Attack detection and elastic control method for multi-vehicle cooperative system

Abstract

The invention relates to an attack detection and elastic control method for a multi-vehicle cooperative system. The method comprises the following steps: step 1, initializing; step 2, prediction: at the moment t, according to the state ellipsoid set epsilon t and the shape matrix Qt, solving a prediction ellipsoid set epsilon t + 1t; step 3, inter-vehicle communication attack detection: judging whether inter-vehicle communication is attacked at the moment t, if not, executing the step 4, and otherwise, executing the step 6; step 4, measurement updating: at the t + 1 moment, solving a minimum ellipsoid set # imgabs0 # and measuring and updating an ellipsoid set epsilon t + 1; step 5, sensor attack detection: at the t + 1 moment, judging whether the sensor is attacked according to an intersection set of epsilon t + 1t and # imgabs1 #, if the intersection set is empty, executing the step 6, otherwise, executing the step 2; step 6, elastic control: according to the attack response, respectively replacing the attacked ellipsoid sets, and respectively carrying out measurement updating and prediction processes at the t + 1 moment; and step 7, repeating the steps 2-6 until the end. Compared with the prior art, the method has the advantages of reducing network attack influence and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-vehicle collaborative control, and in particular to an attack detection and elastic control method for a multi-vehicle collaborative system. Background Art

[0002] Multi-vehicle collaborative systems, such as vehicle-to-everything (V2X) and autonomous driving fleets, achieve functions such as formation control and congestion mitigation through vehicle-to-vehicle (V2V) communication and vehicle-to-infrastructure (V2I) technology, and are a core component of intelligent transportation systems. These systems improve traffic efficiency and safety through real-time data exchange and collaborative decision-making. However, with the popularization of 5G and edge computing technologies, the real-time performance and complexity of multi-vehicle collaborative systems have increased significantly, bringing new challenges at the same time.

[0003] Currently, multi-vehicle collaborative systems mainly rely on traditional encryption and authentication technologies (such as the public key infrastructure PKI system) and anomaly detection algorithms (such as statistical-based threshold judgment) to ensure communication security and system stability. These methods can detect and prevent simple attacks to a certain extent, but they have obvious limitations when facing new types of attacks (such as false data injection attacks, Sybil attacks, and timing attacks). False data injection attacks may cause vehicles to receive incorrect driving instructions, Sybil attacks may interfere with system decision-making by forging multiple identities, and timing attacks may disrupt the system's synchronization by tampering with the timestamps of data transmission.

[0004] In addition, most existing research focuses on the attack detection stage and lacks an effective dynamic recovery mechanism. For example, the multi-threshold network attack detection method based on the comprehensive ellipsoid and polytope state estimation domain disclosed in patent application CN118972133A. Once an attack is detected, the system often can only take simple isolation or restart measures, which may lead to the fracture of the formation structure and a decline in overall performance. For example, in an autonomous driving fleet, if a vehicle is detected to be under attack and isolated, it may cause the formation structure of the fleet to be damaged, affecting the driving efficiency and safety of the entire fleet.

[0005] Therefore, there is an urgent need for a multi-vehicle collaborative system that can effectively detect new types of attacks and has a dynamic recovery mechanism to provide important technical support for the development of future intelligent transportation. Summary of the Invention

[0006] The purpose of the present invention is to provide an attack detection and elastic control method to ensure the queue stability of a multi-vehicle collaborative system.

[0007] The purpose of the present invention can be achieved through the following technical solutions:

[0008] An attack detection and elastic control method for a multi-vehicle collaborative system, comprising the following steps:

[0009] Step 1, Initialization: Determine the initial state ellipsoid set ε0 of the multi-vehicle cooperation system and determine the initial shape matrices Q0 and R0 of the process noise and the measurement noise;

[0010] Step 2, Prediction: At time t, according to the state ellipsoid set ε t of the previous moment and the shape matrix Q t of the process noise, solve the predicted ellipsoid set ε t+1|t through semi-definite programming optimization;

[0011] Step 3, Workshop communication attack detection: At time t, judge whether the workshop communication is attacked according to the predicted ellipsoid set ε t+1|t and the redundant state ellipsoid set . If not, execute Step 4 for measurement update. If so, execute Step 6 for resilient control;

[0012] Step 4, Measurement update: At time t + 1, according to the predicted ellipsoid set ε t+1|t , the measurement value y t+1 of the vehicle's own sensor, and the shape matrix R t+1 of the measurement noise, solve the minimum ellipsoid set and the measurement update ellipsoid set ε t+1 through semi-definite programming optimization;

[0013] Step 5, Sensor attack detection: At time t + 1, judge whether the sensor is attacked according to the intersection of the predicted ellipsoid set ε t+1|t and the minimum ellipsoid set . If the intersection is empty, it means it is attacked and execute Step 6 for resilient control. If the intersection is not empty, it means it is not attacked and execute Step 2 for the next moment's prediction;

[0014] Step 6, Resilient control: According to the workshop communication attack response and the sensor attack response, replace the attacked ellipsoid sets respectively, and perform the measurement update and prediction processes at time t + 1 respectively;

[0015] Step 7, Repeat execution: Repeat Steps 2 - 6 until the end to complete the attack detection and resilient control process.

[0016] Furthermore, in Step 2, the steps of solving the predicted ellipsoid set ε t+1|t include:

[0017] Consider the influence of the process noise and the measurement noise, and construct the state equation of the following vehicle i in the multi-vehicle cooperation system;

[0018] According to the true state x tThe set of state ellipsoids ε t and the state equation of the following vehicle i to obtain the set which is expressed as:

[0019]

[0020] where f is a nonlinear state function;

[0021] Construct a semi-infinite programming problem to solve the smallest ellipsoid set that encloses the set denoted as where the semi-infinite programming problem is expressed as:

[0022]

[0023] where the set is defined as:

[0024]

[0025] where P and are the shape matrix and the center of the ellipsoid obtained from the optimization problem, y is the output, is the center of the ellipsoid set ε0, and P0 is the shape matrix of ε0

[0026] Use the Frank-Wolfe algorithm to solve the semi-infinite programming problem to obtain the smallest ellipsoid set that encloses the set denoted as ;

[0027] Based on the smallest ellipsoid set and the state equation of the following vehicle i, obtain the predicted ellipsoid set ε t+1|t The expression is:

[0028]

[0029] where is the center of the predicted ellipsoid set ε t+1|t P t+1|t is the shape matrix of the predicted ellipsoid set ε t+1|t P t is the shape matrix of the state ellipsoid set ε t E t+1|t is the lower triangular matrix obtained by Cholesky decomposition, and η t+1|t is the free parameter vector.

[0030] Furthermore, the construction steps of the state equation of the following vehicle i include:

[0031] Construct the state equation of the nonlinear dynamics of the following vehicle i in the multi-vehicle cooperative system, which is expressed as:

[0032]

[0033] where s i (t) and v i (t) represent position and velocity, Δt represents the discrete time interval, m i represents mass, η T，i represents the mechanical efficiency of the transmission system, T i (t) represents the aggregated drive / braking torque, F i is the total resistance, u i (t) is the control input, τ i represents the inertial lag of longitudinal dynamics, C A，i represents the air resistance coefficient, r i represents the tire radius, g represents the gravitational constant; f i represents the rolling resistance coefficient;

[0034] For the following vehicle i, its state vector is expressed as x i (t) = [s i (t), v i (t), T i (t)] T , and the output vector is expressed as y i (t) = [s i (t), v i (t)] T , and the state equation of Equation (1) is converted to:

[0035]

[0036] where, ψ i = [0, 0, (1 / τ i )Δt] T , φ i (x i (t)) is:

[0037]

[0038] Considering the influence of process noise and measurement noise, the state equation of Equation (2) is converted to:

[0039]

[0040] where,

[0041] In the formula, f(x t ) = φ(x t ) + ψ·u t 、h(xt ) = γ·x t are the state equation and the measurement equation respectively, ω t and v t are the process noise and the measurement noise respectively, u t is the optimal control quantity at time t calculated by the distributed MPC algorithm, Q t is 's shape matrix, R t is 's shape matrix, is the corresponding noise ellipsoid set.

[0042] Furthermore, the steps of obtaining the minimum ellipsoid set that encloses the set include:

[0043] Input the number of sampling points m and the set

[0044] According to the set generate m sampling points y1, y2,..., y m , let

[0045] Use the Frank-Wolfe algorithm to solve the optimization problem and obtain the measure where the optimization problem is expressed as:

[0046]

[0047] Based on the measure calculate where the calculation expressions are respectively:

[0048]

[0049] Based on obtain the minimum ellipsoid set that encloses the set which is expressed as:

[0050]

[0051] In the formula, is 's center, is the lower triangular matrix obtained by Cholesky decomposition, is the free parameter vector, is 's shape matrix.

[0052] Furthermore, the steps of obtaining the predicted ellipsoid set ε t+1|t include:

[0053] Based on the set of minimum ellipsoids There exists Satisfying Convert the state equation to:

[0054]

[0055] where ω t is the process noise;

[0056] According to the transformed state equation, we get:

[0057]

[0058] where is the Minkowski sum;

[0059] Calculate the outer ellipsoid estimate enclosing the Minkowski sum, and the calculation expression is:

[0060]

[0061] where the optimal solution of p is p * , obtained from the following formula:

[0062]

[0063] where Q t is the shape matrix of, is the set of process noise ellipsoids, and P t+1|t (p) is the predicted ellipsoid set ε t+1|t 's shape matrix;

[0064] Based on the outer ellipsoid estimate result enclosing the Minkowski sum, obtain the predicted ellipsoid set ε t+1|t .

[0065] Furthermore, the steps of using the Frank-Wolfe algorithm to solve the optimization problem include:

[0066] Let At the current solution μ t , perform a first-order Taylor expansion on the function g(μ) to obtain:

[0067] g(μ)≈g(μ t )+(ω t ) T (-μ t )

[0068] where

[0069] Input: Select the initial point μ 0 ∈M;

[0070] Iterative calculation: For t = 1, 2,..., T, perform the following steps:

[0071] ① Calculate

[0072]

[0073] where e i is a unit vector representing a vertex in the set M;

[0074] ② Calculate d t :

[0075]

[0076] where d t is the direction vector;

[0077] ③ Calculate γ t :

[0078]

[0079] where γ t is the step size;

[0080] ④ Update μ t+1 :

[0081] μ t+1 = μ t + γ t d t

[0082] Output: Return μ T and denote it as

[0083] Furthermore, in step 3, the step of determining whether the workshop communication is attacked includes:

[0084] Determine whether the intersection of the predicted ellipsoid set ε t+1|t and the redundant state ellipsoid set is empty. If it is empty, it indicates that the workshop communication is attacked. If it is not empty, it indicates that the workshop communication is not attacked;

[0085] Among them, the step of determining whether the intersection of the predicted ellipsoid set ε t+1|t and the redundant state ellipsoid set is empty includes:

[0086] Combine the predicted ellipsoid set ε t+1|t and the redundant state ellipsoid set Denoted as ε1 and ε2 respectively, and their corresponding centers are denoted as and The corresponding shape matrices are denoted as P1 and P2 respectively;

[0087] If the true state x is in both ε1 and ε2, then the intersection of ε1 and ε2 must not be empty, and there must exist two vectors z1 and z2 such that the following equation (1) holds:

[0088]

[0089] If the intersection of ε1 and ε2 is empty, then vectors z1 and z2 cannot be found to make the above equation (1) hold, indicating that to judge whether the intersection of ε t+1|t and is empty, it is necessary to judge whether there are feasible solutions z1 and z2 for the above equation (1). The steps to judge the feasible solutions include:

[0090] By transposing the above equation (1), we get:

[0091]

[0092] Transform the problem of solving the feasible solution of equation (2) into the solution of the following optimization problem to obtain the result of the intersection of ε t+1|t and . The optimization problem is expressed as:

[0093]

[0094] In the formula, matrices E1 and E2 are the matrices obtained by performing Cholesky decomposition on shape matrices P1 and P2 respectively, and J a is the optimization objective function, and α, β ∈ (0, 1] are newly introduced elastic variables.

[0095] Furthermore, in step 4, the solution steps of the minimum ellipsoid set and the measurement update ellipsoid set ε t+1 include:

[0096] According to the continuity and invertibility of the measurement equation h, there exists a continuous inverse function h -1 , expressed as:

[0097] h -1 (y t+1 -v t+1 ) = Tx t+1

[0098]

[0099] In the formula, v t+1 is the measurement noise at time t + 1, T is the projection matrix, and x t+1, y t+1 are the input and output vectors at time t + 1;

[0100] Based on the measurement value y at time t + 1 t+1 and the set of measurement noise ellipsoids obtain a new set of state ellipsoids which is expressed as:

[0101]

[0102] Construct a semi-infinite programming problem, where the semi-infinite programming problem is expressed as:

[0103]

[0104] wherein, is the shape matrix of the ellipsoid obtained from the optimization problem, z t+1 is the feasible solution variable in Equation (1), is the center of the ellipsoid obtained from the optimization problem;

[0105] Solve the semi-infinite programming problem to obtain the smallest ellipsoid set that encloses the set where based on the smallest ellipsoid set it is obtained that there exists satisfying:

[0106]

[0107] wherein, is the lower triangular matrix obtained by Cholesky decomposition, is the free parameter vector;

[0108] Based on the true state being included in the intersection of the predicted ellipsoid set ε t+1|t and the smallest ellipsoid set by solving the smallest ellipsoid set of the intersection of ε t+1|t and obtain the measurement update ellipsoid set ε t+1 which is expressed as:

[0109]

[0110] wherein, P t+1 is the shape matrix of ε t+1 t+1 is the center of ε t+1 E t+1 is the lower triangular matrix obtained by Cholesky decomposition, η t+1 is the free parameter vector.

[0111] Further, the ε is solved through the following formula t+1|t and the minimum ellipsoid set of the intersection set, and the formula is

[0112]

[0113]

[0114] where P t+1 the variable ρ in the matrix t+1 The optimal ρ is obtained by solving the following optimization problem t+1 :[[]]

[0115] min g(P t+1 )

[0116] s.t. 0 < ρ t+1 <1

[0117] In the formula, g is the optimization function, 0 < ρ t+1 <1

[0118] Further, in step 6, the steps of the elastic control include

[0119] (1) Workshop communication is attacked

[0120] Using the redundant state ellipsoid set Replace the prediction ellipsoid set ε t+1|t , so as to use the redundant state ellipsoid set As the prediction ellipsoid set at time t, and enter the measurement update process at time t + 1

[0121] (2) The sensor is attacked

[0122] Using the prediction ellipsoid set ε t+1|t Replace the measurement update ellipsoid set ε t+1 , so as to use the prediction ellipsoid set ε t+1|t As the measurement update ellipsoid set at time t + 1, and enter the prediction process at time t + 1

[0123] Compared with the prior art, the present invention has the following beneficial effects

[0124] (1) In addition to studying the attack detection and elastic control problems of the multi-vehicle cooperation system, the present invention constructs a multi-vehicle cooperation system model based on vehicle nonlinear dynamics and one-way communication topology, and uses a distributed model predictive control algorithm considering safety and occupant comfort, which can meet the constraint conditions and ensure the queue stability of the multi-vehicle cooperation system

[0125] (2) The present invention is based on the theory of set - membership filtering algorithm, integrating multi - source data (including vehicle status, communication timing, and environmental perception) for joint analysis, realizing the state estimation of non - linear systems under the assumption of unknown but bounded noise, improving the recognition rate of covert attacks, and dynamically adjusting vehicle roles (including leader / follower switching) and communication topologies after detecting attacks to maintain the minimum safety functions of the system.

[0126] (3) The present invention designs an attack detection algorithm based on the theory of set - membership filtering algorithm, which can accurately detect network attacks on the vehicle's own sensors and network attacks on the vehicle - to - vehicle communication channels.

[0127] (4) The present invention designs an elastic control algorithm using the method of state replacement, which can effectively reduce the impact of network attacks on the multi - vehicle cooperative system. Description of the Drawings

[0128] Figure 1 It is a schematic diagram of the method flow of the present invention;

[0129] Figure 2 It is a schematic diagram of the one - way communication topology vehicle queue model of the present invention;

[0130] Figure 3 It is a schematic diagram of the PF and PLF queue models of the distributed MPC controller of the present invention;

[0131] Figure 4 It is a schematic diagram of the speed state of the leading vehicle under acceleration and deceleration conditions of the present invention;

[0132] Figure 5 It is a schematic diagram of the control input calculation method of the present invention;

[0133] Figure 6 It is a schematic diagram of the experimental results without using elastic control under a large - intensity denial - of - service attack of the present invention;

[0134] Figure 7 It is a schematic diagram of the experimental results using elastic control under a large - intensity denial - of - service attack of the present invention;

[0135] Figure 8 It is a schematic diagram of the experimental results without using elastic control under a large - intensity spoofing attack of the present invention;

[0136] Figure 9 It is a schematic diagram of the experimental results using elastic control under a large - intensity spoofing attack of the present invention;

[0137] Figure 10 It is a schematic diagram of the experimental results without using elastic control under a large - intensity replay attack of the present invention;

[0138] Figure 11Schematic diagram of experimental results of elastic control under large-intensity replay attacks of the present invention. Specific embodiments

[0139] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and the detailed implementation manners and specific operation processes are given, but the protection scope of the present invention is not limited to the following embodiments.

[0140] This embodiment provides a method for attack detection and elastic control of a multi-vehicle cooperation system. Based on the set membership filtering theory, this method fuses the joint analysis of multi-source data (such as vehicle state, communication timing, and environmental perception) to improve the recognition rate of covert attacks. After detecting an attack, it dynamically adjusts the vehicle roles (such as leader / follower switching) and communication topologies to maintain the minimum safety function of the system. First, the theory of the set membership filtering algorithm is introduced. By solving a semi-infinite programming problem, the nonlinear system is transformed into a linear system, realizing the state estimation of the nonlinear system under the assumption of unknown but bounded noise. Then, an attack detection algorithm based on set membership filtering is designed, which can detect network attacks on the vehicle's own sensors and network attacks on the vehicle-to-vehicle communication channels. Finally, an elastic control algorithm is designed by using the method of state replacement, which can effectively reduce the impact of network attacks on the multi-vehicle cooperation system.

[0141] Before introducing the specific steps of this method, the mathematical symbols and mathematical definitions in the present invention are described here. And Are used to represent the set of real numbers and the set of complex numbers respectively; Represents the set of m×n real matrices, Is used to represent the set of n-order symmetric matrices; for any positive integer N, the set Given a symmetric matrix Indicates that the matrix is positive semi-definite (positive definite); the relational expression M1≥M2 between symmetric matrices means M1 - M2≥0; I n Represents the n-order identity matrix; diag(a1,..., a N ) represents a diagonal matrix whose main diagonal elements are respectively And the off-diagonal elements are all 0; given a vector x and a positive semi-definite matrix Q≥0, use ||x|| Q =(x T Qx) 1 / 2 To represent the weighted Euclidean norm; the Kronecker product is represented by And it has the following properties for matrix operations: (1) (2)

[0142] Define the ellipsoidal set:

[0143]

[0144] wherein is called the center of the ellipsoidal set χ, and the matrix is an n-order symmetric positive definite matrix, satisfying P = P T > 0, which is called the shape matrix of the ellipsoidal set X. In this paper, the function g(P) of the shape matrix P is used to represent the "size" of the ellipsoidal set X, g(P) = logdet(P), which means the volume of the ellipsoid. According to the properties of symmetric positive definite matrices, through Cholesky decomposition, the lower triangular matrix can be obtained to satisfy P = EE T , thereby obtaining another expression form of the ellipsoidal set:

[0145]

[0146] Specifically, as Figure 1 shown, the method includes the following steps:

[0147] S1. Initialization:

[0148] Select the initial state ellipsoidal set ε0 of the system, whose center is and the shape matrix is P0; for the process noise and measurement noise, select appropriate shape matrices Q0 and R0, and model the process noise and measurement noise as unknown but bounded ellipsoidal sets

[0149] The present invention needs to perform state estimation on the following vehicle in the multi-vehicle cooperative system. The non-linear dynamics of the state equation of the following vehicle i are as follows:

[0150]

[0151] where Δt represents the discrete time interval; s i (t) and v i (t) represent the position and velocity; m i represents the mass; C A，i represents the air resistance coefficient; g represents the gravitational constant; f i represents the rolling resistance coefficient; T i (t) represents the combined driving / braking torque; τ i represents the inertial lag of the longitudinal dynamics; r i represents the tire radius; η T，i represents the mechanical efficiency of the transmission system.

[0152] For the following vehicle i, its state vector can be expressed as and the output vector can be expressed as Rewrite the state equation of the following vehicle \(i\) into a more compact form as follows:

[0153] x i (t + 1)=\(\varphi\) i (x i (t))+\(\psi\) i \(\cdot\)u i (t)

[0154] y i (t)=\(\gamma\)\(\cdot\)x i (t)

[0155] where

[0156]

[0157] For more concise expression, the subscript \(i\) indicating the following vehicle index will be omitted in the subsequent text, and the subscript \(t\) will be used to represent the value of the variable at time \(t\). At the same time, considering the influence of process noise and measurement noise, rewrite the state equation of the following vehicle \(i\) as:

[0158]

[0159] where \(f(x t )=\(\varphi\)(x t )+\(\psi\)\(\cdot\)u t , \(h(x t )=\(\gamma\)\(\cdot\)x t are the state equation and the measurement equation respectively, \(\omega\) t and \(v t are the process noise and the measurement noise respectively, \(u t is the optimal control quantity at time \(t\) calculated by the distributed MPC algorithm, regarded as a given known quantity in the state estimation problem, where the calculation method is as Figure 5 shown.

[0160] Assume that the uncertain noise exists within a bounded ellipsoidal set, that is:

[0161]

[0162] where \(Q t and \(R t are the shape matrices of the ellipsoidal sets and respectively, both of which are known symmetric positive definite matrices, describing the boundaries of the process noise and the measurement noise.

[0163] Assume that the initial state of the system is \(x_0\), and the initial state exists in a given ellipsoidal set \(\varepsilon_0\), that is

[0164]

[0165] where \(x_0\) and \(P_0\) are the center and the shape matrix of the ellipsoid set \(\varepsilon_0\), both of which are known quantities.

[0166] Assume that at time \(t\), the ellipsoid set \(\varepsilon\) t enclosing the true state \(x\) t of the following vehicle \(i\) has been obtained. This assumption is reasonable because the ellipsoid set \(\varepsilon_0\) of the initial state is known. Therefore, we have:

[0167]

[0168] where is the center of the ellipsoid set \(\varepsilon\) t , and \(P\) t is the shape matrix of the ellipsoid set \(\varepsilon\) t , both of which are known quantities. Based on the ellipsoid set \(\varepsilon\) t and the state equation in Equation (3), the predicted ellipsoid set \(\varepsilon\) t+1|t of the following vehicle \(i\) at time \(t\) can be obtained. The specific steps will be elaborated later. Here, it is assumed that the predicted ellipsoid set \(\varepsilon\) t+1|t of the following vehicle \(i\) has been obtained, that is:

[0169]

[0170] where is the center of the ellipsoid set \(\varepsilon\) t+1|t , and \(P\) t+1|t is the shape matrix of the ellipsoid set \(\varepsilon\) t+1|t . Then, using the measurement equation in Equation (3) and the measurement value \(y\) t+1 , the measurement-updated ellipsoid set \(\varepsilon\) t+1 of the following vehicle \(i\) at time \(t + 1\) can be obtained, that is:

[0171]

[0172] where is the center of the ellipsoid set \(\varepsilon\) t+1 , and \(P\) t+1 is the shape matrix of the ellipsoid set \(\varepsilon\) t+1 .

[0173] S2. Prediction step:

[0174] At time \(t\), the state ellipsoid set \(\varepsilon\) t of the system obtained from the measurement-update step at the previous time is known, the process-noise shape matrix \(Q\) t of the system is known, and the optimal control quantity \(u\) t is known. Through semi-infinite programming optimization, the minimum enclosing ellipsoid set of the nonlinear system is solved to achieve high-precision state estimation.

[0175] Assume that at time \(t\), the true state \(x\) of the following vehicle \(i\) has been obtained, t and the ellipsoidal set \(\varepsilon\) t is available. Next, it is desired to obtain a predicted ellipsoidal set \(\varepsilon\) t+1|t at time \(t\) that contains the true state \(x\) t+1 of the following vehicle \(i\) at time \(t + 1\). t+1|t Moreover, on the basis of satisfying this condition, it is desired that the size of the predicted ellipsoidal set \(\varepsilon\)

[0176] is as small as possible, that is, the accuracy of the state estimation is as high as possible.

[0177] Given the ellipsoidal set \(\varepsilon\) t of the true state \(x\) t of the surrounding system at time \(t\), a new set can be obtained through the non - linear state function \(f\) in Equation (3).

[0178]

[0179] Due to the non - linearity of the state equation, the obtained set is not an ellipsoidal set like \(\varepsilon\) t . Therefore, it is necessary to find the smallest ellipsoidal set that encloses the set , that is, This can be obtained by solving the following optimization problem:

[0180]

[0181] Writing the above equation in a more general form gives:

[0182]

[0183] The set is defined as follows:

[0184]

[0185]

[0186] Using the parameterization method, the optimal solution of Equation (11) is:

[0187]

[0188] where \(\mu\) * is the measure and is the optimal solution of the following optimization problem:

[0189]

[0190] where μ is a measure, denotes the Cartesian product of the set

[0191] and the set {1}. Some points can be randomly sampled from the set so that the optimization problem (16) can be approximated as:

[0192]

[0193] Since therefore, it can be obtained by randomly sampling y from the set in the way that i where i = 1, 2,..., m. where i = 1, 2,..., m.

[0194] Next, the Frank-Wolfe algorithm is used to solve the optimization problem of equation (17).

[0195] First, let:

[0196]

[0197] At the current solution μ t perform a first-order Taylor expansion on the objective function g(μ), and we can get:

[0198] g(μ) ≈ g(μ t ) + (ω t ) T (μ - μ t ) (19)

[0199] where Then, we can consider maximizing this linear function on the unit simplex set M, and the analytical solution lies at a vertex, that is, the unit vector e i , which means the i-th component is 1 and the other components are 0. Geometrically, the unit vector e i represents a vertex in the set M, corresponding to a vertex of the simplex, and the other components being 0 means that this vertex is on the coordinate axis defined by the unit vector e i . Therefore, we hope to update μ t along the direction from μ i to e t+1 , and the specific algorithm is as follows:

[0200] (1) Input: Select an initial point μ 0 ∈ M;

[0201] (2) For t = 1, 2,..., T, perform the following steps:

[0202] ① Calculate

[0203]

[0204] ② Calculate d t :

[0205]

[0206] ③ Calculate γ t :

[0207]

[0208] ④ Update μ t+1 :

[0209] μ t+1 = μ t + γ t d t (23)

[0210] (3) Return μ T 。

[0211] In summary, the Frank-Wolfe algorithm is used to solve the semi-infinite programming problem in the form of equation (11). The specific algorithm is as follows:

[0212] (1) Input: the number of sampling points m, the set

[0213] (2) Generate sampling points y1, y2,..., y according to the set m , and let

[0214] (3) Use the Frank-Wolfe algorithm to solve the optimization problem (17) to obtain

[0215] (4) Calculate

[0216]

[0217] From equations (24) and (25), the minimum ellipsoid set enclosing the set can be obtained.

[0218] Based on the above derivation, the solution method for the optimization problem in equation (10) is obtained. By solving the optimization problem in equation (10), the minimum ellipsoid set enclosing the set is obtained, that is:

[0219]

[0220] Therefore, there must exist satisfying The state equation in Equation (3) can be written as:

[0221]

[0222] From Equation (27), we can obtain:

[0223]

[0224] Although the Minkowski sum is not an ellipsoidal set, an external ellipsoidal estimate enclosing the Minkowski sum can be calculated, i.e., Its calculation formula is:

[0225]

[0226] The optimal solution of Equation (30), i.e., the optimal external ellipsoidal estimate enclosing the Minkowski sum, defines the optimal solution of p as p * , which can be obtained from the following equation

[0227]

[0228] Thus, the predicted ellipsoidal set ε t+1|t of the shape matrix P t+1|t = P t+1|t (p * ).

[0229] S3. Workshop communication attack detection:

[0230] At time t, the predicted ellipsoidal set ε t+1|t of the system is known, and the redundant state ellipsoidal set of the system is known. If report "Workshop communication is not under attack" and jump to the measurement update step; if report "Workshop communication is under attack" and switch to the resilient control mode.

[0231] In the above attack detection algorithm, it is necessary to determine whether the intersection of two ellipsoidal sets is empty. For this problem, the following algorithm is designed:

[0232] Suppose there are currently two ellipsoidal sets ε1 and ε2, and their centers are and respectively, and their shape matrices are P1 and P2. Suppose the true state x of the system is in both ε1 and ε2 at this time. Then, the intersection of the ellipsoidal sets ε1 and ε2 must not be empty. According to the definition of the ellipsoidal set in Equation (2), there must exist two vectors z1 and z2 such that the following equation holds:

[0233]

[0234] Among them, matrices E1 and E2 are the matrices obtained by performing Cholesky decomposition on matrices P1 and P2 respectively.

[0235] If the intersection of ε1 and ε2 is an empty set, then it is certain that vectors z1 and z2 cannot be found to make equation (32) hold, and vice versa. Thus, the problem of determining whether the intersection of two ellipsoid sets is an empty set is transformed into the problem of whether there is a feasible solution for equation (32).

[0236] Shift the right side of equation (32) to obtain:

[0237]

[0238] To more conveniently use computer-aided solution, the problem of solving the equation of equation (33) is transformed into the solution of the following optimization problem:

[0239]

[0240] Among them, α, β ∈ (0, 1] are newly introduced elastic variables with a default value of 1, which are used to limit the size of the state ellipsoid set and can reflect the confidence level of the state ellipsoid set.

[0241] S4. Measurement update step:

[0242] At time t + 1, the system prediction ellipsoid set ε obtained from the prediction step at the previous moment t+1|t is known, the sensor measurement value y t+1 is known, and the measurement noise shape matrix R of the system t+1 is known. Randomly sample m points in the measurement noise ellipsoid set and calculate the set Solve the optimization problem to obtain the minimum ellipsoid set enclosing the set

[0243] After the prediction step, the prediction ellipsoid set ε t+1|t is obtained, whose center is and the shape matrix is P t+1|t . In the measurement update step, the goal is to use the measurement equation in equation (3) and the measurement value y t+1 to obtain the measurement update ellipsoid set ε t+1 .

[0244] Obviously, the measurement equation h in equation (3) is continuous and invertible, and it has a continuous inverse function h -1 , that is

[0245] h-1 (y t+1 -v t+1 ) = Tx t+1 (35)

[0246] where T is the projection matrix,

[0247]

[0248] Based on the measurement value y at time t+1 t+1 and the set of measurement noise ellipsoids a new set of state ellipsoids is obtained:

[0249]

[0250] Similar to the prediction step, it is desired to find the smallest set of ellipsoids that encloses the set , which can be obtained by solving the following semi-infinite programming problem:

[0251]

[0252] The semi-infinite programming problem of the form of Equation (38) also has the same form as Equation (11). Assume that the smallest set of ellipsoids that encloses the set has been found, so there must exist that satisfies

[0253]

[0254] where

[0255] Since the true state is contained in both the ellipsoid set ε t+1|t and the ellipsoid set , the true state must be contained in the intersection of the ellipsoid set ε t+1|t and the ellipsoid set . By solving the smallest ellipsoid set that encloses the intersection of the two sets, the measurement update ellipsoid set ε t+1 can be obtained.

[0256] The smallest ellipsoid set that encloses the intersection of two ellipsoid sets can be obtained from the following formula:

[0257]

[0258] where 0 < ρ t+1 < 1. The expression of the P t+1 matrix contains only one variable ρ t+1 , and the optimal ρ t+1 can be easily obtained by solving the following optimization problem:

[0259]

[0260] S5. Sensor attack detection:

[0261] At time t+1, the system prediction ellipsoid set ε obtained from the prediction step at the previous time t+1|t is known, and the ellipsoid set obtained from the measured values at the current time is known. If report "the sensor is under attack" and switch to the resilient control mode; if report "the sensor is not under attack" and calculate the measurement update state ellipsoid set ε at time t+1 t+1 , and then enter the prediction step at the next time.

[0262] S6. Resilient control algorithm:

[0263] 1. Sensor attack response: Replace the contaminated measurement ellipsoid set with the uncontaminated prediction ellipsoid set ε t+1|t . 2. Communication attack response: Replace the attacked prediction ellipsoid set with the redundant ellipsoid set .

[0264] Assume that at time t, the measurement update ellipsoid set ε of the system t is not under attack. The resilient control algorithms designed for the two types of network attacks are as follows:

[0265] (1) The in-plant communication is under attack

[0266] Triggering condition: At time t, it is detected that

[0267] ① Use to replace ε t+1|t , and use as the prediction ellipsoid set at time t;

[0268] ② Enter the measurement update step at time t+1.

[0269] (2) The ego-vehicle sensor is under attack

[0270] Triggering condition: At time t+1, it is detected that

[0271] ① Use ε t+1|t to replace ε t+1 , and use ε t+1|t as the measurement update ellipsoid set at time t+1;

[0272] ② Enter the prediction step at time t+1.

[0273] This embodiment is based onFigure 2 and Figure 3 Taking the multi-vehicle cooperative system shown as an example, MATLAB / Simulink software is used for simulation. On this basis, the SecCT-AUTO automotive information security compliance detection tool platform is adopted to implement network attack injection, and the Speedgoat real-time target machine hardware platform is used to conduct hardware-in-the-loop experimental verification on the attack detection algorithm and elastic control algorithm proposed by the present invention. The first 3 vehicles in Table 1 are selected as the following vehicles. The reference trajectory of the leading vehicle still adopts the acceleration and deceleration working conditions as shown in Figure 4 The simulation results are as shown in Figures 6 - 10 .

[0274] As Figure 6 shown, without elastic control, the Denial-of-Service (DoS) attack with increased intensity has a greater adverse impact on the multi-vehicle cooperative system. Even after the attack is removed, the multi-vehicle cooperative system cannot rely on its own robustness to restore the system to the normal working state.

[0275] Table 1 Simulation parameters and following vehicle parameters

[0276]

[0277] According to Figure 7 it can be seen that: with elastic control, when it is detected that the vehicle-to-vehicle communication channel is under a network attack, the control strategy can be switched in a timely manner. Although the overall following vehicle effect is slightly decreased compared with the situation without network attack, it is significantly better than the situation without elastic control. This shows that after adopting the elastic control algorithm, the impact of the Denial-of-Service attack on the multi-vehicle cooperative system can be significantly reduced, verifying the effectiveness of the elastic control algorithm.

[0278] According to Figure 8 it can be seen that: without elastic control, the spoofing attack with increased intensity has a greater adverse impact on the multi-vehicle cooperative system. Even after the attack is removed, the multi-vehicle cooperative system cannot rely on its own robustness to restore the system to the normal working state.

[0279] According to Figure 9 it can be seen that: after the spoofing attack at time step t = 100, the speed curves of following vehicle 2 and following vehicle 3 adopting the elastic control algorithm are smoother. When it is detected that the on-vehicle sensor is under a network attack, the control strategy can be switched in a timely manner. Although the overall following vehicle effect is slightly decreased compared with the situation without network attack, it is significantly better than the situation without elastic control. This shows that after adopting the elastic control algorithm, the impact of the spoofing attack on the multi-vehicle cooperative system can be significantly reduced, verifying the effectiveness of the elastic control algorithm.

[0280] According to Figure 10It can be seen that without elastic control, the replay attack after increasing the strength has a greater adverse impact on the multi-vehicle cooperative system. In the second half of the attack duration, that is, from time step t = 120 to time step t = 140, the leader vehicle has started to accelerate. The follower vehicle 1 can respond quickly without being affected by any attack, while the speed measurement value received by the controller of the follower vehicle 2 at this time is the measured value affected by the replay attack, which affects the calculation of the control quantity, resulting in the follower vehicle 2 being unable to keep up with the speed change of the follower vehicle 1. Even after the replay attack is removed, the multi-vehicle cooperative system cannot return to the normal working state.

[0281] According to Figure 11 It can be seen that after the replay attack at time step t = 100, the speed curves of the follower vehicle 2 and the follower vehicle 3 using the elastic control algorithm are smoother. When it is detected that the vehicle's sensor is under a cyber attack, the control strategy can be switched in a timely manner. Although the overall following effect is slightly decreased compared with the situation without being under a cyber attack, it is significantly better than the situation without using elastic control. This shows that after using the elastic control algorithm, the impact of spoofing attacks on the multi-vehicle cooperative system can be significantly reduced, verifying the effectiveness of the elastic control algorithm.

[0282] If the above functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage medium includes: USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs and other various media that can store program codes.

[0283] Those skilled in the art should understand that the embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes. The solutions in the embodiments of the present invention can be implemented using various computer languages. For example, object-oriented programming languages such as Java and interpreted scripting languages such as JavaScript.

[0284] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, and combinations of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing device to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing device generate means for implementing the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0285] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a particular manner, such that the instructions stored in the computer-readable memory produce a manufacture including instruction means that implement the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0286] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0287] Although the preferred embodiments of the present invention have been described, additional changes and modifications can be made to these embodiments by those skilled in the art once they learn of the basic inventive concept. Therefore, the appended claims are intended to be construed to include the preferred embodiments as well as all changes and modifications that fall within the scope of the present invention.

[0288] Obviously, those skilled in the art can make various changes and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these modifications and variations.

Claims

1. An attack detection and resilient control method for a multi-vehicle cooperation system, characterized in that, It includes the following steps: Step 1, Initialization: Determine the initial state ellipsoid set ε0 of the multi-vehicle cooperative system and determine the initial shape matrices Q0 and R0 of the process noise and the measurement noise; Step 2, Prediction: At time t, based on the state ellipsoid set ε t and the shape matrix Q of the process noise t , optimize and solve the prediction ellipsoid set ε t+1|t through semi-definite programming; Step 3, Workshop communication attack detection: At time t, according to the predicted ellipsoid set ε t+1|t and the redundant state ellipsoid set judge whether the workshop communication is under attack. If not, execute Step 4 for measurement update. If so, execute Step 6 for resilient control; Step 4, Measurement Update: At time t+1, based on the predicted ellipsoid set ε t+1|t , the ego-vehicle sensor measurement value y t+1 and the shape matrix R of the measurement noise t+1 , the minimum ellipsoid set and the measurement update ellipsoid set ε t+1 are obtained by optimizing and solving the semi-definite programming; Step 5, Sensor Attack Detection: At time t+1, based on the predicted ellipsoid set ε t+1|t and the minimum ellipsoid set to determine whether the sensor is under attack by their intersection set. If the intersection set is empty, it means an attack has occurred, and proceed to Step 6 for resilient control. If the intersection set is not empty, it means no attack has occurred, and proceed to Step 2 for prediction at the next time instant; Step 6, Resilient control: According to the vehicle-to-vehicle communication attack response and the sensor attack response, replace the attacked ellipsoid sets respectively, and perform the measurement update and prediction process at the (t + 1)-th moment respectively; Step 7, Repeat execution: Repeat Steps 2 - 6 until the end to complete the attack detection and resilient control process.

2. The attack detection and elastic control method for a multi-vehicle cooperation system according to claim 1, characterized in that In step 2, the step of solving the prediction ellipsoid set ε t+1|t comprises: Considering the influence of the process noise and the measurement noise, construct the state equation of the follower vehicle i in the multi-vehicle cooperative system; According to the state ellipsoid set ε t surrounding the true state x of the following vehicle i at time t t and the state equation of the following vehicle i, the set is expressed as: In the formula, f is a nonlinear state function; Construct a semi-infinite programming problem to solve for the enclosing set of the minimum ellipsoidal set where the semi-infinite programming problem is expressed as: Among them, the set is defined as: where P and are the shape matrix and the center of the ellipsoid obtained for the optimization problem, y is the output, is the center of the ellipsoid set ε0, and P0 is the shape matrix of ε0; Solve the semi-infinite programming problem using the Frank-Wolfe algorithm to obtain the minimum ellipsoid set that encloses the set ​ Based on the set of minimum ellipsoids and the state equation of the following vehicle i, the predicted ellipsoid set ε t+1|t is obtained, and the expression is as follows: wherein, is the center of the prediction ellipsoid set ε t+1|t , P t+1|t is the shape matrix of the prediction ellipsoid set ε t+1|t , P t is the shape matrix of the state ellipsoid set ε t , E t+1|t is the lower triangular matrix obtained by Cholesky decomposition, satisfying P = EE T , η t+1|t is the free parameter vector.

3. The attack detection and resilience control method for a multi-vehicle cooperation system according to claim 2, characterized in that, The construction steps of the state equation of the follower vehicle i include: Construct the state equation of the nonlinear dynamics of the follower vehicle i in the multi-vehicle cooperative system, expressed as: where s i (t) and v i (t) represent position and velocity, Δt represents the discrete time interval, m i represents mass, η T,i represents the mechanical efficiency of the drive system, T i (t) represents the aggregated drive / braking torque, F i is the total resistance, u i (t) is the control input, τ i represents the inertia lag of longitudinal dynamics, C A，i represents the air resistance coefficient, r i represents the tire radius, g represents the gravitational constant; f i represents the rolling resistance coefficient; For the following vehicle i, its state vector is expressed as x i (t) = [s i (t), v i (t), T i (t)] T , and the output vector is expressed as y i (t) = [s i (t), v i (t)] T , and the state equation of Equation (1) is converted to: Among them, ψ i = [0, 0, (1 / τ i )Δt] T , φ i (x i (t)) is as follows: Considering the influence of the process noise and the measurement noise, transform the state equation of Equation (2) into: Among them, where \(f(x t ) = \varphi(x t )+\psi\cdot u t \) and \(h(x t )=\gamma\cdot x t \) are the state equation and the measurement equation respectively, \(\omega t \) and \(v t \) are the process noise and the measurement noise respectively, \(u t \) is the optimal control quantity at time \(t\) calculated by the distributed MPC algorithm, \(Q t \) is the shape matrix of \), \(R t \) is the shape matrix of \), and \) is the corresponding noise ellipsoid set.

4. The attack detection and elastic control method for a multi-vehicle cooperation system according to claim 2, characterized in that The step of obtaining the enclosed set of the minimum ellipsoid set includes: Input the number of sampling points m and the set According to the said set generate m sampling points y1, y2,..., y m , and let The Frank-Wolfe algorithm is used to solve the optimization problem to obtain the measure where the optimization problem is expressed as: Based on the said measure calculate P, where the calculation expressions are respectively: Based on P, obtain the set of minimum ellipsoids that enclose the set which is expressed as: In the formula, is 's center, is the lower triangular matrix obtained by Cholesky decomposition, is the free parameter vector, is 's shape matrix.

5. The attack detection and elastic control method for a multi-vehicle cooperation system according to claim 4, characterized in that The step of obtaining the predicted ellipsoid set ε t+1|t includes: Based on the set of minimum ellipsoids There exists Satisfying Convert the state equation to: where ω t is the process noise; According to the transformed state equation, obtain: In the formula, is the Minkowski sum; Calculate the external ellipsoid estimation of the enclosing Minkowski sum, and the calculation expression is: Among them, the optimal solution of p is p * , which is obtained from the following formula: where Q t is the shape matrix of the process noise ellipsoid set, and P t+1|t (p) is the predicted ellipsoid set ε t+1|t 's shape matrix; Based on the estimation results of the outer ellipsoid of the enclosed Minkowski sum, a set of predictive ellipsoids ε is obtained t+1|t .

6. The attack detection and resilience control method for a multi-vehicle cooperation system according to claim 4, wherein The steps of solving the optimization problem by using the Frank-Wolfe algorithm include: Let perform a first-order Taylor expansion of the function g(μ) at the current solution μ t , and we get: g(μ)≈g(μ t )+(ω t ) T (μ - μ t ) Among them, Input: Select an initial point μ 0 ∈ M; Iterative calculation: For t = 1, 2,..., T, perform the following steps: ①Calculation where, e i is a unit vector representing a vertex in the set M; ② Calculate d t : where d t is the direction vector; ③ Calculate γ t : where γ t is the step size; ④ Update μ t+1 : μ t+1 = μ t + γ t d t Output: Return μ T , denoted as 7. The attack detection and resilience control method for a multi-vehicle cooperation system according to claim 1, characterized in that, In Step 3, the steps of judging whether the vehicle-to-vehicle communication is attacked include: Determine the intersection set of the predicted ellipsoid set ε t+1|t and the redundant state ellipsoid set If the intersection set is empty, it indicates that the workshop communication is under attack. If it is not empty, it indicates that the workshop communication is not under attack; Among them, the step of determining whether the intersection of the predicted ellipsoid set ε t+1|t and the redundant state ellipsoid set is an empty set includes: Denote the set of predicted ellipsoids ε t+1|t and the set of redundant state ellipsoids as ε1 and ε2 respectively, and denote the corresponding centers as and respectively; denote the corresponding shape matrices as P1 and P2; If the true state x is both in ε1 and in ε2, then the intersection set of ε1 and ε2 must not be empty, and there must exist two vectors z1 and z2 such that the following formula (1) holds: If the intersection of ε1 and ε2 is an empty set, it is impossible to find vectors z1 and z2 such that the above equation (1) holds, indicating that to determine whether the intersection of ε t+1|t and is an empty set, it is necessary to determine whether there are feasible solutions z1 and z2 for the above equation (1). The steps for determining the feasible solutions include: Move the terms in the above formula (1) to get: The problem of solving the feasible solution of formula (2) is transformed into the solution of the following optimization problem to obtain ε t+1|t and The intersection set result, and the optimization problem is expressed as: where the matrices E1 and E2 are the matrices obtained by performing Cholesky decomposition on the shape matrices P1 and P2 respectively, and J a is the optimization objective function, and α, β ∈ (0, 1] are newly introduced elastic variables.

8. The attack detection and elastic control method for a multi-vehicle cooperation system according to claim 1, characterized in that In step 4, the set of minimum ellipsoids and the measurement update ellipsoid set ε t+1 The solution steps are as follows: Due to the continuity and invertibility of the measurement equation h, there exists a continuous inverse function h -1 , expressed as: h -1 (y t+1 -v t+1 ) = Tx t+1 where \(v\) t+1 is the measurement noise at time \(t + 1\), \(T\) is the projection matrix, \(x\) t+1 , \(y\) t+1 are the input and output vectors at time \(t + 1\); Based on the measurement value y at time t+1 t+1 and the set of measurement noise ellipsoids obtain a new set of state ellipsoids which is expressed as: Construct a semi-infinite programming problem, where the semi-infinite programming problem is expressed as: In the formula, is the shape matrix of the ellipsoid obtained from the optimization problem, and z t+1 is the feasible solution variable in Equation (1), is the center of the ellipsoid obtained from the optimization problem; Solve the semi-infinite programming problem to obtain the enclosing set of the minimum ellipsoid set wherein, based on the minimum ellipsoid set it is obtained that there exists satisfying: In the formula, is a lower triangular matrix obtained by Cholesky decomposition, is a free parameter vector; is included in the intersection of the predicted ellipsoid set ε t+1|t and the minimum ellipsoid set . By solving the minimum ellipsoid set of the intersection of ε t+1|t and , the measurement update ellipsoid set ε t+1 is obtained, which is expressed as: where, P t+1 is the shape matrix of ε t+1 , is the center of ε t+1 , E t+1 is the lower triangular matrix obtained by Cholesky decomposition, η t+1 is the free parameter vector.

9. The attack detection and resilience control method for a multi-vehicle cooperation system according to claim 8, characterized in that, Solve for the said ε through the following formula t+1|t and The set of minimum ellipsoids of the intersection set, the formula is: where P t+1 the variable ρ in the matrix t+1 the optimal ρ is obtained by solving the following optimization problem t+1 : min g(P t+1 ) s.t. 0 < ρ t+1 <1 where g is the optimization function, 0 < ρ t+1 < 1.

10. The attack detection and resilience control method for a multi-vehicle collaboration system according to claim 1, characterized in that, In Step 6, the steps of the resilient control include: (1) The vehicle-to-vehicle communication is attacked: Using the set of redundant state ellipsoids to replace the set of predicted ellipsoids ε t+1|t , so that the set of redundant state ellipsoids is used as the set of predicted ellipsoids at time t, and enter the measurement update process at time t+1; (2) The sensor is attacked: Using the predicted ellipsoid set ε t+1|t to replace the measurement update ellipsoid set ε t+1 , so that the predicted ellipsoid set ε t+1|t is used as the measurement update ellipsoid set at time t + 1, and the prediction process at time t + 1 is entered.

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