] .

[0163] In this embodiment, step S7 involves solving the reconstructed standard quadratic programming problem using the Karush-Kuhn-Tucker conditions to obtain the optimal control input for the current following vehicle, including:

[0164] S71. Construct a Lagrangian function based on the auxiliary variable z and the total prediction cost function under the perturbation scenario s, that is:

[0165] ;

[0166] In the formula, The augmented objective function after introducing Lagrange multipliers; For predicting time-domain control input; As an auxiliary variable; This represents the upper bound constraint on the cost of the s-th scenario;

[0167] S72. Convert the cost function to a standard quadratic form to obtain:

[0168] ;

[0169] In the formula, Let be the Hessian matrix of the quadratic cost function with respect to the control input; This represents the coefficient vector of the first-order term in the s-th scenario; This represents the constant term in the s-th scenario; Indicates the transpose operation;

[0170] The optimality condition is further transformed into:

[0171] ; ;

[0172] In the formula, Let represent the Hessian matrix of the quadratic cost function with respect to the control input; Indicates the optimal control input; This represents the normal cone term corresponding to the input constraints and safety constraints; Denotes the equivalent linear term obtained by weighting the KKT multipliers;

[0173] S73. At each sampling time, based on the current vehicle state information, robust reference state, scene disturbance set, and input buffer history information, a set of optimal control input sequences is obtained. , ,…, }, the first optimal control input The actuators applied to the current vehicle are followed by the other control inputs, which are then re-optimized at the next sampling time.

[0174] A second embodiment of this application provides a robust hierarchical control system for connected autonomous vehicle platooning against FDI attacks, comprising:

[0175] Fleet building module 10 is used to build a longitudinal convoy consisting of one lead vehicle and multiple follower vehicles;

[0176] The first module 20 is used to establish a longitudinal dynamics model for the current following vehicle in the longitudinal convoy, and obtain a discrete state longitudinal dynamics model after discretization.

[0177] The second module 30 is used to introduce input time delay into the discrete state longitudinal dynamics model to construct the attacked discrete state longitudinal dynamics model affected by time delay, and to construct the state information receiving model under FDI attack.

[0178] The link filtering module 40 is used to obtain unattacked available communication links from all communication links, divide the unattacked available communication links into multiple candidate available communication link subsets, and filter the optimal trusted communication link subset based on the consistency index of the candidate available communication link subsets.

[0179] The third module 50 is used to convert the difference between the random input time delay and the maximum allowable time delay into a time delay mismatch, and to convert the time delay mismatch into an additive bounded perturbation to construct a discretized vehicle state prediction model that considers the random input time delay.

[0180] Optimization module 60 is used to construct a multi-scenario perturbation set, and construct a scenario mini-maximum optimization problem with the goal of minimizing the worst-case scenario cost, and transform the scenario mini-maximum optimization problem into a standard quadratic programming problem;

[0181] The solution module 70 uses the Karush-Kuhn-Tucker conditions to solve the reconstructed standard quadratic programming problem and obtain the optimal control input for the current following vehicle.

[0182] In this embodiment, the first module 20 establishes a longitudinal dynamics model for the current following vehicle in the longitudinal convoy, and obtains a discrete-state longitudinal dynamics model after discretization, including:

[0183] Based on the position, velocity, and acceleration state of the following vehicle, a longitudinal dynamics model of the following vehicle is established, namely:

[0184] ;

[0185] In the formula, To follow the car Position status obtained from the vehicle in front; To follow the car The first derivative of the position state obtained from the vehicle in front; To follow the car Speed ​​status obtained from the vehicle in front; To follow the car Acceleration status obtained from the vehicle in front; To follow the car Control input; The vehicle's inertial time constant;

[0186] In this embodiment, the kinematic model of the navigator vehicle is as follows:

[0187]

[0188] In the formula, , , They are respectively The position, speed, and acceleration status of the navigator vehicle are monitored at all times.

[0189] Based on following vehicle The following vehicle is calculated by combining its own state information with the received reference state information of the preceding vehicle. The control input, namely:

[0190] ;

[0191] In the formula, Represents the optimal control law function; Discrete time Following vehicle The obtained reference status information of the preceding vehicle, with the superscript B indicating that it comes from the preceding vehicle's broadcast or reference information.

[0192] The longitudinal dynamics model of the following vehicle is discretized according to the sampling period to obtain the discrete-state longitudinal dynamics model, namely:

[0193] ;

[0194] , ;

[0195] In the formula, Discrete time Following vehicle Its own state information, Discrete time points Following vehicle Position, velocity, and acceleration; For the sampling period and vehicle inertial time constant A defined state transition matrix; Represents the control input matrix; Discrete time Following vehicle Control input.

[0196] In this embodiment, the second module 30 introduces an input time delay into the discrete-state longitudinal dynamics model to construct an attacked discrete-state longitudinal dynamics model affected by the time delay, and constructs a state information receiving model subject to FDI attacks, including:

[0197] Based on following vehicle The received real preceding vehicle reference state information, spoofed data injected by the attacker, and communication noise or measurement disturbances are used to obtain the attacked preceding vehicle reference state information received by the future prediction step-following vehicle, i.e.:

[0198] ;

[0199] In the formula, Indicates following vehicle The reference state information of the attacked vehicle ahead received at discrete time k for the h-th prediction step in the future; Indicates following vehicle At discrete time k, the real reference state information of the vehicle ahead is received for the h-th prediction step in the future. To follow the car The received data is fake data injected by the attacker; This could be communication noise or measurement disturbance. To predict the step size.

[0200] The control input for the attacked following vehicle is constructed based on its own state information and the reference state information of the attacked preceding vehicle, and a control input time delay is introduced. Construct a longitudinal dynamic model of the attacked discrete state under time delay, namely:

[0201] ;

[0202] ;

[0203] In the formula, To follow the car At discrete time k, the control input is attacked; To follow the car At discrete time Received reference status information of the attacked vehicle ahead.

[0204] Set the car in front To the following car pass Independent and insecure communication links broadcast the preceding train Reference status information, following vehicle Received at discrete time k Group redundancy information is represented as:

[0205] ;

[0206] In the formula, Indicates following vehicle At discrete time from The stacking matrix of redundant status information of the preceding vehicle received by the communication link; To follow the car At discrete time Through the first The reference status information of the attacked preceding vehicle received by the communication link;

[0207] Each communication link Received reference status information of the attacked vehicle ahead satisfy:

[0208] ;

[0209] In the formula, To follow the car At discrete time Through the first Communication noise received by the communication link; To follow the car At discrete time Through the first The communication link received fake data injected by the attacker.

[0210] Ultimately, it was found that an FDI attack existed. The state information reception model under the influence, namely:

[0211] ;

[0212] In the formula, Indicates following vehicle At discrete time from The stacking matrix of redundant status information of the preceding vehicle received by the communication link; express A matrix consisting entirely of 1s; To follow the car At discrete time Data on the attacks received; Indicates following vehicle The number of communication links; Indicates following vehicle At discrete time Received communication noise; Indicates following vehicle At discrete time Received reference status information of the vehicle ahead; For Kronecker product.

[0213] In this embodiment, the link filtering module 40 obtains unattacked available communication links from all communication links, divides the unattacked available communication links into multiple candidate available communication link subsets, and filters the optimal trusted communication link subset based on the consistency index of the candidate available communication link subsets, including:

[0214] Assuming at most The communication link was attacked by a fake data injection attack, and From all communication links The process involves identifying unattacked, usable communication links and dividing these links into multiple candidate subsets of usable communication links. .

[0215] Based on each candidate subset of available communication links Receive the reference state information of the preceding vehicle and calculate a subset of candidate available communication links. The mean state estimate of the preceding vehicle, i.e.:

[0216] ;

[0217] In the formula, Indicates a subset of candidate available communication links The obtained mean state estimate of the preceding vehicle; Indicates following vehicle At discrete time Through the first The preceding vehicle's reference status information received via the communication link.

[0218] A subset of candidate available communication links is calculated based on the average state estimation of the preceding vehicle. Each available communication link in the future The residuals at each prediction time, i.e.:

[0219] ;

[0220] In the formula, Indicates following vehicle Through the first The residual of an available communication link at discrete time k for the next h-th prediction step relative to the average estimate of the candidate subset; Indicates accompanying the vehicle At discrete pre-processing time Through the first The preceding vehicle's reference status information received via the communication link; Indicates following vehicle Through the first The available communication links estimate the average state of the vehicle ahead at discrete time k for the next predicted step h.

[0221] Based on the future The residuals at each prediction time are used to introduce the covariance matrix. The standardized residual index is constructed using Mahalanobis distance, namely:

[0222] ;

[0223] In the formula, Indicates following vehicle Through the first The standardized residual index of an available communication link at discrete time k for the next h-th prediction step; Indicates the transpose operation;

[0224] Wherein, the covariance matrix Represented as:

[0225] ; ;

[0226] In the formula, This is the state transition matrix; This is the initial covariance matrix; A function for generating diagonal matrices; These represent the variances of the vehicle's position, speed, and acceleration errors, respectively.

[0227] Calculate a subset of candidate available communication links based on standardized residual indices. The multi-step consistency metric, namely:

[0228] ;

[0229] In the formula, Indicates a subset of candidate available communication links A multi-step consistency index at discrete time k.

[0230] The subset of candidate available communication links with the smallest multi-step consistency index is selected as the optimal trusted communication link subset, and the state information of the optimal trusted communication link subset is used as the robust reference state. .

[0231] In this embodiment, the step of converting the difference between the random input time delay and the maximum permissible time delay into a time delay mismatch, and converting the time delay mismatch into an additive bounded perturbation to construct a discretized vehicle state prediction model considering the random input time delay, includes:

[0232] Set the maximum allowable input delay. And construct a time delay of the maximum allowable length. The input buffer stores historical control instructions and delays random input. This is converted into the time delay mismatch between the fixed maximum time delay and the actual time delay, i.e.:

[0233] ; ;

[0234] In the formula, This is the time-delay mismatch; This refers to the historical control input applied to the vehicle under actual random time delay. This refers to the historical control input retrieved according to the maximum time-delay input buffer; To control the upper limit of the input amplitude;

[0235] By converting the time-delay mismatch into an additive bounded perturbation, the complex stochastic time-delay problem is simplified into a deterministic bounded perturbation problem, resulting in a discretized vehicle state prediction model that considers stochastic input time delays, namely:

[0236] ;

[0237] , ;

[0238] In the formula, This is the additional disturbance term caused by input time delay mismatch; This is the upper bound for the additional perturbation.

[0239] In this embodiment, the optimization module 60 constructs a multi-scenario perturbation set, and constructs a scenario mini-maximum optimization problem with the objective of minimizing the worst-case scenario cost, and transforms the scenario mini-maximum optimization problem into a standard quadratic programming problem; including:

[0240] Construct a multi-scenario perturbation set including extreme scenarios, nominal scenarios, and internal sampling scenarios, as follows:

[0241] Explicitly select perturbation boundary values and As an extreme scenario; and within the range of disturbance Generate using the Latin hypercube sampling method The first internal sample is used as the internal sampling scenario. Internal scene sample Represented as:

[0242] ;

[0243] In the formula, It is a random arrangement; Let be a uniformly distributed random variable in the range [0,1]. This represents the number of internal samples. Indicates an internal sampling scenario;

[0244] Using the zero-disturbance scenario as the nominal scenario, that is: .

[0245] In the prediction time domain The goal is to minimize the cost of the worst-case scenario, thus constructing a scenario-based minimum-maximum optimization problem, namely:

[0246] For any scenario The predicted state, safety constraints, and control input constraints are as follows:

[0247] ;

[0248] ;

[0249] ;

[0250] In the formula, For scenario s, predict the vehicle state within the time domain with prediction step size j; This represents the control input to be optimized; Represents the perturbation input matrix; Let represent the bounded perturbation at step j in scenario s; This represents the predicted position at step j+1 in scenario s; This represents the reference position at step j+1 in scenario s; Indicates the safety distance constraint margin; These represent the lower and upper bounds of the control input, respectively.

[0251] A prediction total cost function is constructed based on the tracking error between the vehicle state and the reference state for all future prediction steps under the disturbance scenario s. ,Right now:

[0252] ;

[0253] in, This provides the actual state information of the following vehicle at discrete time k; The control input for the following vehicle at discrete time k; To predict the length of the time domain; Indicates the prediction step size Predicted vehicle state and reference state in scenario s Tracking error between; Represents the weighted L2 norm; Indicates the stage state tracking error weights, Indicates the terminal error weight. Control input weights; To predict step size Follow vehicle control input; To predict the tracking error in the final step of the time domain;

[0254] Predict the total cost function Transformed into a minimum-maximum optimization problem:

[0255] ;

[0256] in, This represents the set of control inputs for the following vehicle; For multi-scenario perturbation sets.

[0257] By introducing an auxiliary variable z as a common upper bound for the total cost function across all scenarios, the mini-max optimization problem is transformed into a standard quadratic programming problem. Minimizing the auxiliary variable z forces the cost in all scenarios to not exceed z, and the optimal control input for the auxiliary variable z is achieved at the optimum.

[0258] ;

[0259] in, The optimal solution for the auxiliary variable z represents the comprehensive control cost under the worst-case scenario; This is the optimal control input.

[0260] In this embodiment, the solution module 70 uses the Karush-Kuhn-Tucker conditions to solve the reconstructed standard quadratic programming problem to obtain the optimal control input for the current following vehicle, including:

[0261] A Lagrangian function is constructed based on the auxiliary variable z and the total prediction cost function under the perturbation scenario s, namely:

[0262] ;

[0263] In the formula, The augmented objective function after introducing Lagrange multipliers; For predicting time-domain control input; As an auxiliary variable; This represents the upper bound constraint on the cost of the s-th scenario.

[0264] Transforming the cost function into a standard quadratic form, we get:

[0265] ;

[0266] In the formula, Let be the Hessian matrix of the quadratic cost function with respect to the control input; This represents the coefficient vector of the first-order term in the s-th scenario; This represents the constant term in the s-th scenario; Indicates the transpose operation;

[0267] The optimality condition is further transformed into:

[0268] ;

[0269] ;

[0270] In the formula, Let represent the Hessian matrix of the quadratic cost function with respect to the control input; Indicates the optimal control input; This represents the normal cone term corresponding to the input constraints and safety constraints; Let represent the equivalent linear term obtained by weighting the KKT multipliers.

[0271] At each sampling time, based on the current vehicle state information, robust reference state, scene disturbance set, and input buffer history information, a set of optimal control input sequences is obtained. , ,…, }, the first optimal control input The actuators applied to the current vehicle are followed by the other control inputs, which are then re-optimized at the next sampling time.

[0272] Embodiments of this application provide an electronic device, including:

[0273] At least one processor; and a memory communicatively connected to the at least one processor;

[0274] The memory stores a computer program that can be executed by at least one processor. When the computer program is executed by at least one processor, it implements the hierarchical robust control method for connected autonomous vehicle queues against FDI attacks.

[0275] The embodiments and descriptions above are merely illustrative of the principles and preferred embodiments of the present invention. Various changes and modifications may be made to the present invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed.

Claims

1. A hierarchical robust control method for connected autonomous vehicle platoons against FDI attacks, characterized in that, include: Construct a longitudinal convoy consisting of one lead vehicle and multiple follower vehicles; A longitudinal dynamics model is established for the current following vehicle in the longitudinal platoon, and then discretized to obtain a discrete-state longitudinal dynamics model; Introducing input time delay into the discrete-state longitudinal dynamics model, we construct an attack-affected discrete-state longitudinal dynamics model influenced by time delay, and also construct a state information receiving model subject to FDI attacks. From all communication links, obtain the unattacked available communication links, divide the unattacked available communication links into multiple candidate available communication link subsets, and select the optimal trusted communication link subset based on the consistency index of the candidate available communication link subsets; The difference between the random input time delay and the maximum allowable time delay is transformed into a time delay mismatch, and the time delay mismatch is transformed into an additive bounded perturbation to construct a discretized vehicle state prediction model that considers the random input time delay. Construct a multi-scenario perturbation set, and with the goal of minimizing the worst-case cost, construct a scenario mini-maximum optimization problem, and transform the scenario mini-maximum optimization problem into a standard quadratic programming problem; The Karush-Kuhn-Tucker conditions are used to solve the reconstructed standard quadratic programming problem to obtain the optimal control input for the current following vehicle.

2. The hierarchical robust control method for connected autonomous vehicle platoons against FDI attacks according to claim 1, characterized in that: A longitudinal dynamics model is established for the current following vehicle in the longitudinal platoon. After discretization, a discrete-state longitudinal dynamics model is obtained, including: Based on the position, velocity, and acceleration state of the following vehicle, a longitudinal dynamics model of the following vehicle is established; The control input of the following vehicle is calculated based on its own state information and the received reference state information of the preceding vehicle. The longitudinal dynamics model of the following vehicle is discretized according to the sampling period to obtain the discrete-state longitudinal dynamics model.

3. The hierarchical robust control method for connected autonomous vehicle platoons against FDI attacks according to claim 2, characterized in that: Introducing input time delays into the discrete-state longitudinal dynamics model, a time delay-affected discrete-state longitudinal dynamics model is constructed, and a state information reception model under FDI attack is also constructed, including: Based on the real reference state information of the preceding vehicle received by the following vehicle, the false data injected by the attacker, and communication noise or measurement disturbances, the reference state information of the attacked preceding vehicle received by the following vehicle for future prediction step size is obtained. The control input of the attacked following vehicle is constructed based on the following vehicle's own state information and the reference state information of the attacked preceding vehicle. The control input time delay is introduced to construct a longitudinal dynamic model of the attacked discrete state affected by the time delay. The system configures the preceding vehicle to broadcast its reference status information to the following vehicle via multiple independent and insecure communication links; each communication link... Received reference status information of the attacked vehicle ahead satisfy: ； In the formula, To follow the car At discrete time Through the first Communication noise received by the communication link; To follow the car At discrete time Through the first The communication link received false data injected by the attacker; Indicates at discrete time Following vehicle Obtained reference status information of the vehicle ahead; Ultimately, it was found that an FDI attack existed. The state information reception model under the influence is as follows: ； In the formula, Indicates following vehicle At discrete time from The stacking matrix of redundant status information of the preceding vehicle received by the communication link; express A matrix consisting entirely of 1s; To follow the car At discrete time Data on the attacks received; Indicates following vehicle The number of communication links; Indicates following vehicle At discrete time Received communication noise; Indicates following vehicle At discrete time Received reference status information of the vehicle ahead; For Kronecker product.

4. The hierarchical robust control method for connected autonomous vehicle platoons against FDI attacks according to claim 3, characterized in that: The longitudinal dynamic model of the discrete state under attack affected by the time delay is expressed as follows: ； ； In the formula, To follow the car At discrete time k, the control input is attacked; To follow the car At discrete time Received reference status information of the attacked vehicle ahead; To control input delay; Represents the optimal control law function; Discrete time Following vehicle Its own state information.

5. The hierarchical robust control method for connected autonomous vehicle platoons against FDI attacks according to claim 4, characterized in that: From all communication links, identify unattacked and usable communication links, and divide these unattacked usable communication links into multiple candidate usable communication link subsets. Based on the consistency metrics of these candidate usable communication link subsets, select the optimal trusted communication link subset, including: Assuming at most The communication link was attacked by a fake data injection attack, and From all communication links The system identifies unattacked available communication links and divides these links into multiple candidate subsets. Based on the preceding vehicle reference state information received by each candidate available communication link subset, calculate the average preceding vehicle state estimate for the candidate available communication link subset; The residuals of each available communication link in the candidate subset of available communication links are calculated at future prediction times based on the mean state estimation of the preceding vehicle. Based on the residuals at future prediction times, a standardized residual index is constructed using the covariance matrix and Mahalanobis distance. Calculate the multi-step consistency index of candidate available communication link subsets based on standardized residual index; The candidate available communication link subset with the smallest multi-step consistency index is selected as the optimal trusted communication link subset, and the state information of the optimal trusted communication link subset is used as the robust reference state.

6. The hierarchical robust control method for connected autonomous vehicle platoons against FDI attacks according to claim 5, characterized in that: The difference between the random input time delay and the maximum permissible time delay is transformed into a time delay mismatch, and the time delay mismatch is transformed into an additive bounded perturbation to construct a discretized vehicle state prediction model that considers the random input time delay, including: Set the maximum allowable input delay and construct an input buffer with a length equal to the maximum allowable delay to store historical control instructions, thus converting the random input delay into a delay mismatch between the fixed maximum delay and the actual delay; By converting the time delay mismatch into an additive bounded perturbation, the complex stochastic time delay problem is simplified into a deterministic bounded perturbation problem, resulting in a discretized vehicle state prediction model that considers the random input time delay.

7. The hierarchical robust control method for connected autonomous vehicle platoons against FDI attacks according to claim 6, characterized in that: Construct a multi-scenario perturbation set, and build a scenario mini-maximum optimization problem with the goal of minimizing the worst-case cost. Then, transform the scenario mini-maximum optimization problem into a standard quadratic programming problem; including: Construct a multi-scenario perturbation set that includes extreme scenarios, nominal scenarios, and internal sampling scenarios; A total prediction cost function is constructed under the disturbance scenario s based on the tracking error between the vehicle state and the reference state for all future prediction steps. Transform the prediction of the total cost function into a mini-maximum optimization problem; By introducing an auxiliary variable as a common upper bound for the total cost function in all scenarios, the mini-max optimization problem is transformed into a standard quadratic programming problem. By minimizing the auxiliary variable, the cost in all scenarios is forced not to exceed the auxiliary variable, and the optimal control input of the auxiliary variable is achieved at the optimum point.

8. The hierarchical robust control method for connected autonomous vehicle platoons against FDI attacks according to claim 7, characterized in that: The reconstructed standard quadratic programming problem is solved using the Karush-Kuhn-Tucker conditions to obtain the optimal control input for the following vehicle, including: Construct a Lagrangian function based on the auxiliary variable z and the total prediction cost function under the perturbation scenario s; Transform the total cost function into a standard quadratic form; At each sampling time, an optimal control input sequence is obtained by solving based on the current vehicle state information, robust reference state, scene disturbance set, and historical information of the input buffer. The first optimal control input is added to the actuator of the vehicle currently being followed, and the remaining control inputs are re-optimized at the next sampling time.

9. A hierarchical robust control system for connected autonomous vehicle platoons against FDI attacks, characterized in that, include: The fleet building module is used to build a longitudinal fleet consisting of one lead vehicle and multiple follower vehicles; The first module is used to establish a longitudinal dynamics model for the current following vehicle in the longitudinal convoy, and the discrete state longitudinal dynamics model is obtained by discretization. The second module is used to introduce input time delay into the discrete state longitudinal dynamics model to construct the attacked discrete state longitudinal dynamics model affected by time delay, and to construct the state information receiving model under FDI attack. The link filtering module is used to obtain unattacked available communication links from all communication links, divide the unattacked available communication links into multiple candidate available communication link subsets, and filter the optimal trusted communication link subset based on the consistency index of the candidate available communication link subsets. The third module is used to convert the difference between the random input time delay and the maximum allowable time delay into a time delay mismatch, and to convert the time delay mismatch into an additive bounded perturbation to construct a discretized vehicle state prediction model that considers the random input time delay. The optimization module is used to construct a multi-scenario perturbation set, and to construct a scenario mini-maximum optimization problem with the goal of minimizing the worst-case cost, and then transform the scenario mini-maximum optimization problem into a standard quadratic programming problem. The solution module uses the Karush-Kuhn-Tucker conditions to solve the reconstructed standard quadratic programming problem and obtain the optimal control input for the current following vehicle.

10. An electronic device, comprising: At least one processor; and memory that is communicatively connected to at least one processor; The memory stores a computer program that can be executed by at least one processor, characterized in that, when the computer program is executed by at least one processor, it implements the hierarchical robust control method for connected autonomous vehicle queues against FDI attacks as described in any one of claims 1-8.

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