An event-triggered control method for vehicle platoon under denial-of-service attack

Abstract

The present application relates to a kind of event triggered control method of vehicle queue under denial of service attack, and the method content includes the following steps: establishing vehicle queue model with parameter uncertainty;Vehicle queue communication relationship is characterized based on graph theory knowledge and DoS attack model is established;Design event-based distributed event triggered controller.The method of the present application is based on the distributed event triggered controller designed based on the vehicle queue model with parameter uncertainty established and DoS attack model, the flexibility to DoS attack and the robustness of parameter uncertainty are realized, solve the vehicle queue control problem in the prior art for the existence of DoS attack, limited communication resources and parameter uncertainty.

Description

Technical fields:

[0001] This invention belongs to the field of intelligent vehicle safety and autonomous driving, and specifically relates to an event-triggered control method for vehicle queues under denial-of-service attacks. Background technology:

[0002] Intelligent vehicles, which perceive their surroundings and perform cooperative behaviors through onboard sensors and inter-vehicle communication, are considered a revolutionary force in transportation systems. Based on vehicle self-organizing networks / vehicle-to-everything (V2X) networks, vehicle platoons composed of highly autonomous and information-exchange-capable intelligent vehicles exhibit natural cooperative advantages, enabling advanced multi-vehicle cooperative driving modes such as platooning. This effectively increases road capacity and alleviates the ever-increasing traffic congestion in modern cities. Numerous studies and applications have demonstrated that vehicle platooning can significantly improve road safety, traffic flow, and fuel efficiency.

[0003] While data exchange based on vehicular ad hoc networks / vehicle-to-everything (V2X) networks can improve vehicle platoon control performance, the openness and vulnerability of wireless communication networks also present two key problems: First, malicious attackers may launch denial-of-service (DoS) attacks by interfering with radio frequencies or overwhelming vehicle-to-vehicle communications with excessive requests to disrupt intended control objectives. Second, due to the scarcity of wireless spectrum resources, the bandwidth capacity of vehicular ad hoc networks / vehicle-to-everything (V2X) networks limits the quantity and quality of data transmission between vehicles. Furthermore, during vehicle platoon control, varying driving conditions introduce uncertainty into the vehicle engine time constant parameter. All of these factors can affect vehicle platoon control performance and even lead to traffic accidents. Summary of the Invention:

[0004] The purpose of this invention is to address the vehicle queue control problems in existing technologies, particularly those involving DoS attacks, limited communication resources, and parameter uncertainties. It proposes an event-triggered control method for vehicle queues under DoS attacks. Based on the designed distributed event-triggered controller, it achieves resilience against DoS attacks and robustness against parameter uncertainties, while conserving communication resources.

[0005] The technical solution of this invention is: an event-triggered control method for vehicle queues under a denial-of-service attack, the method comprising the following steps:

[0006] Step 1: Establish a vehicle queue model with parameter uncertainty.

[0007] Step 2: Represent the communication relationships of the vehicle queue based on graph theory knowledge and establish a DoS attack model.

[0008] Step 3: Design an event-based distributed event triggering controller.

[0009] Furthermore, the process of establishing the vehicle queuing model with parameter uncertainty is as follows:

[0010] Considering that the vehicle platoon is operating under different driving conditions, utilizing Using the reciprocal of the vehicle engine time constant, a dynamic model of a vehicle convoy with parametric uncertainties is established as follows:

[0011] Lead vehicle 0:

[0012] Following vehicle i: in, The parameter is the reciprocal of the nominal engine time constant. The uncertainty parameter is the reciprocal of the vehicle engine time constant. For the nominal system matrix, Here is the system uncertainty matrix. For the nominal input matrix, As the input uncertainty matrix, u i (t)∈R 3 For the control input to follow vehicle i, x0(t) = [p0(t), v0(t), a0(t)] T ∈R 3 ,x i (t)=[p i (t),v i (t),a i (t)] T ∈R 3 Let each represent a state vector containing position p, velocity v, and acceleration a for the leading vehicle 0 and the following vehicle i, respectively.

[0013] Furthermore, the method of representing the communication relationships of vehicle queues based on graph theory knowledge and establishing a DoS attack model is as follows:

[0014] First, the communication relationships of the vehicle queue are represented based on graph theory:

[0015] Represent the communication relationships of N following vehicles as a directed graph. in, Represents the group of vehicles following. Let (i,j) represent the set of edges that establish communication relationships between following vehicles, where (i,j) represents the directed edge from vehicle i to vehicle j. Represents the adjacency matrix in graph theory, if Then a ij =1, otherwise a ij =0; directed graph Laplace matrix in, in, diag{} is a diagonal matrix formed by the elements within {}; the communication relationship between the lead vehicle 0 and the N following vehicles is represented as a directed graph. use describe The algebraic characteristics of H, where H = diag{h1,h2,…,h N If the following vehicle i can receive information from the lead vehicle, then h i =1, otherwise h i =0, matrix The real eigenvalues ​​are represented as λ i The real part of the conjugate complex eigenvalue is represented by λ. i +λ i * .

[0016] Secondly, establish a DoS attack model:

[0017] A DoS attack can intermittently disrupt communication between all vehicles, using A c =a c ∪[a c ,a c +h c ) represents the interval of the c-th attack, where a c ,a c +h c These represent the attack initiation and termination times, respectively. The attack activity and dormancy intervals within the time range [t1, t2) are represented as follows:

[0018] The total number of attacks is expressed as Limitations are given on the length of the attack range and the number of attacks:

[0019] Attack range length:

[0020] Number of attacks:

[0021] Considering the limited attack energy, D1>0,T1>0 are the limiting parameters for the attack interval length and the number of attacks, and D2>1,T2>0 are the regularization parameters that make the attack valid.

[0022] Furthermore, the design is based on an event-triggered controller:

[0023]

[0024] Where K∈R 3 Indicates the controller gain, l i,j=[(ij)*l,0,0] T Let l represent the expected inter-vehicle distance between vehicle i and vehicle j, and l represent the specified inter-vehicle distance. The open-loop estimator expression is:

[0025]

[0026] in, This indicates the k-th trigger sampling time for vehicle i. This represents the state estimate.

[0027]

[0028] Where inf is the maximum infimum. Let $\frac{i}{i}$ be the tracking error of the neighboring vehicles of vehicle $i$. Let β1 and β2 be the state estimation error of vehicle i, and θ be the threshold parameters. i (t) is an internal dynamic variable, θ i The derivative of (t) satisfies the expression:

[0029]

[0030] in, η i ≥0,

[0031] Furthermore, the present invention also includes establishing a vehicle tracking error system model and proving the robust stability of the tracking error system, as follows.

[0032] First, define e i (t)=x i (t)-x0(t)-l i,0 For vehicle i, establish a tracking error system model:

[0033]

[0034] Where, e(t)=[e1(t) T ,e2(t) T ,…,e N (t) T ] T ∈R 3N Let ε(t) be the row vector augmented form of the vehicle tracking error, where ε1(t) = [ε1(t)]. T ,ε2(t) T ,…,ε N (t) T ] T ∈R 3N This represents the row vector augmented form of the vehicle state estimation error. Indicates the Kronecker product. When, make u i (t)=0,

[0035] Secondly, prove the robust stability of the tracking error system:

[0036] Solve for: Controller gain That is, to solve in, The maximum value of the uncertainty parameter, which is the reciprocal of the vehicle engine time constant, is given by P > 0, α > 0, and 0 < μ ≤ λ. i +λ i *;

[0037] Limitation parameters for attack range length:

[0038] Attack count limit parameter: in, φ is the gain that satisfies P < φQ and Q < φP;

[0039] Construct the Lyapunov function as follows:

[0040] in,

[0041] exist In this context, the derivative of V1(t) is:

[0042]

[0043] Where α = α1 + α2, and ψ is a relaxation parameter, such that and

[0044] exist In this context, the derivative of V(t) is:

[0045]

[0046] exist In this context, the derivative of V(t) is:

[0047]

[0048] Throughout the entire time period:

[0049]

[0050] in, The tracking error system is robust and stable.

[0051] Compared with the prior art, the present invention has the following advantages:

[0052] 1. Taking into account the collaborative control problem of connected vehicle fleets under DoS attack, the duration and number of attacks were analyzed in conjunction with the stability proof of the vehicle tracking error system, achieving resilience against DoS attack.

[0053] 2. Considering the limited network bandwidth capacity required for data exchange in vehicle ad hoc networks / vehicle networks, an event-based distributed event triggering controller was designed. This controller reduces the number of triggers while ensuring system stability and saving communication resources.

[0054] 3. The modeling process of the vehicle platoon takes into account the parameter uncertainty of the vehicle under different driving conditions, and the proposed controller design method is robust to parameter uncertainty. Attached image description:

[0055] Figure 1 This is a block diagram of the distributed event triggering control in an embodiment of the present invention;

[0056] Figure 2 A flowchart illustrating the steps of an event-triggered control method for vehicle queues under a denial-of-service attack, provided by the present invention; Detailed implementation method:

[0057] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0058] This invention provides an event-triggered control method for vehicle queues under denial-of-service attacks. Figure 2 This invention provides a flowchart of an event-triggered control method for vehicle queues under a denial-of-service attack. Specifically, it includes the following steps:

[0059] Step 1, considering that the vehicle convoy is operating under different driving conditions, utilize... Using the reciprocal of the vehicle engine time constant, a dynamic model of a vehicle convoy with parametric uncertainties is established as follows:

[0060] Lead vehicle 0:

[0061] Following vehicle i: in, The parameter is the reciprocal of the nominal engine time constant. The uncertainty parameter is the reciprocal of the vehicle engine time constant. For the nominal system matrix, Here is the system uncertainty matrix. For the nominal input matrix, As the input uncertainty matrix, u i(t)∈R 3 For the control input to follow vehicle i, x0(t) = [p0(t), v0(t), a0(t)] T ∈R 3 ,x i (t)=[p i (t),v i (t),a i (t)] T ∈R 3 Let each represent a state vector containing position p, velocity v, and acceleration a for the leading vehicle 0 and the following vehicle i, respectively.

[0062] Step 2: Represent the communication relationships of the vehicle queue based on graph theory and establish a DoS attack model:

[0063] First, the communication relationships of the vehicle queue are represented based on graph theory:

[0064] Represent the communication relationships of N following vehicles as a directed graph. in, Represents the group of vehicles following. Let (i,j) represent the set of edges that establish communication relationships between following vehicles, where (i,j) represents the directed edge from vehicle i to vehicle j. Represents the adjacency matrix in graph theory, if Then a ij =1, otherwise a ij =0; directed graph Laplace matrix in, in, diag{} is a diagonal matrix formed by the elements within {}; the communication relationship between the lead vehicle 0 and the N following vehicles is represented as a directed graph. use describe The algebraic characteristics of H, where H = diag{h1,h2,…,h N If the following vehicle i can receive information from the lead vehicle, then h i =1, otherwise h i =0, matrix The real eigenvalues ​​are represented as λ i The real part of the conjugate complex eigenvalue is represented by λ. i +λ i * .

[0065] Secondly, establish a DoS attack model:

[0066] DoS attacks can intermittently disrupt communication between all vehicles, using A c =a c∪[a c ,a c +h c ) represents the interval of the c-th attack, where a c ,a c +h c Let represent the attack initiation and termination times, and represent the attack activity and dormancy intervals within the time range [t1, t2).

[0067] The total number of attacks is expressed as Limitations are given on the length of the attack range and the number of attacks:

[0068] Attack range length:

[0069] Number of attacks:

[0070] Considering the limited attack energy, D1>0,T1>0 are the limiting parameters for the attack interval length and the number of attacks, and D2>1,T2>0 are the regularization parameters that make the attack valid.

[0071] Step 3, design an event-based distributed event triggering controller:

[0072]

[0073] Figure 1 This is a distributed event triggering control block diagram in an embodiment of the present invention, where K∈R 3 Indicates the controller gain, l i,j =[(ij)*l,0,0] T Let l represent the expected inter-vehicle distance between vehicle i and vehicle j, and l represent the specified inter-vehicle distance. The open-loop estimator expression is:

[0074]

[0075] in, This indicates the k-th trigger sampling time for vehicle i. This represents the state estimate.

[0076]

[0077] Where inf is the maximum infimum. Let $\frac{i}{i}$ be the tracking error of the neighboring vehicles of vehicle $i$. Let β1 and β2 be the state estimation error of vehicle i, and θ be the threshold parameters. i (t) is an internal dynamic variable, θ i The derivative of (t) satisfies the expression:

[0078]

[0079] in, η i ≥0,

[0080] Step 4: Establish a tracking error system model and prove the robust stability of the tracking error system.

[0081] First, define e i (t)=x i (t)-x0(t)-l i,0 For vehicle i, establish a tracking error system model:

[0082]

[0083] Where, e(t)=[e1(t) T ,e2(t) T ,…,e N (t) T ] T ∈R 3N Let ε(t) be the row vector augmented form of the vehicle tracking error, where ε1(t) = [ε1(t)]. T ,ε2(t) T ,…,ε N (t) T ] T ∈R 3N This represents the row vector augmented form of the vehicle state estimation error. Indicates the Kronecker product. When, make u i (t)=0,

[0084] Secondly, prove the robust stability of the tracking error system:

[0085] Solve for: Controller gain That is, to solve in, P > 0, α > 0, 0 < μ ≤ λ i +λ i * ;

[0086] Limitation parameters for attack range length:

[0087] Attack count limit parameter: in, φ is the gain that satisfies P < φQ and Q < φP;

[0088] Construct the Lyapunov function as follows:

[0089] in,

[0090] exist In this context, the derivative of V1(t) is:

[0091]

[0092] Where α = α1 + α2, and ψ is a relaxation parameter, such that and

[0093] exist In this context, the derivative of V(t) is:

[0094]

[0095] exist In this context, the derivative of V(t) is:

[0096]

[0097] Throughout the entire time period:

[0098]

[0099] in, The tracking error system is robust and stable.

Claims

1. An event-triggered control method for vehicle queues under a denial-of-service attack, characterized in that, Includes the following steps: Step 1: Establish a vehicle queuing model with parameter uncertainty, as follows: Considering that the vehicle platoon is operating under different driving conditions, utilizing Using the reciprocal of the vehicle engine time constant, a dynamic model of a vehicle convoy with parametric uncertainties is established as follows: Lead vehicle : Following vehicle : in, The parameter is the reciprocal of the nominal engine time constant. The uncertainty parameter is the reciprocal of the vehicle engine time constant. For the nominal system matrix, Here is the system uncertainty matrix. For the nominal input matrix, To input the uncertainty matrix, To follow the vehicle The control input, These represent the lead vehicle. With following vehicles Includes location ,speed and acceleration The state vector; Step 2: Represent the communication relationships of the vehicle queue based on graph theory and establish a DoS attack model, as follows: First, the communication relationships of the vehicle queue are represented based on graph theory: Will The communication relationship between following vehicles can be represented as a directed graph. ,in, Represents the group of vehicles following. This represents the set of edges that establish communication relationships between following vehicles. Representative vehicle To the vehicle The directed edge, Represents the adjacency matrix in graph theory, if but ,otherwise Directed graph Laplace matrix ,in, ,in, , For The elements within form a diagonal matrix; the leading vehicle and The communication relationship between following vehicles can be represented as a directed graph. ,use describe The algebraic characteristics of which, If following the vehicle If it can receive information from the lead vehicle, then ,otherwise matrix The real eigenvalues ​​are represented as The real part of the eigenvalue of the conjugate complex number is represented as ; Secondly, establish a DoS attack model: A DoS attack can intermittently disrupt communication between all vehicles, using Indicates the first The range of the second attack, in which... These represent the start and end times of the attack, respectively. The attack activity and dormancy intervals in the data are represented as follows: The total number of attacks is expressed as The attack range length and the number of attacks are given as constraints: Attack range length: Number of attacks: Considering the limited attack energy, among which, These are the limiting parameters for the attack range length and the number of attacks. Regularization parameters required for the attack to succeed; Step 3: Design an event-based distributed event triggering controller, as follows: in, Indicates controller gain. Indicates vehicle With vehicles Expected workshop distance Given the specified workshop distance, the open-loop estimator expression is: in, Indicates vehicle The The next sampling time. This represents the state estimate; in, For the maximum lower bound, For vehicles Neighbor vehicle tracking error, For vehicles The state estimation error, For threshold parameters, For internal dynamic variables, The derivative satisfies the expression: in, .

2. The event-triggered control method for vehicle queues under a denial-of-service attack according to claim 1, characterized in that, This also includes establishing a vehicle error system model and proving the robust stability of the tracking error system, using the following methods: First, define For vehicles The tracking error was determined and a vehicle tracking error system model was established: in, This represents the row vector augmented form of the vehicle tracking error. This represents the row vector augmented form of the vehicle state estimation error. Indicates the Kronecker product. At that time, ; Secondly, prove the robust stability of the tracking error system: Solve for: Controller gain That is, to solve in, , This represents the maximum value of the uncertainty parameter, which is the reciprocal of the vehicle engine time constant. ; Limitation parameters for attack range length: Attack count limit parameter: in, In order to make Satisfactory gain; Construct the Lyapunov function as follows: in, ; exist middle, The derivative is: in, Let be the relaxation parameter, such that and ; exist middle, The derivative is: exist middle, The derivative is: Throughout the entire time period: in, The tracking error system is robust and stable.

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