Intelligent electric vehicle platoon control method for defending denial of service network attack

Abstract

The application discloses an intelligent electric vehicle platoon control method for defending against denial of service network attacks, and belongs to the field of automobile intelligent safety and automatic driving. For the vehicle platoon control problem of DoS attacks and external disturbances, the vehicle-mounted sensor and the V2X wireless communication system are utilized to realize information interaction of the self and other vehicles, the inverse model compensation and feedback linearization technology are adopted, the vehicle queue closed-loop control model with external disturbances is established, and a switching queue robust control method for defending against DoS attacks based on an observer model is designed. A switching controller which only depends on relative output information for updating is designed for the longitudinal queue system of the electric vehicle, so that the information transmission hidden danger of the queue system caused by the Dos attack is effectively defended against, the external disturbance is inhibited, and the performance index of the platoon control is realized. The stability of the queue system is realized, and the expected vehicle-to-vehicle distance and the expected driving speed of each vehicle in the queue are ensured.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent automobile safety and autonomous driving, and in particular relates to a method for controlling a formation of intelligent electric vehicles for defending against denial-of-service network attacks. Background Art

[0002] As the number of vehicles on the road increases, traffic congestion and the resulting road accidents are becoming increasingly serious. This not only increases travel costs and risks, but also increases energy consumption due to frequent vehicle starts and stops. As a key branch of intelligent transportation systems, intelligent electric vehicle platooning technology can effectively alleviate this energy waste and has great potential for solving road congestion and traffic accident problems.

[0003] Intelligent electric vehicle platoon control technology refers to the process in which each vehicle in a longitudinal queue adjusts its own driving posture in real time based on the driving information sent by other vehicles, thereby ensuring that adjacent vehicles have the desired spacing and a speed consistent with the lead vehicle. Reference 1 (L. Zuo, P. Wang and M. Yan, et al. Platoon Tracking Control With Road-Friction Based Spacing Policy for Nonlinear Vehicles [J]. IEEE Transactions on Intelligent Transportation Systems, 2022, 23 (11): 20810-20819.) proposes a nonlinear intelligent electric vehicle platoon control method for driving conditions considering road friction coefficients. Reference 2 (Y. Zheng, M. Xu and S. Wu, et al. Development of Connected and Automated Vehicle Platoons With Combined Spacing Policy [J]. IEEE Transactions on Intelligent Transportation Systems, 2023, 24 (1): 596-614.) proposes a distributed control method for vehicle platoons based on a hybrid spacing strategy.

[0004] In open communication networks, the information transmission channels of smart electric vehicle platoons can be interrupted by denial of service (DoS) attacks, thus affecting information delivery. Furthermore, due to factors such as changes in vehicle characteristics and environmental disturbances, external interference is inevitable during vehicle operation. These factors can undermine the stability of the platooning system and cause traffic accidents. Summary of the Invention

[0005] The purpose of this invention is to address the existing problem of vehicle platooning control in the presence of DoS attacks and external interference, by providing a method for intelligent electric vehicle platooning control that protects against denial-of-service network attacks. Based on a designed state error observer, a switching controller is designed for the electric vehicle longitudinal platoon system that relies solely on relative output information for updates. This effectively protects the platoon system from information transmission risks posed by DoS attacks, while simultaneously suppressing external interference and achieving the performance indicators of platooning control.

[0006] The present invention comprises the following steps:

[0007] Step 1: A platoon consists of N+1 vehicles, numbered 0,…,N. Vehicle 0 is the lead vehicle, and vehicles 1,…,N are the following vehicles. Vehicle-to-vehicle sensors and the V2X wireless communication network collect real-time information about the vehicle's motion state and the output information from the preceding and lead vehicles.

[0008] The first step is to use on-board sensors and GPS to perceive the vehicle's status information in real time, that is, to determine the location, measure the driving speed and acceleration, and calculate the vehicle's output information;

[0009] In the second step, the ego vehicle exchanges information with the pilot vehicle and other following vehicles in the platoon through the V2X wireless communication network, receives the corresponding vehicle output information in real time, and broadcasts the ego vehicle's output information.

[0010] Step 2: Design a linearized dynamic model for a single vehicle. Utilize information from onboard sensors and the V2X wireless communication network to establish a single-vehicle longitudinal control model with external disturbances.

[0011] The first step is to derive the nonlinear longitudinal dynamics expression of a single vehicle using Newton's second law. Feedback linearization is then performed based on inverse model compensation technology to obtain the linearized longitudinal dynamics model of the single vehicle.

[0012] In the second step, the position, velocity, and acceleration information of the ego vehicle are used as the state vector, and the external interference term of the system is considered to establish the longitudinal motion model of a single vehicle;

[0013] Step 3: Based on graph theory knowledge, characterize the structure of the queue system communication topology and give the considered DoS attack model;

[0014] The first step is to use graph theory knowledge to describe the communication topology of the queue system;

[0015] The second step is to propose a DoS attack model and provide two important descriptive indicators: attack frequency and attack length ratio;

[0016] Step 4: Design an error observer model and establish a vehicle platoon switching safety controller under DoS attacks and external interference to calculate the wheel motor driving torque required for platoon control in real time.

[0017] The first step is to establish an error observer and design sub-controllers for normal communication and under attack respectively. These sub-controllers are then substituted into the formation model to establish a closed-loop error control system for the vehicle platoon consisting of two subsystems.

[0018] The second step is to establish the objective function of the intelligent electric vehicle platoon control based on the constructed platoon closed-loop error system;

[0019] In the third step, based on Lyapunov stability theory and linear matrix inequality method, the conditions for achieving stability of the queue closed-loop error system by the switching safety control protocol are given, and the design method of the controller gain matrix is ​​obtained;

[0020] The fourth step is to substitute the safety controller into the single-vehicle longitudinal control model in step 2, calculate the expected driving torque of the vehicle wheels in real time, and realize the formation control of smart electric vehicles.

[0021] This paper utilizes on-board sensors and a V2X wireless communication system to enable information exchange between the vehicle itself and other vehicles. It employs inverse model compensation and feedback linearization techniques to establish a closed-loop control model for vehicle platooning with external interference. It also designs a robust switching platoon control method based on an observer model to protect against DoS attacks. It also proposes a switching safety control protocol based solely on relative output information to achieve platoon system stability and ensure the desired inter-vehicle spacing and speed for each vehicle in the platoon. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is a schematic diagram of a smart electric vehicle formation control system under a DoS attack according to the present invention.

[0023] Figure 2 This is a schematic diagram of the communication topology changes of a smart electric vehicle formation under a DoS attack according to the present invention.

[0024] Figure 3 This is a flowchart of a bicycle internal switching control system for defending against DoS attacks according to the present invention.

[0025] Figure 4 This is a queue communication topology diagram under the influence of a DoS attack according to the present invention.

[0026] Figure 5 This is a simulation result diagram of the queue system control under the influence of DoS attack according to the present invention. DETAILED DESCRIPTION

[0027] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the following embodiments will be further described in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0028] like Figure 1 As shown in Figure 1, consider a smart electric vehicle platoon consisting of one pilot vehicle and N following vehicles. In an open communication network, the information transmitted between vehicles is based on the communication module (including the V2X wireless communication network, sensor measurement, and broadcast). This channel may be intercepted by external DoS attacks, thereby affecting the transmission of information. At the same time, due to factors such as changes in vehicle characteristics and environmental disturbances, the vehicle's perception module will inevitably be subject to external interference during driving. i (t). Under the condition of limited energy, the effective time period of DoS attack can be divided into the communication interruption time due to the attack and the normal communication time. During the communication interruption time, the vehicle cannot send or receive information. Based on the state error observer, this design designs a switching control scheme (including safety controller and feedback controller) to generate control signals, thereby achieving the stability of the vehicle platoon system under the presence of DoS attacks and external interference. Figure 2 As shown in Figure 1, under a DoS attack, the vehicle platoon communication topology changes randomly. It can be seen that when φ(t) = 1 and φ(t) = 2, vehicle 1 and vehicle N-1 are attacked respectively. Figure 3 As shown in the figure, this design aims at the vehicle longitudinal platooning system under external interference and DoS attack. Based on the error observer, a switching safety control scheme is designed to achieve the stability of the vehicle platoon system.

[0029] The embodiment of the present invention specifically includes the following steps:

[0030] Step 1: A platoon consists of N+1 vehicles, numbered 0,…,N. Vehicle 0 is the lead vehicle, and vehicles 1,…,N are the following vehicles. Vehicle-to-vehicle sensors and the V2X wireless communication network provide real-time information on the ego vehicle's motion status, as well as output from the leading and lead vehicles.

[0031] Step 1.1: Use on-board sensors and GPS to measure the vehicle's driving status information in real time, including distance, speed, and acceleration, and calculate the vehicle's output information.

[0032] Step 1.2: Receive the output information of the pilot vehicle and other following vehicles in real time through the V2X wireless communication network, and send its own output information.

[0033] Step 2: Design a dynamic model for a single vehicle and, using the information sensed by the on-board sensors, establish a feedback linearization model with external disturbance terms.

[0034] Step 2.1: Based on the longitudinal dynamics analysis of the vehicle, Newton's second law is used to derive the nonlinear longitudinal dynamics model of the i-th electric vehicle in the platoon.

[0035] F d,i (t)-F c,i (t)-m i gμ i =m i a i (t) (1)

[0036]

[0037]

[0038]

[0039] Among them, F d,i (t) represents the actual driving force of the vehicle, F c,i (t) represents air resistance, T d,i (t) represents the actual driving torque of the vehicle, T de,i (t) represents the desired driving torque of the vehicle, m i is the vehicle mass, g is the gravitational acceleration constant, μ i is the rolling resistance coefficient, r a,i is the tire radius, C c is the air resistance coefficient, ρ c is the air density, S c,i is the frontal area of ​​the vehicle, v i (t) is the vehicle speed, τ i is the time constant of vehicle dynamics.

[0040] The inverse model compensation technique is used for feedback linearization, and the desired torque of the vehicle is designed as:

[0041]

[0042] Combining (1)(2)(3)(4)(5), and assuming that the dynamics of the vehicles in the platoon are homogeneous, τ i =τ>0, considering the possible external interference terms, the feedback linearization model of the i-th electric vehicle can be obtained:

[0043]

[0044] Among them, a i is the vehicle acceleration, ui is the control input, w i For external disturbances.

[0045] Step 2.2: Take the position, velocity, and acceleration of the ego vehicle as the state vector: Considering the external interference term of the system, the feedback linearization model of the i-th smart electric vehicle is established:

[0046]

[0047] in, is the system output; To satisfy (A, C) is an observable output matrix; at the same time, there is a positive constant θ such that ‖ω i ‖ 2 <θ; the feedback linearization model of the pilot vehicle is defined as:

[0048]

[0049] Step 3: Use graph theory to establish the communication topology of the vehicle platoon system and establish a random DoS attack model;

[0050] Step 3.1: For a vehicle platoon system consisting of 1 leading CV (labeled 0) and N following CVs (labeled 1…N respectively), define a directed graph in, Represents the set of CVs in the queue, Represents the set of edges with direct connectivity between CVs. Edge (i, j)∈ε indicates that vehicle j can receive information from vehicle i and vehicle j is within the area of ​​vehicle i. Directed graph The information flow relationship in can refer to the adjacency matrix in algebraic graph theory and the Laplacian matrix To characterize, they are defined as:

[0051]

[0052] Step 3.2: DoS attack can paralyze the communication function of the corresponding topology edge, and the topology edge will not be able to transmit information until the attack ends. When vehicle i is attacked by DoS, all information topologies connected to i will be Disconnect and Restore the connection. Define a piecewise constant function φ(·) to represent the attack signal:

[0053]

[0054] At this point, the communication topology of the table queue system is Correspondingly, the adjacency matrix and the Laplacian matrix are expressed as as well as And there In addition, assuming that the communication is normal, the topology diagram It always contains a directed spanning tree with the pilot vehicle as a node. Let the total attack duration and total number of attacks of the DoS attack on the vehicle queue system in the time interval [t0,) be expressed as T a [t0,) and N a [t0,), and abbreviated as T a and N a Then the attack length ratio t l and attack frequency a f Can be defined as T a / (t-t0) and N a / -t0).

[0055] In particular, due to With a directed spanning tree, then is a non-singular M matrix; in this case, there exists Γ=diag{γ1,…, N}>0 makes in, And all The eigenvalues ​​in are all positive, so all The eigenvalues ​​of are all real numbers, j = 2,…,k. Definition

[0056] Step 4: Design an observer model based only on relative output information and provide a switching safety control protocol to defend against DoS attacks, and calculate the wheel motor driving torque required for vehicle platooning control in real time.

[0057] Step 4.1: Set the queue error variable e i =x i -x0-D i0 , relative state error variable Given the following state error observer

[0058]

[0059]

[0060] Where W = -B[(CB) T (CB)] -1 (CB) T ,=I+WC, and is the parameter matrix that makes RA-ΞC stable; D ij =[d i ' ,j 00T ,d i ' ,j is the headway between vehicles i and j, defined as is the fixed headway between two adjacent electric vehicles. is the vehicle body length. Then from RB=0 we get:

[0061]

[0062] Based on the designed observer model, a switching safety controller is established as shown below:

[0063]

[0064] Among them, q>0 is the coupling strength coefficient, F and and are the gain matrices to be designed, i=1,…,N. Combining the above formula, we can get:

[0065]

[0066] in, because Then we can get through calculation:

[0067]

[0068] Rewrite (13) as:

[0069]

[0070] in, because According to (16)-(17), we can get:

[0071]

[0072] Step 4.2: For a platoon system consisting of one pilot vehicle (8) and N following vehicles (7), when the system is subjected to DoS attacks and external interference, design a safety controller (14) based on relative output information, so that it can In the case of So that the following formula holds:

[0073]

[0074] At this point, the vehicle platoon system can be stabilized.

[0075] Step 4.3: Construct the Lyapunov function:

[0076]

[0077] in, is a constant to be designed. When subjected to DoS attacks and external interference w i (t), the stability condition of the vehicle platoon closed-loop system (18) is:

[0078] If F=-B T Q -1 , And q>κ / μ m , and for any t>t0, the attack length ratio t l and attack frequency a f Satisfy respectively:

[0079]

[0080]

[0081] in, as well as is a feasible solution to the following LMI:

[0082] AQ+QA T -κBB T +v M ΩΩ T +ρ1Q<0, (23)

[0083]

[0084] Where ρ1>0, ρ2>0, and κ>0 are positive constants. ρ3>0 is a solution that satisfies the following LMI:

[0085]

[0086] Among them, P>0,o2>0,ρ=min{ρ1,ρ3}, and satisfy Proof: Taking the derivative of V1 and combining it with formula (18) we can get:

[0087]

[0088] Applying Young's inequality to the last term of the above equation, we can get:

[0089]

[0090] On the one hand, due to Q -1 BB T Q -1 and Q -1 ΩΩ T Q -1 is symmetric, and from the relevant lemma we can get:

[0091]

[0092] in,

[0093] 1) When the system is in the communication period, that is, when Sometimes, there are Combined with (28), we have:

[0094]

[0095] Substituting equation (29) back into equation (26) and combining it with equation (23), we can obtain:

[0096]

[0097] in, Similarly, taking the derivative of V2 and V4, combined with (25), we can obtain:

[0098]

[0099] in, Therefore When , combining formula (30) and formula (31), we can get:

[0100]

[0101] in, Easy to know Then, from the relevant lemma, we can see that Ψ < 0 if and only if:

[0102]

[0103] At the same time, Π1<0 is equivalent to:

[0104]

[0105] Combining equations (32)-(34), we can see that:

[0106]

[0107] Where ρ = min{ρ1,ρ3}.

[0108] 2) When the system is in the attack period, that is, when When , similar to formula (30), take the derivative of V3 and combine the relevant lemma with formula (24) to obtain:

[0109]

[0110] in, Similar to formula (31), combined with formula (36), we can get:

[0111]

[0112] in, From the relevant lemma, we can see that If and only if:

[0113]

[0114] At the same time, Π2<0 is equivalent to:

[0115]

[0116] in, Considering (37)-(39), we can get:

[0117]

[0118] in,

[0119] 3) Comprehensive analysis. as well as because when When , according to formula (35)

[0120]

[0121] when When, according to formula (40:

[0122]

[0123] Considering equations (41) and (42), we can obtain:

[0124]

[0125] for When , considering formula (43), we can get:

[0126]

[0127] for When , considering formula (43), we can get:

[0128]

[0129] According to formulas (44) and (45), we can know that:

[0130]

[0131] Wherein, c=1 or c=1 / η. Substituting (21) and (22) into (46) yields:

[0132]

[0133] That is, the distributed error variable δ of the queuing system is eventually uniformly bounded, and the vehicle queuing system can be stable at this time.

[0134] Step 4.4: Substitute the obtained controller into the feedback linearization strategy (5) to obtain the real-time desired control torque and achieve the corresponding vehicle control.

[0135] Consider a platoon consisting of one leading vehicle and six following vehicles. The vehicle dynamic models are given by Equations (7) and (8), respectively. The initial state values ​​are randomly selected. The leading vehicle's stable speed is set to 25 / , and the inter-vehicle distance is set to d′=10. The external disturbance w0 and w i The simulation is performed using a temporal sine or cosine function with randomly selected amplitudes. The external disturbance is constant throughout the entire travel of the platoon.

[0136] Assume that the queuing system is subject to a random distributed DoS attack, that is, each vehicle may be subject to independent DoS attacks. Under normal circumstances, each vehicle can send and receive information normally. When a vehicle is under a DoS attack, it will not be able to obtain information from other vehicles and will not be able to broadcast its own driving data. In the simulation process, assume that vehicle 1 and vehicle 3 are subjected to malicious attacks, such as Figure 4 When the queue system communication is normal, the communication topology diagram is as shown. Figure 4 When the queuing system is attacked by DoS, the communication topology is shown in (b) and (c) in the figure, that is, when φ(t) = 2 and 3, vehicle 1 and vehicle 3 are attacked respectively.

[0137] Let κ=2.7, ρ1=1.9, ρ2=0.3, ρ * =0.75. Select coupling gain Gain matrix F = [-0.2500-1.0433-0.1900]. From equations (12) and (14), the error observer and the switching safety controller can be obtained respectively. The observers of all vehicles The initial value of is randomly selected. In addition, from Equation (21), we can see that the maximum allowed attack length ratio is 0.5227.

[0138] Here, the maximum attack length ratio of DoS attack is set to t l=0.5, and the most demanding attack environment will be simulated, that is, each DoS attack is at its maximum attack length ratio level (all 0.5). For each time interval [n,n+1), assume that:

[0139] Where n = 0, 1, 2,….

[0140] from Figure 5 As can be seen, under the aforementioned DoS attack, the vehicle platooning system, using the switchable safety controller proposed in this invention, achieved system stability within approximately 10 seconds. Specifically, the distance error and velocity error curves of the following vehicle successfully converged to zero, and the velocity and acceleration trajectory curves successfully followed the lead vehicle. Furthermore, even in the presence of persistent external interference, the vehicle's acceleration curve remained smooth, without significant jitter. This demonstrates the robust performance of the distributed controller proposed in this invention.

[0141] Supplement the experimental data verification of the technical effect of the present invention to prove that the present invention solves the problems existing in the above-mentioned prior art and achieves the above-mentioned technical effect.

Claims

1. A method for controlling a formation of intelligent electric vehicles to defend against denial of service network attacks, characterized in that The following steps are involved: Step 1: A platoon consists of N+1 vehicles, numbered 0,…,N. Vehicle 0 is the lead vehicle, and vehicles 1,…,N are the following vehicles. Vehicle-to-vehicle sensors and the V2X wireless communication network collect real-time information about the vehicle's motion state and the output information from the preceding and lead vehicles. Step 1.1: Use on-board sensors and GPS to measure the vehicle's driving status information in real time, determine its position, including distance information, speed information, and acceleration information, and calculate the vehicle's output information; Step 1.2: The ego vehicle exchanges information with the pilot vehicle and other following vehicles in the platoon via the V2X wireless communication network, receives the corresponding vehicle output information in real time, and broadcasts the ego vehicle's output information. Step 2: Design a feedback linearization model for each vehicle. This model, combined with information from onboard sensors and the V2X wireless communication network, establishes a single-vehicle longitudinal control model with external disturbances. Step 2.1: Use Newton's second law to derive the nonlinear longitudinal dynamics expression of a single vehicle, perform feedback linearization based on the inverse model compensation technique, and obtain the linearized longitudinal dynamics model of the single vehicle; Step 2.2: Use the position, velocity, and acceleration information of the ego vehicle as the state vector, consider the external disturbance term of the system, and establish the longitudinal motion model of a single vehicle; Step 3: Based on graph theory knowledge, characterize the communication topology of the vehicle platoon system and establish a random DoS attack model; Step 3.1: Use graph theory to describe the communication topology of the queue system. For a vehicle platoon system consisting of 1 leading CV (labeled as 0) and N following CVs (labeled as 1…N respectively), define the directed graph in, Represents the set of CVs in the queue, Represents the set of edges with direct connectivity between CVs; edge (i, j)∈ε indicates that vehicle j can receive information from vehicle i, and vehicle j is within the area of ​​vehicle i; directed graph The information flow relationship in the reference algebraic graph theory adjacency matrix and the Laplacian matrix To characterize, they are defined as: Step 3.2: Propose a DoS attack model and provide two important descriptive indicators: attack frequency and attack length ratio; DoS attack can paralyze the communication function of the corresponding topology edge, and the topology edge will not be able to transmit information before the attack ends; when vehicle i suffers a DoS attack, all information topologies connected to i will be Disconnect and Restore the connection; define a piecewise constant function φ(·) to represent the attack signal: At this point, the communication topology of the table queue system is Correspondingly, the adjacency matrix and the Laplacian matrix are expressed as as well as And there In addition, assuming that the communication is normal, the topology diagram There is always a directed spanning tree with the pilot vehicle as a node; let the total attack duration and total number of attacks of the DoS attack on the vehicle queue system in the time interval [t0, t) be expressed as T a [t0,t) and N a [t0,t), and abbreviated as T a and N a ; then the attack length ratio t l and attack frequency a f They are defined as T a / (t-t0) and N a / (t-t0); Step 4: Design an error observer model and establish a vehicle formation switching safety controller under DoS attacks and external interference to calculate the wheel motor driving torque required for vehicle formation control in real time; Step 4.1: Establish an error observer and design sub-controllers for normal communication and attack respectively. Substitute them into the formation model to establish a closed-loop error control system for the vehicle platoon consisting of two subsystems. Step 4.2: Based on the constructed platoon closed-loop error system, establish the objective function of the intelligent electric vehicle platoon control; Step 4.3: Based on Lyapunov stability theory and linear matrix inequality methods, the conditions for achieving stability of the queue closed-loop error system with a switched safety controller are given, and the design method for the controller gain matrix is ​​obtained. Step 4.4: Substitute the safety controller into the feedback linearization model in step 2 to calculate the desired wheel driving torque of the vehicle in real time to achieve platoon control of smart electric vehicles.

2. A method for controlling a formation of intelligent electric vehicles for defending against denial of service network attacks as claimed in claim 1, characterized in that In step 2, the specific steps of establishing the single-vehicle longitudinal control model with external interference are: (1) Based on the longitudinal dynamics analysis of the vehicle, Newton's second law is used to derive the nonlinear longitudinal dynamics model of the i-th electric vehicle in the platoon: F d,i (t)-F c,i (t)-m i gμ i =m i a i (t) (1) Among them, F d,i (t) represents the actual driving force of the vehicle, F c,i (t) represents air resistance, T d,i (t) represents the actual driving torque of the vehicle, T de,i (t) represents the desired driving torque of the vehicle, m i is the vehicle mass, g is the gravitational acceleration constant, μ i is the rolling resistance coefficient, r a,i is the tire radius, C c is the air resistance coefficient, ρ c is the air density, S c,i is the frontal area of ​​the vehicle, v i (t) is the vehicle speed, τ i is the time constant of vehicle dynamics; The inverse model compensation technique is used for feedback linearization, and the desired torque of the vehicle is designed as: Combining equations (1)(2)(3)(4)(5), assuming that the dynamics of the vehicles in the platoon are isomorphic, that is, τ i =τ>0, considering the possible external interference terms, the feedback linearization model of the i-th electric vehicle is obtained: Among them, a i is the vehicle acceleration, u i is the control input, w i is an external disturbance; (2) The position, velocity, and acceleration of the vehicle are taken as the state vector: Considering the external interference term of the system, the feedback linearization model of the i-th smart electric vehicle is established: Where i = 1,…,N; is the system output; To satisfy (A, C) is an observable output matrix; at the same time, there is a positive constant θ such that ||ω i || 2 <θ; the feedback linearization model of the pilot vehicle is defined as:

3. A method for controlling a formation of intelligent electric vehicles to defend against denial of service network attacks as claimed in claim 2, characterized in that In step 3, the topology diagram when the communication is normal With a directed spanning tree, then is a non-singular M matrix; in this case, there exists Γ=diag{γ1,…,γ N }>0 makes in, And all The eigenvalues ​​in are all positive, so all The eigenvalues ​​of are all real numbers, j = 2,…,k; definition 4. A method for controlling a formation of intelligent electric vehicles for defending against denial of service network attacks as claimed in claim 3, characterized in that In step 4, the specific steps of calculating the wheel motor driving torque required for vehicle platoon control in real time are as follows: (1) Let the queue error variable e i =x i -x0-D i0 , relative state error variable Given the following state error observer Where W = -B[(CB) T (CB)] -1 (CB) T , R=I+WC, and is the parameter matrix that makes RA-ΞC stable; D ij =[d' i,j 0 0] T ,d' i,j is the headway between vehicles i and j, defined as d'>0 is the fixed headway between two adjacent electric vehicles, is the vehicle body length; Then from RB=0 we get: Based on the designed observer model, a switching safety controller is established as shown below: Among them, q>0 is the coupling strength coefficient, F and and are the gain matrices to be designed, i=1,…,N; Combining the above formula, we can get: in, because Then we get through calculation: Rewrite (13) as: in, because According to formula (16)-(17), we can get: (2) For a car platoon system consisting of one pilot vehicle (8) and N following vehicles (7), when the system is subjected to DoS attacks and external interference, a safety controller (14) based on relative output information is designed to enable it to In the case of So that the following formula holds: At this point, the vehicle platoon system can be stabilized; (3) Construct Lyapunov function: in, ι1>0,ι2>0 are constants to be designed; when subjected to DoS attacks and external interference w i (t), the stability condition of the vehicle platoon closed-loop system (18) is: If F=-B T Q -1 , and q>κ / μ m , and for any t>t0, the attack length ratio t l and attack frequency a f Satisfy respectively: in, Q>0 and is a feasible solution to the following LMI: AQ+QA T -κBB T +v M ΩΩ T +ρ1Q<0 (23) Among them, ρ1>0, ρ2>0, κ>0 are positive constants; ρ3>0 is a solution that satisfies the following LMI: Among them, P>0,o2>0,ρ=min{ρ1,ρ3}, and satisfy Proof: Taking the derivative of V1 and combining it with formula (18) we get: Applying Young's inequality to the last term of the above equation, we get: On the one hand, due to Q -1 BB T Q -1 and Q -1 ΩΩ T Q -1 is symmetric, and from the relevant lemma we have: in, 1) When the system is in the communication period, that is, when Sometimes, there are Combined with (28), we have: Substituting equation (29) back into equation (26) and combining it with equation (23), we can obtain: in, Similarly, take the derivative of V2 and V4 and combine (25) to obtain: Among them, o2>0, Therefore When , combining formula (30) and formula (31), we can get: in, Easy to know Then, from the relevant lemma, we can see that Ψ<0 if and only if: At the same time, Π1<0 is equivalent to: Combining equations (32)-(34), we can obtain: Where, ρ = min{ρ1,ρ3}; 2) When the system is in the attack period, that is, when When , similar to formula (30), take the derivative of V3 and combine the relevant lemma with formula (24) to obtain: in, Similar to formula (31), combined with formula (36), we get: in, According to the relevant lemma, If and only if: At the same time, Π2<0 is equivalent to: in, Considering (37)-(39), we get: in, 3) Comprehensive analysis; as well as because when When , according to formula (35) when When , according to formula (40): Considering equations (41) and (42), we get: for When , considering formula (43), we get: for When , considering formula (43), we get: According to formulas (44) and (45), we can know that: Where c = 1 or c = 1 / η; Substituting equations (21) and (22) into equation (46), we obtain: That is, the distributed error variable δ of the queuing system is eventually uniformly bounded, and the vehicle queuing system is stable at this time; (4) The obtained controller is substituted into the feedback linearization strategy (5) to obtain the real-time desired control torque and realize the corresponding vehicle control.

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