Automatic driving vehicle tracking safety control method under false data injection attack

Abstract

The invention discloses an automatic driving vehicle tracking safety control method under a false data injection attack, and the method comprises the following steps: building a system state space equation according to a vehicle tracking two-degree-of-freedom dynamics model, and designing an FDI model; collecting input and output data of a vehicle when the vehicle is not subjected to FDI attack, and training a recurrent neural network to describe a relation between automatic driving tracking input and output according to the input and output data; constructing an unknown input augmentation system according to the trained recurrent neural network model, and obtaining an unknown input observer gain by adopting a robust estimation method for estimating a system state and an attack signal; the estimated attack signal is used for feedforward compensation of the sliding mode controller, and the stability of the safety control system is verified according to the Lyapunov stability theorem. According to the method, the system state and the attack signal can be estimated, stable control over tracking of the automatic driving vehicle is achieved through feedforward compensation sliding mode control, and it is ensured that the vehicle can still run safely and reliably when attacked.

Description

Technical Field

[0001] The present invention relates to the field of autonomous driving technology, and in particular to a method for safely controlling the tracking of an autonomous driving vehicle under a false data injection attack. Background Art

[0002] As autonomous driving technology is booming, vehicle tracking, as a key link in the autonomous driving system, faces many challenges in terms of safety and reliability. With the increasing degree of vehicle networking, network security issues are becoming increasingly prominent, among which false data injection (FDI) attacks pose a serious threat to the tracking control of autonomous vehicles.

[0003] In recent years, a large number of studies have focused on the field of network security for autonomous driving. In terms of vehicle tracking, accurate sensor data is the basis for ensuring that the vehicle follows the predetermined trajectory. However, once attacked by FDI, these erroneous data may mislead the control system, causing the vehicle to deviate from the expected path and cause potential safety accidents. Traditional control methods often have limitations when dealing with such attacks. Existing research mainly focuses on the detection level of simple models. For example, Chinese patent CN112363456A discloses a vehicle data anomaly detection system that detects data anomalies by setting specific thresholds. However, this method can only achieve preliminary screening of anomalies and cannot accurately estimate false data. Therefore, it is difficult to effectively identify and respond to complex and changeable attack methods, and cannot provide strong support for subsequent control.

[0004] Recurrent neural networks (RNNs) have shown great potential in processing complex nonlinear relationships in vehicle dynamic systems due to their ability to process time series data. Some studies have begun to explore the application of RNNs in related fields such as vehicle state estimation. For example, Chinese patent CN113435023A provides a vehicle driving state prediction device and method based on a recurrent neural network, using RNN to estimate the vehicle driving state. However, there is still a large research gap in combining RNN to design an unknown input observer to estimate FDI attacks and apply it to vehicle tracking safety control. Summary of the invention

[0005] In response to the problems existing in the above-mentioned prior art, the present invention aims to provide a method for safely controlling the tracking of an autonomous driving vehicle under a false data injection attack, which can estimate the system state and the attack signal, and achieve stable control of the tracking of the autonomous driving vehicle through feedforward compensation sliding mode control, thereby ensuring that the vehicle can still operate safely and reliably when attacked.

[0006] To achieve the above object, the present invention proposes a method for tracking safety control of an autonomous vehicle under false data injection attacks, including the following steps: establishing a system state space equation according to the two-degree-of-freedom dynamics model of vehicle tracking, and designing an FDI model; collecting the input and output data of the vehicle when it is not under FDI attacks, and training a recurrent neural network with this data to characterize the relationship between the input and output of autonomous vehicle tracking; constructing an augmented system with unknown inputs according to the trained recurrent neural network model, and using a robust estimation method to obtain the gain of the unknown input observer for estimating the system state and attack signals; using the estimated attack signals for the feedforward compensation of the sliding mode controller, and verifying the stability of the safety control system according to the Lyapunov stability theorem to achieve stable control performance of the vehicle tracking system of the autonomous vehicle under FDI attacks.

[0007] In the above solution, the method for tracking safety control of an autonomous vehicle under false data injection attacks specifically includes the following steps:

[0008] Step 1, establishing a system state space equation according to the two-degree-of-freedom dynamics model of vehicle tracking, obtaining matrix parameters, and thus designing an FDI model;

[0009] Step 1.1, applying Newton's second law in the y-axis direction of the vehicle body to establish the formula:

[0010]

[0011] where m is the vehicle mass, is the lateral force of the ground on the front wheels, is the lateral force of the ground on the rear wheels; a y is the lateral acceleration at the vehicle's center of mass;

[0012]

[0013] where, is the acceleration generated by the vehicle's lateral movement along the y-axis of the vehicle body, a n is the centripetal acceleration generated by the vehicle's yaw movement, is the yaw rate of the vehicle, v x is the vehicle's x-axis speed, so:

[0014]

[0015] Step 1.2, establishing the torque balance equation of the vehicle around the z-axis:

[0016]

[0017] where I z is the moment of inertia of the vehicle around the z-axis, is the vehicle's yaw angular acceleration, l y is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, ΔM z is the additional yaw moment of the vehicle;

[0018] Step 1.3, establish the expressions for the sideslip angles of the front and rear wheels:

[0019]

[0020] where δ is the steering angle of the vehicle's front wheels, θ vf is the angle between the direction of the front wheel speed of the vehicle and the x-axis, θ vr is the angle between the direction of the rear wheel speed of the vehicle and the x-axis;

[0021] Step 1.4, establish the expressions for the lateral tire forces of the front and rear wheels:

[0022]

[0023] where C αf is the cornering stiffness of the vehicle's front wheels, C αr is the cornering stiffness of the vehicle's rear wheels;

[0024] Step 1.5, consider the vehicle's center of mass to the wheels as a rigid body, and according to rigid body kinematics, we get:

[0025]

[0026] where v y is the vehicle's y-axis speed;

[0027] Step 1.6, taking the lateral position y, the lateral position change rate the vehicle's yaw angle the vehicle's yaw angle change rate as state variables, according to the formula in Step 1.1, the lateral position change rate is obtained as:

[0028]

[0029] According to the formula in Step 1.2, the vehicle's yaw angle change rate is obtained as:

[0030]

[0031] Therefore, the state space equation of the vehicle's two-degree-of-freedom dynamic model is expressed as:

[0032]

[0033] Step 2, through the lateral displacement error e 1 of the vehicle state variable and the yaw angle error e 2, establish the state equation of the vehicle tracking error model;

[0034] Step 2.1, the yaw angle error e 2 and the change rate of the yaw angle error are:

[0035]

[0036] where, is the vehicle yaw angle, is the road yaw angle;

[0037] Step 2.2, the lateral acceleration deviation is:

[0038]

[0039] Integrating the above equation gives:

[0040]

[0041] Step 2.3, taking the lateral position error e 1 between the vehicle and the road, the change rate of the lateral position error the yaw angle error e 2 and the change rate of the yaw angle error as state variables, then the change rate of the lateral position error is:

[0042]

[0043] The change rate of the yaw angle error is:

[0044]

[0045] Step 2.4, ignoring Regarding as the system disturbance, ρ is the road curvature, and the final error state equation is:

[0046]

[0047] Step 2.5, matrixize the state space equation, let:

[0048]

[0049] where the state space equation is:

[0050]

[0051] where:

[0052]

[0053] Step 3: Design a residual detector to verify that the designed FDI model can avoid the detector;

[0054] Step 3.1: Design a detector based on the residual and establish the following discrete linear system:

[0055]

[0056] where A k = AT + I, B k = BT, T is the simulation step size, I is the identity matrix. Assume that the system noise ω(k) and the measurement noise v(k) are both Gaussian white noises. The covariance of ω(k) is Q, and the covariance of v(k) is R, i.e., ω(k) ~ N(0, Q), v(k) ~ N(0, R);

[0057] Step 3.2: Calculate the prior estimate according to the system state equation:

[0058]

[0059] Step 3.3: Obtain the update equation of the Kalman filter as follows:

[0060]

[0061] where the Kalman gain matrix is as follows:

[0062] K(k) = P(k|k - 1)C T [CP(k|k - 1)C - + R]-1 -1

[0063] In the formula, P(k|k - 1) is the prior state estimation error covariance matrix, and its expression is as follows:

[0064] P(k|k - 1) = AP(k - 1|k - 1)AT T + Q

[0065] Step 3.4: Finally, update the posterior state estimation error covariance matrix:

[0066] P(k|k) = (I - K(k)C)P(k|k - 1)

[0067] In the above formula, the Kalman gain K(k) will converge in several recursive steps. Therefore, K can be defined as:

[0068]

[0069] where Therefore, the Kalman filter can be simplified to the following estimator with a fixed gain:

[0070]

[0071] Step 3.5, define the residual z(k) as:

[0072]

[0073] From the above equation, the covariance matrix of the residual can be obtained:

[0074]

[0075] Therefore, the obtained residual z(k) is Gaussian white noise with a mean of 0 and a covariance of S, i.e., z(k) ~ N(0, S);

[0076] Step 3.6, deploy a residual-based X 2 detector in the controller to detect signal anomalies. The detection function is as follows:

[0077] g(k) = z T (k)S -1 z(k)

[0078] where g(k) follows a chi-square distribution. For a specified threshold Ψ, if g(k) > Ψ, the residual detector will trigger an alarm indicating an anomaly;

[0079] Step 3.7, design an FDI attack based on the system state-space equation obtained in Step 2 and prove that it can avoid the detection of the residual detector. Based on the discrete linear system in Step 3.1, assume that the attacker can read the data transmitted through the feedback channel and does not consider network latency and packet loss. When the sensor is under FDI attack, the dynamic equation of the system is expressed as:

[0080]

[0081] where x a (k), u a (k), y a (k) are the state variables, system input, and system output of the system under FDI attack, respectively. Then the sensor measurement value finally reaching the controller end becomes:

[0082]

[0083] where ∧ = diag{λ 1 , λ 2 , ···, λ n} is the attack coefficient matrix, and λ i = 1 indicates that the i-th sensor measurement value is under attack, and α(k) is the designed attack signal;

[0084] Step 3.8, when the feedback channel of the network system is under attack α(k), the system residual becomes:

[0085]

[0086] Step 3.9, at this time the test function becomes:

[0087]

[0088] where

[0089]

[0090] Step 3.10, the attack sequence α(k) is designed as:

[0091]

[0092] where ξ(k) is a random sequence generated by the attacker, ξ(k) ~ N(0, S);

[0093] Step 3.11, is the state estimate obtained by using false sensors and is thus called the false state estimate, and its calculation is as follows:

[0094]

[0095] Step 3.12, if all sensors are attacked, then the sensor measurement values after the attack become

[0096]

[0097] Then the system residual under the FDI attack is:

[0098]

[0099] Step 3.13, so z a (k) ~ N(0, S), then the residual detector is as follows:

[0100]

[0101] Satisfying g a (k) ≤ Ψ, so the designed FDI attack can evade the test of the χ 2 detector;

[0102] Step 4, establish an unknown input observer based on a recurrent neural network model;

[0103] Step 4.1: By offline training a recurrent neural network model, obtain the weight matrices required in the state space equation, use the weights to describe the dynamic behavior of vehicle path tracking, and finally convert the recurrent neural network model into a discrete-time state space equation. The recurrent neural network model is expressed as:

[0104] From the input layer to the hidden layer:

[0105] h t =f(W ih x t +b ih +W hh h t-1 +b hh )

[0106] From the hidden layer to the output layer:

[0107] y t =W y h t +b y

[0108] where h t is the hidden state at the current moment, x t is the current input, y t is the output, b ih is the bias with respect to x t , W ih is the weight matrix from the input layer to the hidden layer, b hh is the bias of the previous hidden state, W hh is the weight matrix from the hidden layer to the hidden layer, f is the activation function, which is tanh, W y is the weight matrix from the hidden layer to the output layer, b y is the bias of the output layer;

[0109] Step 4.2: Train the recurrent neural network based on Carsim data. Given a series of vehicle path tracking conditions, use the PID algorithm inside Carsim for path tracking, import the input data and output data of the vehicle into Excel, and shuffle their order to improve performance and reduce the data requirements. After collecting the data, perform data processing to generate the input tensor X and output tensor Y for training;

[0110] Step 4.3: Edit the pseudocode for defining the recurrent neural network model to implement the definition of the recurrent neural network model;

[0111] Step 4.4: Based on the input tensor X and output tensor Y in Step 4.2, edit the pseudocode for training the recurrent neural network model to implement the training of the recurrent neural network model;

[0112] Step 4.5, training the recurrent neural network model based on the vehicle tracking condition, and constructing the state space equation:

[0113]

[0114] y = C R x

[0115] where A R is the weight from the linear part hidden layer to the hidden layer, B R is the weight from the input layer to the hidden layer, σ is the activation function tanh, A 0 is the output weight of the activation function, E 0 is the input weight of the activation function, C R is the output layer weight;

[0116] Step 4.6, linearize σ(E 0 x) using the mean value theorem for differentials. For a non-linear function g(x) that is continuously differentiable on a certain interval, it can be linearly approximated at a certain point b, and the approximation form is:

[0117] σ(E 0 x) = σ(b) + M b (E 0 x - b)

[0118] where, M b represents the gradient matrix of the activation function at the operating point. At this operating point b, take the input value of the previous moment:

[0119] b = E 0 x(k - 1)

[0120] The calculation of M b is as follows:

[0121]

[0122] where each term is the partial derivative of the activation function at the operating point b. For a multi-variable activation function, use the matrix form to expand the Jacobian matrix:

[0123]

[0124] where e j,l is the matrix parameter;

[0125] The final linearization result is:

[0126] σ(E 0 x) ≈ Mx + d

[0127] where M = M b E 0 and d = σ(E0 x(k - 1)) - M b E 0 x(k - 1)

[0128] The final state - space equation becomes:

[0129]

[0130] y = C R x

[0131] Step 4.7, establish an unknown - input observer based on the model trained by the recurrent neural network. To estimate the FDI attack designed in Step 3.10, expand the state - space model of the recurrent neural network:

[0132]

[0133] Assume that the second - order derivative of the attack α is 0, and assume that the second - order derivative of the attack signal is 0. The new system model is as follows:

[0134]

[0135] where d can be regarded as the perturbation of the system;

[0136] Step 4.8, to estimate the above - augmented system, the UIO system is designed as:

[0137]

[0138] where z is the state vector of the UIO system, is the estimated augmented state vector, and F, T, H, and K u are matrices of parameters to be determined. K u = K 1 + K 2 , increasing the degree of freedom of K u , and reducing the difficulty of selecting F;

[0139] Step 4.9, define Substitute the above state - space equation to get:

[0140]

[0141] Step 4.10, take the derivative of e to obtain:

[0142]

[0143] Step 4.11, if the UIO parameter - related matrices satisfy

[0144]

[0145] That is

[0146]

[0147] Then can be replaced by:

[0148]

[0149] Step 4.12, define the Lyapunov function of the state vector error e as:

[0150] V(e) = e T Pe

[0151] The derivative of V(e) is:

[0152]

[0153] Where

[0154] Step 4.13, to ensure system stability and limit the influence of disturbances on the error, combined with the negative definiteness of the derivative of the Lyapunov function, construct a linear matrix inequality expression;

[0155] For the augmented system in Step 4.7, if there exist a positive definite matrix P, square matrices N and Q, then:

[0156]

[0157] Step 4.14, within the framework of the Lyapunov function, the influence of the disturbance on the error satisfies:

[0158] ‖e‖ 2 ≤ r 2 ‖d‖ 2

[0159] Where r is the energy coefficient, d is the system disturbance in Step 4.6, and e is the estimation error in Step 4.9;

[0160] Step 4.15, according to the Schur complement lemma, if there exist matrices P, N, and Q that satisfy Step 4.13, then Therefore it can be deduced that without the influence of disturbances prove that the observation system is stable;

[0161] Step 4.16, if there are disturbances, the error energy can also be limited within a certain range. Let:

[0162] Φ = ∫ 0 t (e Te - r 2 d T d / dt

[0163] By introducing

[0164]

[0165] where Ω is the linear matrix in step 4.13;

[0166] Step 4.17, since If Ω < 0, then Φ < 0, which can prove that the inequality in step 4.14 holds, and at the same time, it can also prove that the derivative of the Lyapunov function is negative definite, that is, the system is stable;

[0167] Step 4.18, solve the matrices P, N, and Q through the LMI toolbox provided by Matlab, and obtain the relevant gain matrices H and K of the observer in step 4.11 1 , and finally obtain the designed matrices F, T, H, and K u ;

[0168]

[0169] Step 4.19, according to the matrices F, T, H, and K designed in step 4.11 u the estimated augmented state vector of the UIO can be obtained and design the following form of estimated state correction method:

[0170]

[0171] where is the finally estimated augmented state vector, L is the feedback gain matrix, is the estimated output vector derived from , expressed as:

[0172]

[0173] Step 4.20, the estimated state variable and the sensor attack signal are generated in the following way:

[0174]

[0175] Step 5, based on the FDI attack estimated in step 4, establish a feedforward sliding mode controller;

[0176] Step 5.1, design the feedforward error fusion function e m :

[0177]

[0178] where e 1a is the lateral displacement deviation after being attacked, and e 2a is the heading angle deviation after being attacked;

[0179] Step 5.2, obtain the error fusion function e according to the state space equation established in Step 1 m :

[0180]

[0181] where a i , b i , d i (i = 1, 2, …) are the matrix parameters of the state space equation in Step 2.4;

[0182] Step 5.3, the error state equation is:

[0183]

[0184] Let That is:

[0185] Step 5.4, design the sliding surface:

[0186]

[0187] where λ is the gain parameter. Take the derivative of the sliding mode function with respect to the system state to obtain:

[0188]

[0189] Step 5.5, design the reaching law function:

[0190]

[0191] Obtain the control law:

[0192]

[0193] In the formula, ε 1 and ε 2 are positive numbers. ε 1 determines the reaching speed of the reaching mode, and ε 2 determines the convergence speed of the sliding mode converging to the equilibrium point. sat(s) is the saturation function, expressed as:

[0194]

[0195] where s 0 (s 0 > 0) is the saturation boundary constant;

[0196] Step 5.6, Stability analysis of the control system, construct the following Lyapunov function:

[0197]

[0198] where s is the sliding mode surface designed in Step 5.4, and the first derivative of the Lyapunov function can be expressed as:

[0199]

[0200] Step 5.7, Substitute the saturation function to obtain:

[0201]

[0202] Therefore, when s≠0 always holds. According to the Lyapunov stability criterion, the sliding mode exists and is reachable, and the control system is asymptotically stable.

[0203] The beneficial effects of the present invention are as follows:

[0204] 1. Verified by the Matlab-Carsim co-simulation, the results show that the present invention can effectively estimate and compensate for FDI attacks, enabling the lateral error and heading angle error of the vehicle to quickly converge to zero. That is, the present invention improves the safety and reliability of the path tracking system of autonomous vehicles, can accurately estimate the FDI attack signal, and compensate in a timely manner. 2. The present invention realizes the modeling and control of complex nonlinear systems, can enhance the anti-interference ability against FDI attacks, and models the vehicle path tracking system through an RNN model, which can better capture the dynamic characteristics of the system. 3. In the present invention, the feedforward sliding mode controller can quickly suppress the influence of FDI attacks on the system performance, improve the vehicle path tracking accuracy, and make the lateral error and heading angle error quickly converge. Description of the Drawings

[0205] Figure 1 is the structure diagram of the vehicle path tracking safety control strategy under false data injection attack.

[0206] Figure 2 is the two-degree-of-freedom dynamic model diagram of the vehicle.

[0207] Figure 3 is the vehicle path tracking error model diagram.

[0208] Figure 4 is the structure diagram of the recurrent neural network.

[0209] Figure 5 is the lateral error diagram without feedforward compensation.

[0210] Figure 6It is the heading error graph without feedforward compensation.

[0211] Figure 7 It is the lateral error graph with feedforward compensation.

[0212] Figure 8 It is the heading error graph with feedforward compensation.

[0213] Figure 9 It is the false data injection attack graph estimated by RNN-UIO.

[0214] Figure 10 It is the false data injection attack graph estimated by UIO. Specific implementation manners

[0215] As Figure 1 —shown in Figure 10, a method for tracking safety control of an autonomous vehicle under false data injection attack mainly consists of the following steps:

[0216] Step 1, establish the system state space equation according to the two-degree-of-freedom dynamic model of vehicle tracking, obtain the matrix parameters, and thus design the FDI model.

[0217] Step 1.1, apply Newton's second law in the y-axis direction of the vehicle body to establish the formula:

[0218]

[0219] Among them, m is the vehicle mass, is the lateral ground force received by the front wheels, is the lateral ground force received by the rear wheels; a y is the lateral acceleration at the vehicle's center of mass;

[0220]

[0221] Among them, is the acceleration generated by the vehicle's lateral movement along the y-axis of the vehicle body, a n is the centripetal acceleration generated by the vehicle body's yaw movement, is the vehicle's yaw angle change rate, v x is the vehicle's x-axis speed, so:

[0222]

[0223] Step 1.2, establish the torque balance equation of the vehicle around the z-axis:

[0224]

[0225] Among them, I z is the moment of inertia of the vehicle around the z-axis, is the vehicle's yaw angular acceleration, ly is the distance from the centroid to the front axle, l r is the distance from the centroid to the rear axle, ΔM z is the additional yaw moment of the vehicle.

[0226] Step 1.3, establish the expressions for the front and rear wheel sideslip angles:

[0227]

[0228] where δ is the front wheel steering angle of the vehicle, θ vf is the angle between the front wheel speed direction of the vehicle and the x-axis, θ vr is the angle between the rear wheel speed direction of the vehicle and the x-axis.

[0229] Step 1.4, establish the expressions for the front and rear wheel lateral tire forces:

[0230]

[0231] where C αf is the front wheel sideslip angle stiffness of the vehicle, C αr is the rear wheel sideslip angle stiffness of the vehicle.

[0232] Step 1.5, consider the distance from the vehicle centroid to the wheels as a rigid body, and according to rigid body kinematics, we get:

[0233]

[0234] where v y is the vehicle speed in the y-axis direction.

[0235] Step 1.6, taking the lateral position y, the lateral position change rate the vehicle yaw angle the vehicle yaw angle change rate as state variables, according to the formula in Step 1.1, the lateral position change rate is obtained as:

[0236]

[0237] According to the formula in Step 1.2, the vehicle yaw angle change rate is obtained as:

[0238]

[0239] Therefore, the state space equation of the vehicle two-degree-of-freedom dynamics model is expressed as:

[0240]

[0241] Step 2, establish the state equation of the vehicle tracking error model through the lateral displacement error e 1 and the yaw angle error e 2 of the vehicle state variables.

[0242] Step 2.1, the yaw angle error e 2 and the change rate of the yaw angle error are:

[0243]

[0244] where, is the vehicle yaw angle, is the road yaw angle.

[0245] Step 2.2, the lateral acceleration deviation is:

[0246]

[0247] Integrating the above equation gives:

[0248]

[0249] Step 2.3, taking the vehicle-road lateral position error e 1 , the change rate of the lateral position error , the yaw angle error e 2 , and the change rate of the yaw angle error as state variables, then the change rate of the lateral position error is:

[0250]

[0251] The change rate of the yaw angle error is:

[0252]

[0253] Step 2.4, can be ignored ( is the derivative of ), regarded as system disturbance, ρ is the road curvature, and the final error state equation is:

[0254]

[0255] Step 2.5, matrixize the state space equation, let:

[0256]

[0257] where the state space equation is:

[0258]

[0259] where:

[0260]

[0261] Step 3: Design a residual detector to verify that the designed FDI model can avoid the detector.

[0262] Step 3.1: Design a detector based on the residual and establish the following discrete linear system:

[0263]

[0264] where A k = AT + I, B k = BT, T is the simulation step size, I is the identity matrix. Assume that the system noise ω(k) and the measurement noise v(k) are both Gaussian white noises. The covariance of ω(k) is Q, and the covariance of v(k) is R, that is, ω(k) ~ N(0, Q), v(k) ~ N(0, R).

[0265] Step 3.2: Calculate the prior estimate according to the system state equation:

[0266]

[0267] Step 3.3: Obtain the following update equation of the Kalman filter:

[0268]

[0269] where the Kalman gain matrix is as follows:

[0270] K(k) = P(k|k - 1)C T [CP(k|k - 1)C T + R] -1

[0271] In the formula, P(k|k - 1) is the prior state estimation error covariance matrix, and its expression is as follows:

[0272] P(k|k - 1) = AP(k - 1|k - 1)A T + Q

[0273] Step 3.4: Finally, update the posterior state estimation error covariance matrix:

[0274] P(k|k) = (I - K(k)C)P(k|k - 1)

[0275] Although the Kalman gain K(k) in the above formula changes with time, it usually converges in several recursive steps. Therefore, K can be defined as:

[0276]

[0277] where Therefore, the Kalman filter can be simplified to the following estimator with a fixed gain:

[0278]

[0279] Step 3.5, define the residual z(k) as:

[0280]

[0281] From the above equation, the covariance matrix of the residual can be obtained:

[0282]

[0283] Therefore, the obtained residual z(k) is Gaussian white noise with a mean of 0 and a covariance of S, i.e., z(k) ∼ N(0, S).

[0284] Step 3.6, in order to detect signal anomalies, a χ 2 detector based on the residual is usually deployed in the controller, and the detection function is as follows:

[0285] g(k) = z T (k)S -1 z(k)

[0286] where g(k) follows a chi-square distribution. For a specified threshold Ψ, if g(k) > Ψ, the residual detector will trigger an alarm, indicating that an anomaly has occurred.

[0287] Step 3.7, design an FDI attack according to the system state-space equation obtained in Step 2 and prove that it can avoid the detection of the residual detector. Considering the discrete linear system in Step 3.1, assume that the attacker can read the data transmitted through the feedback channel, and network delay and packet loss are not considered. Under the condition that the sensor is under FDI attack, the dynamic equation of the system is expressed as:

[0288]

[0289] where, x a (k), u a (k), y a (k) are the state variables, system input, and system output of the system under FDI attack, respectively. Then the sensor measurement value finally reaching the controller side becomes:

[0290]

[0291] where ∧ = diag{λ 1 , λ 2 , ···, λ n} is the attack coefficient matrix, and λ i = 1 indicates that the i-th sensor measurement value is under attack, and α(k) is the designed attack signal.

[0292] Step 3.8, when the network system feedback channel is under attack α(k), the system residual becomes:

[0293]

[0294] Step 3.9, at this time the test function becomes:

[0295]

[0296] where

[0297]

[0298] Step 3.10, compared with when there is no attack in Step 3.6, there are more terms. From this, it can be seen that when the sensor is under attack, the test function may exceed the threshold ψ. Therefore, the residual-based detector can detect general feedback channel FDI attacks. From the above analysis, to achieve the concealment of FDI attacks, the attack sequence α(k) is designed as:

[0299]

[0300] where ξ(k) is a random sequence generated by the attacker, and ξ(k) ~ N(0, S).

[0301] Step 3.11, is the state estimate obtained by using the false sensor measurement , so it is called the false state estimate, and its calculation is as follows:

[0302]

[0303] Step 3.12, if all sensors are under attack, the sensor measurement value after the attack becomes

[0304]

[0305] Then the system residual under FDI attack is:

[0306]

[0307] Step 3.13, therefore z a (k) ~ N(0, S), then the residual detector is as follows:

[0308]

[0309] Satisfying g a (k) ≤ Ψ, so the designed FDI attack can avoid the test of the χ 2 detector.

[0310] Step 4: Establish an unknown input observer based on the recurrent neural network model.

[0311] Step 4.1: First, train the recurrent neural network model offline to obtain the weight matrices required in the state space equation. These weights are used to describe the dynamic behavior of vehicle path tracking. Finally, the recurrent neural network model is transformed into a discrete-time state space equation. First, establish the recurrent neural network model. As shown in Figure 4, it is the RNN network structure, which is expressed by the following formula:

[0312] From the input layer to the hidden layer:

[0313] h t = f(W ih x t + b ih + W hh h t-1 + b hh )

[0314] From the hidden layer to the output layer:

[0315] y t = W y h t + b y

[0316] where h t is the hidden state at the current moment; x t is the current input; y t is the output; b ih is the bias with respect to x t ; W ih is the weight matrix from the input layer to the hidden layer; b hh is the bias of the previous hidden state; W hh is the weight matrix from the hidden layer to the hidden layer (recursive part); f is the activation function, usually tanh or ReLU. Here, tanh is used as the activation function; W y is the weight matrix from the hidden layer to the output layer; b y is the bias of the output layer.

[0317] Step 4.2: Train the recurrent neural network based on Carsim data. Given a series of vehicle path tracking conditions, use the PID algorithm inside Carsim for path tracking. Import the input data (front wheel angle and additional yaw moment) and output data (lateral error, heading angle error, lateral error change rate, and heading angle error change rate) of the vehicle into Excel, and shuffle their order to improve performance and reduce the data requirements. After collecting the data, perform data processing to generate the input tensor X and output tensor Y for training;

[0318] The following is the pseudocode:

[0319]

[0320]

[0321] Step 4.3, edit the pseudo-code for the definition of the recurrent neural network model to implement the definition of the recurrent neural network model;

[0322] The following is the pseudo-code for the model definition:

[0323]

[0324] Step 4.4, based on the input tensor X and output tensor Y in Step 4.2, edit the pseudo-code for the training of the recurrent neural network model to implement the training of the recurrent neural network model;

[0325] The pseudo-code is as follows:

[0326]

[0327]

[0328] Step 4.5, train the recurrent neural network model based on the vehicle tracking working condition to construct the state space equation:

[0329]

[0330] y = C R x

[0331] where A R is the weight from the hidden layer to the hidden layer of the linear part, B R is the weight from the input layer to the hidden layer, σ is the activation function tanh, A 0 is the output weight of the activation function, E 0 is the input weight of the activation function, and C R is the output layer weight.

[0332] Step 4.6, linearize σ(E 0 x) using the mean value theorem for differentials. For a non-linear function g(x) that is continuously differentiable on a certain interval, it can be linearly approximated at a certain point b, and the approximate form is:

[0333] σ(E 0 x) = σ(b) + M b (E 0 x - b)

[0334] where M b represents the gradient matrix of the activation function at the operating point. At this operating point, b takes the input value of the previous moment:

[0335] b = E 0 x(k - 1)

[0336] M b is calculated as follows:

[0337]

[0338] where each term is the partial derivative of the activation function at the operating point b. For a multi - variable activation function, the Jacobian matrix is extended in matrix form:

[0339]

[0340] where e j,l is the matrix parameter;

[0341] The final linearized result is:

[0342] σ(E 0 x) ≈ Mx + d

[0343] where M = M b E 0 , d = σ(E 0 x(k - 1)) - M b E 0 x(k - 1)

[0344] The final state - space equation becomes:

[0345]

[0346] y = C R x

[0347] Step 4.7, establish an unknown - input observer according to the model trained by the recurrent neural network. To estimate the FDI attack designed in step 3.10, expand the state - space model of the recurrent neural network:

[0348]

[0349] Assume that the second - order derivative of the attack α is 0, assume that the second - order derivative of the attack signal is 0, and the new system model is as follows:

[0350]

[0351] where d can be regarded as the perturbation of the system;

[0352] Step 4.8, to estimate the above - augmented system, the UIO system is designed as:

[0353]

[0354] where z is the state vector of the UIO system, is the estimated augmented state vector, and F, T, H, and K u are parameter-related matrices to be determined, and K u = K 1 + K 2 , increasing the degree of freedom of K u and reducing the difficulty of selecting F.

[0355] Step 4.9, define Substituting the above spatial equation gives:

[0356]

[0357] Step 4.10, differentiating e gives:

[0358]

[0359] Step 4.11, if the UIO parameter-related matrix satisfies

[0360]

[0361] i.e.,

[0362]

[0363] then can be replaced by:

[0364]

[0365] Step 4.12, define the Lyapunov function of the state vector error e as:

[0366] V(e) = e T Pe

[0367] The derivative of V(e) is:

[0368]

[0369] where

[0370] Step 4.13, to ensure system stability and limit the influence of disturbances on the error, combined with the negative definiteness of the derivative of the Lyapunov function, construct a linear matrix inequality expression;

[0371] For the augmented system in Step 4.7, if there exist positive definite matrices P, square matrices N, and Q, then:

[0372]

[0373] Step 4.14, within the framework of the Lyapunov function, the influence of the perturbation on the error satisfies:

[0374] ‖e‖ 2 ≤r 2 ‖d‖ 2

[0375] where r is the energy coefficient, d is the system perturbation in Step 4.6, and e is the estimation error in Step 4.9;

[0376] Step 4.15, according to the Schur complement lemma, if there exist matrices P, N, and Q that satisfy Step 4.13, then Therefore it can be deduced that without the influence of the perturbation to prove that the observation system is stable.

[0377] Step 4.16, if there is a perturbation, the error energy can also be limited within a certain range. Let:

[0378]

[0379] By introducing

[0380]

[0381] where Ω is the linear matrix in Step 4.13.

[0382] Step 4.17, since if Ω < 0, then Φ < 0, then it can be proved that the inequality in Step 4.14 holds, and at the same time, it can also be proved that the derivative of the Lyapunov function is negative definite, that is, the system is stable.

[0383] Step 4.18, solve the matrices P, N, and Q through the LMI toolbox in Matlab, and obtain the relevant gain matrices H and K of the observer in Step 4.11 1 , and finally obtain the designed matrices F, T, H, and K u ;

[0384]

[0385] Step 4.19, according to the matrices F, T, H, and K designed in Step 4.11 u the estimated augmented state vector of the UIO can be obtained However, the estimated error of the augmented system state is not accurate enough. To further weaken the influence from the residual perturbation, an estimated state correction method in the following form is designed:

[0386]

[0387] where is the augmented state vector of the final estimate, and L is the feedback gain matrix, is the estimated output vector derived from

[0388]

[0389] Step 4.20, the estimated state variable and the sensor attack signal are generated by the following method:

[0390]

[0391] Step 5, based on the FDI attack estimated in Step 4, establish a feedforward sliding mode controller.

[0392] Step 5.1, design the feedforward error fusion function e m :

[0393]

[0394] where e 1a is the lateral displacement deviation after being attacked, and e 2a is the heading angle deviation after being attacked.

[0395] Step 5.2, according to the state space equation established in Step 1, find the error fusion function e m :

[0396]

[0397] where a i , b i , d i (i = 1, 2, …) are the matrix parameters of the state space equation in Step 2.4.

[0398] Step 5.3, the error state equation is:

[0399]

[0400] Let That is:

[0401] Step 5.4, design the sliding mode surface:

[0402]

[0403] where λ is the gain parameter. Differentiating the sliding mode function with respect to the system state gives:

[0404]

[0405] Step 5.5, Selecting a suitable reaching law can effectively suppress system chattering and improve the dynamic response quality of the sliding mode motion. The reaching law can make the system state quickly tend to equilibrium and effectively suppress system chattering. In addition, a saturation function is used in the reaching law to replace the traditional sign function to ensure continuous change of the control quantity and further suppress system chattering. Therefore, the reaching law function is designed as follows:

[0406]

[0407] Obtain the control law:

[0408]

[0409] In the formula, ε 1 and ε 2 are positive numbers. ε 1 determines the reaching speed of the reaching mode, and ε 2 determines the convergence speed of the sliding mode converging to the equilibrium point. sat(s) is the saturation function, expressed as:

[0410]

[0411] where s 0 (s 0 >0) is the saturation boundary constant.

[0412] Step 5.6, Analyze the stability of the control system and construct the following Lyapunov function:

[0413]

[0414] where s is the sliding mode surface designed in Step 5.4. The first derivative of the Lyapunov function can be expressed as:

[0415]

[0416] Step 5.7, Substitute the saturation function to obtain:

[0417]

[0418] Therefore, when s≠0 always holds. According to the Lyapunov stability criterion, the sliding mode exists and is reachable, and the control system is asymptotically stable.

[0419] Figure 5 、 Figure 6 are the lateral error and the heading angle error without feedforward compensation respectively, Figure 7 、 Figure 8 are the lateral error and the heading angle error with feedforward compensation respectively,Figure 9 and Figure 10 It shows the comparison diagram of the FDI attack estimated by the RNN-UIO and the UIO. As can be seen from the above figure, under the condition of road curvature (4-6 s), the estimation attack accuracy of the present invention is high, and the proposed feedforward sliding mode control can make the state variables converge when under attack (7-9 s).

Claims

1. A method for controlling the tracking safety of an autonomous driving vehicle under a false data injection attack, characterized in that: The following steps are involved: The system state space equation is established based on the vehicle tracking two-degree-of-freedom dynamics model, and the FDI model is designed; The input and output data of the vehicle when it is not attacked by FDI are collected to train the recurrent neural network, which is used to characterize the relationship between the input and output of the autonomous driving tracking system. Based on the trained recurrent neural network model, an unknown input augmented system is constructed, and the unknown input observer gain is obtained by the robust estimation method, which is used to estimate the system state and attack signal. The estimated attack signal is used for feedforward compensation of the sliding mode controller, and the stability of the safety control system is verified according to the Lyapunov stability theorem, so that the autonomous driving vehicle tracking system can maintain stable control performance when it is attacked by FDI.

2. The method for controlling the tracking safety of an autonomous driving vehicle under a false data injection attack according to claim 1, characterized in that: The specific steps include: Step 1: Establish the system state space equation according to the vehicle tracking two-degree-of-freedom dynamics model, obtain the matrix parameters, and then design the FDI model; Step 1.1, apply Newton's second law in the y-axis direction of the vehicle body and establish the formula: Where m is the mass of the vehicle, is the lateral ground force on the front wheels, is the lateral ground force on the rear wheels; a y is the lateral acceleration at the center of mass of the vehicle; in, is the acceleration generated by the lateral motion of the vehicle along the y-axis, a n is the centripetal acceleration caused by the yaw motion of the vehicle body, is the vehicle yaw angle change rate, v x is the vehicle's x-axis speed, so: Step 1.2, establish the torque balance equation of the vehicle around the z-axis: Among them, I z is the moment of inertia of the vehicle around the z-axis, is the vehicle yaw angular acceleration, l y is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, ΔM z Adding yaw moment to the vehicle; Step 1.3, establish the expression of front and rear wheel slip angle: Among them, δ is the front wheel steering angle of the vehicle, θ vf is the angle between the vehicle's front wheel speed direction and the x-axis, θ vr is the angle between the vehicle's rear wheel speed direction and the x-axis; Step 1.4, establish the expression of the lateral tire force of the front and rear wheels: Among them, C αf is the vehicle front wheel slip angle stiffness, C αr is the rear wheel slip angle stiffness of the vehicle; Step 1.5, consider the vehicle center of mass to the wheels as a rigid body, and obtain the following according to rigid body kinematics: Among them, v y is the vehicle y-axis speed; Step 1.6, using the lateral position y and the lateral position change rate Vehicle yaw angle Vehicle yaw rate of change As a state quantity, according to the formula in step 1.1, the lateral position change rate is obtained: According to the formula in step 1.2, the vehicle yaw angle change rate is: Therefore, the state space equation of the vehicle two-degree-of-freedom dynamics model is expressed as: Step 2, establishing the state equation of the vehicle tracking error model through the lateral displacement error e1 and the yaw angle error e2 of the vehicle state variables; Step 2.1, yaw angle error e2 and yaw angle error change rate for: in, is the vehicle yaw angle, is the road yaw angle; Step 2.2, the lateral acceleration deviation is: Integrating the above formula gives: Step 2.3: Take the lateral position error between the vehicle and the road e1 and the lateral position error change rate Yaw angle error e2, yaw angle error change rate As a state variable, the lateral position error change rate is: The yaw angle error change rate is: Step 2.4, ignore Will As the system disturbance, ρ is the road curvature, and the final error state equation is: Step 2.5, matrix the state space equation, let: The state space equation is: in: Step 3: Design a residual detector to verify that the designed FDI model can evade the detector; Step 3.1, residual-based detector design, establish the following discrete linear system: Among them A k =AT+I,B k =BT, T is the simulation step size, I is the unit matrix, assuming that the system noise ω(k) and the measurement noise v(k) are both Gaussian white noise, the covariance of ω(k) is Q, and the covariance of v(k) is R, that is, ω(k)~N(0,Q), v(k)~N(0,R); Step 3.2, calculate the prior estimate based on the system state equation: Step 3.3, the update equation of Kalman filter is as follows: The Kalman gain matrix is ​​as follows: K(k)=P(k|k-1)C T [CP(k|k-1)C T +R] -1 Where P(k|k-1) is the prior state estimation error covariance matrix, expressed as follows: P(k|k-1)=AP(k-1|k-1)A T +Q Step 3.4, finally update the posterior state estimation error covariance matrix: P(k|k)=(IK(k)C)P(k|k-1) In the above formula, the Kalman gain K(k) will converge in several recursive steps, so K can be defined as: in Therefore, the Kalman filter can be simplified to the following estimator with fixed gain: Step 3.5, define the residual z(k) as: From the above formula, we can get the covariance matrix of the residual: Therefore, the residual z(k) is a Gaussian white noise with a mean of 0 and a covariance of S, that is, z(k)~N(0,S); Step 3.6, deploy the residual-based χ in the controller 2 Detector, to detect signal anomalies, the detection function is as follows: g(k)=z T (k)S -1 z(k) Where g(k) follows a chi-square distribution. For a specified threshold Ψ, if g(k)>Ψ, the residual detector will trigger an alarm, indicating an abnormality. Step 3.7, design the FDI attack based on the system state space equation obtained in step 2, and prove that it can evade the detection of the residual detector. According to the discrete linear system in step 3.1, assume that the attacker can read the data transmitted by the feedback channel, and do not consider network delay and packet loss. When the sensor is attacked by FDI, the dynamic equation of the system is expressed as: where x a (k) and u a (k), y a (k) are the state variables, system input and system output of the system under FDI attack, and the sensor measurement value finally reaching the controller becomes: where ∧=diag{λ1,λ2,···,λ n } is the attack coefficient matrix, λ i =1 means that the measurement value of the i-th sensor is attacked, and α(k) is the designed attack signal; Step 3.8, when the feedback channel of the network system is attacked by α(k), the system residual becomes: Step 3.9, the test function becomes: in Step 3.10, the attack sequence α(k) is designed as: Where ξ(k) is a random sequence generated by the attacker, ξ(k)~N(0,S); Step 3.11, To measure using a fake sensor The obtained state estimate, hence called the pseudo-state estimate, is calculated as follows: Step 3.12: If all sensors are attacked, the sensor measurement value after the attack becomes Then the system residual under FDI attack is: Step 3.13, so z a (k)~N(0,S), then the residual detector is as follows: Satisfy a (k)≤Ψ, so the designed FDI attack can avoid χ 2 Inspection of detectors; Step 4, establishing an unknown input observer based on the recurrent neural network model; Step 4.1, by offline training the recurrent neural network model, the weight matrix required in the state space equation is obtained, the weight is used to describe the dynamic behavior of vehicle tracking, and finally the recurrent neural network model is converted into a discrete time state space equation; the recurrent neural network model is expressed as: Input layer to hidden layer: h t =f(W ih x t +b ih +W hh h t-1 +b hh ) Hidden layer to output layer: y t =W y n t +b y Among them, h t is the hidden state at the current moment, x t is the current input, y t is the output, b ih It's about x t Bias, W ih is the weight matrix from the input layer to the hidden layer, b hh is the bias of the previous hidden state, W hh is the weight matrix from hidden layer to hidden layer, f is the activation function, which is tanh, W y is the weight matrix from the hidden layer to the output layer, b y is the bias of the output layer; Step 4.2, train the recurrent neural network based on Carsim data. Given a series of vehicle tracking conditions, use the PID algorithm inside Carsim to track the vehicle. Import the vehicle input data and output data into Excel and shuffle their order to improve performance and reduce the demand for data. After collecting the data, perform data processing to generate the input tensor X and output tensor Y for training. Step 4.3, edit the recurrent neural network model definition pseudocode to implement the recurrent neural network model definition; Step 4.4, based on the input tensor X and the output tensor Y in step 4.2, edit the recurrent neural network model training pseudo code to implement the recurrent neural network model training; Step 4.5, train the recurrent neural network model based on the vehicle tracking condition and construct the state space equation: y=C R x Among them A R is the weight from hidden layer to hidden layer in the linear part, B R is the weight from the input layer to the hidden layer, σ is the activation function tanh, A0 is the activation function output weight, E0 is the activation function input weight, C R is the output layer weight; Step 4.6, use the differential mean value theorem to linearize σ(E0x). For a nonlinear function g(x) that is continuously differentiable in a certain interval, a linear approximation can be made at a certain point b. The approximate form is: σ(E0x)=σ(b)+M b (E0x-b) Among them, M b Represents the gradient matrix of the activation function at the working point, where b takes the input value of the previous moment: b=E0x(k-1) M b The calculation of is as follows: Each of these is the partial derivative of the activation function at the working point b. For multivariate activation functions, the Jacobian matrix is ​​expanded in matrix form: where e j,l is the matrix parameter; The final linearization result is: σ(E0x)≈Mx+d where M = M b E0, d = σ(E0x(k - 1)) - M b E0x(k - 1) The final state space equation becomes: y=C R x Step 4.7, establish an unknown input observer based on the model trained by the recurrent neural network. To estimate the FDI attack designed in step 3.10, expand the recurrent neural network state space model: Assuming that the second-order derivative of the attack α is 0, assuming that the second-order derivative of the attack signal is 0, the new system model is as follows: in d can be regarded as a disturbance of the system; Step 4.8, to estimate the above augmented system, the UIO system is designed as: Where z is the state vector of the UIO system, is the estimated augmented state vector, F, T, H and K u is the parameter correlation matrix to be determined, K u =K1+K2, increase K u degrees of freedom, reducing the difficulty of choosing F; Step 4.9, Definition Substituting the above space equation into the equation: Step 4.10, take the derivative of e and get: Step 4.11, if the UIO parameter correlation matrix satisfies Right now but Can be replaced by: Step 4.12, define the Lyapunov function of the state vector error e as: V(e)=e T On The derivative of V(e) is: in Step 4.13, to ensure the stability of the system and limit the influence of disturbance on the error, the linear matrix inequality expression is constructed by combining the negative definiteness of the derivative of the Lyapunov function; For the augmented system in step 4.7, if there exist positive definite matrices P, square matrices N and Q, then: Step 4.14, within the framework of the Lyapunov function, the effect of the disturbance on the error satisfies: ‖e‖ 2 ≤r 2 ‖d‖ 2 Where r is the energy coefficient, d is the system disturbance in step 4.6, and e is the estimation error in step 4.9; Step 4.15, according to Schur's complement lemma, if there exist matrices P, N, and Q that satisfy step 4.13, then therefore It can be deduced that in the absence of disturbance Prove that the observing system is stable; Step 4.16, if there is disturbance, the error energy can also be limited to a certain range, let: Φ=∫0 t (e T e-r 2 d T d)dt By introducing Where Ω is the linear matrix in step 4.13; Step 4.17, due to If Ω<0, then Φ<0, which proves that the inequality in step 4.14 holds, and it can also prove that the derivative of the Lyapunov function is negative definite, that is, the system is stable; Step 4.18, solve the matrices P, N and Q through the LMI toolbox provided by Matlab, and obtain the relevant gain matrices H and K1 of the observer in step 4.11, and finally obtain the designed matrices F, T, H and K u ; Step 4.19, according to the matrices F, T, H and K designed in step 4.11 u The estimated augmented state vector of UIO can be obtained And design the estimated state correction method in the following form: in is the final estimated augmented state vector, L is the feedback gain matrix, Is The derived estimated output vector is expressed as: Step 4.20, estimated state variables and sensor attack signals Generated by: Step 5, establish a feedforward sliding mode controller based on the FDI attack estimated in step 4; Step 5.1, design the feedforward error fusion function e m : where e 1a is the lateral displacement deviation after the attack, e 2a is the heading angle deviation after being attacked; Step 5.2: Calculate the error fusion function e according to the state space equation established in step 1 m : where a i ,b i , d i (i=1,2…) is the matrix parameter of the state space equation in step 2.4; Step 5.3, the error state equation is: make Right now: Step 5.4, design sliding surface: Where λ is the gain parameter, and the derivative of the sliding mode function along the system state is: Step 5.5, design the reaching law function: Find the control rate: In the formula, ε1 and ε2 are positive numbers, ε1 determines the approach speed of the approaching mode, ε2 determines the convergence speed of the sliding mode to the equilibrium point, and sat(s) is the saturation function, which is expressed as: Where s0 (s0>0) is the saturation boundary constant; Step 5.6, control system stability analysis, construct the following Lyapunov function: Where s is the sliding surface designed in step 5.4, and the first-order derivative of the Lyapunov function can be expressed as: Step 5.7, substituting the saturation function into the equation yields: Therefore, when s≠0 According to the Lyapunov stability criterion, the sliding mode exists and is reachable, and the control system is asymptotically stable.

Images