Dynamic event triggering design method of unmanned vehicle cooperative system under asynchronous denial of service attack

Abstract

The invention relates to the field of unmanned vehicle cooperative system control and the field of malicious network attack defense, in particular to a design method for an event triggering mechanism under the condition that a large unmanned vehicle cooperative system faces asynchronous denial of service (DoS) attack and communication resource shortage. Particularly, the invention provides a signal transmission strategy based on a dynamic event triggering mechanism by considering the condition that a signal transmission channel in the unmanned vehicle cooperative system bears asynchronous DoS attacks, and communication resources are saved on the premise of ensuring the performance requirements of the system. A switching method based on a network attack time sequence is designed, and a switching system thought and a Lyapunov stability theory are utilized to obtain a sufficient condition that the attenuation rate of each subsystem of the unmanned vehicle system is consistent with the unmanned vehicle in the system under the asynchronous DoS attack. The invention designs an equivalent attenuation rate method, and discloses a relationship between the maximum attack intensity which can be borne by an unmanned vehicle system and parameters in an event triggering mechanism, so that the method disclosed by the invention can be used for solving the problem in actual application by adjusting design parameters according to an actual network attack environment and a control target. And the response speed and the attack bearing capacity of the system are balanced.

Description

Technical Field

[0001] The present invention relates to the fields of unmanned vehicle collaborative system control and malicious network attack defense, and particularly to a design method for an event-triggered mechanism in the case of an asynchronous denial-of-service (DoS) attack and a shortage of communication resources faced by a large-scale unmanned vehicle collaborative system. Background Art

[0002] An unmanned vehicle is an intelligent device with a certain adaptability and self-learning ability that can autonomously sense the surrounding environment and make real-time autonomous decisions according to preset tasks without human intervention in its movement. In recent years, unmanned vehicle collaborative systems have attracted increasing attention and have become an important field in modern industry, society, and scientific research. With continuous breakthroughs in research in intelligent fields such as multi-sensor fusion technology, intelligent driving technology, and artificial intelligence, the related technologies of intelligent control and collaborative operation of unmanned vehicles have become increasingly mature and are widely used in military, civilian, rescue, and other fields. With the continuous in-depth research on unmanned vehicles and the continuous expansion of their applications, single unmanned vehicles can no longer meet the growing real-world needs due to their own characteristic limitations, and thus a new direction of multi-unmanned vehicle collaborative operation has emerged, avoiding the disadvantages of single unmanned vehicles being greatly affected by the environment and having limited carried resources, and being widely used in actual production. Multiple unmanned vehicles transmit data through a wireless network, thus overcoming the geographical limitations brought by wired transmission. However, they will also face challenges brought by network attacks. Therefore, how to achieve the control of an unmanned vehicle collaborative system under network attacks plays a crucial role.

[0003] Traditional periodic control methods can no longer meet the control requirements of unmanned vehicle collaborative systems. As a new type of control method, event-triggered control can reduce the communication and computational overhead of the system and improve the control performance of the system. Therefore, it has broad research value and application prospects. In an unmanned vehicle collaborative system, the state and control information of unmanned vehicles are updated through network transmission. However, in actual situations, the bandwidth and transmission rate of communication network media are usually limited. In order to effectively utilize limited computational and communication resources to complete various collaborative control tasks, an event-triggered mechanism has been developed. The dynamic event-triggered mechanism proposed by the present invention can significantly reduce the triggering frequency while ensuring a certain system performance. By introducing a dynamic threshold parameter, compared with the static event-triggered mechanism, it can further save communication resources.

[0004] The unmanned vehicle collaborative system belongs to a type of multi-agent system. With the increasing prevalence of multi-agent networks in various fields, the communication, computing, and control in network systems have been deeply integrated. When communicating over the network, data is transmitted over long distances, which greatly improves the frequency and rate of information interaction but also poses a huge challenge to system security. In recent years, network attack incidents have emerged in an endless stream, and network security issues have gradually risen from the individual level to the national level, quickly becoming a hot research topic in disciplines such as computer science, communication, and control. Currently, the most common types of network attacks are spoofing attacks and DoS attacks. In a spoofing attack, an attacker can hijack and tamper with the data or control instructions transmitted over the network, or directly inject false interference data into the data packet, thereby interfering with the system's performance or even causing the system state to develop towards a preset situation. Different from a DoS attack, a DoS attack, also known as a denial-of-service attack, is an attack in which an attacker prevents ordinary users from accessing a network, website, or service, thereby denying them service. It is an attack aimed at disabling, shutting down, or interrupting a network, website, or service.

[0005] In a large-scale unmanned vehicle collaborative system, due to reasons such as geographical distribution, the communication between multiple unmanned vehicles within the system often does not use a single communication channel. Therefore, each channel has the possibility of being subjected to different network attacks. Therefore, when studying the consensus problem of the unmanned vehicle collaborative system, it is very meaningful to consider the impact of asynchronous DoS attacks on system performance.

[0006] The present invention proposes a design method for a dynamic event-triggering mechanism of an unmanned vehicle collaborative system under asynchronous DoS attacks. By designing an event-triggering pulse controller, the problems of consensus and communication resource tension in the unmanned vehicle collaborative system in the presence of asynchronous DoS attacks are solved. Summary of the Invention

[0007] The present invention proposes a design method for a dynamic event-triggering mechanism of an unmanned vehicle collaborative system under asynchronous DoS attacks. By designing an event-triggering pulse controller, the problems of consensus and communication resource tension in the unmanned vehicle collaborative system in the presence of asynchronous DoS attacks are solved.

[0008] To achieve the above object, the present invention provides the following solution:

[0009] An event-triggered control method for an unmanned vehicle collaborative system under asynchronous denial-of-service attacks, including:

[0010] Step 1. Establish a linear leaderless unmanned vehicle collaborative system model;

[0011]

[0012] where N is the set of natural numbers, i ∈ N is the unmanned vehicle number, xi (t) is the state of the i-th autonomous vehicle, and its dimension is related to the type of real autonomous vehicle. It usually includes parameter variables such as position, speed, angular velocity, and acceleration, u i (t) is the input of the i-th autonomous vehicle, y i (t) is the output of the i-th autonomous vehicle, and A, B, and C are matrices of appropriate dimensions.

[0013] Step 2. Construct an asynchronous denial-of-service attack model. According to the communication status (secure state and attacked state) between autonomous vehicles, divide the time interval into multiple sub-intervals with the same state, and establish a switched system model;

[0014] Denial-of-service attacks can cause transmission channel congestion and signal transmission failures. Considering that network attackers have limited energy, the method for establishing an attack model with limited duration dimension is as follows:

[0015]

[0016] where, |D ij (t 1 ,t 2 )| is the total duration of the DoS attack on the ij channel within the time interval (t 1 ,t 2 ), is a positive real number, 0 < μ ij < 1;

[0017] The method for establishing the switched system model in step (2) includes:

[0018] Γ(t) = {(i, j) ∈ ε | t ∈ D ij (0, ∞)};

[0019] where, Γ(t) is the set of transmission channels in the denial-of-service attack interval at time t;

[0020]

[0021] where Ε Γ(t) (t 1 ,t 2 ) represents the set of time intervals divided by Γ(t), and then different Ε Γ(t) (t 1 ,t 2 ) are used as switching vectors to establish a switched system model.

[0022] Step 3. Construct a dynamic event-triggering mechanism under asynchronous denial-of-service attacks;

[0023] The method for designing the event-triggering function of the event-triggering mechanism is as follows:

[0024]

[0025] Among them, η i (t) is a dynamic variable related to the dynamic event-triggering mechanism and the internal information of the system, is the observation error, ξ i , θ i are positive real numbers, Φ i is a symmetric positive definite matrix of appropriate dimension;

[0026] Step 4. Based on the Lyapunov stability theory and the idea of switched systems, using the linear matrix inequality tool, obtain the sufficient conditions for the unmanned vehicle cooperative system to maintain consistency under asynchronous denial-of-service attacks and the design method of each parameter of the dynamic event-triggering mechanism;

[0027] Based on the event-triggering mechanism, construct a tracking error model for the unmanned vehicle cooperative system, and transform the consistency problem into a stability problem;

[0028] The method for constructing the tracking error model includes:

[0029] The unmanned vehicle cooperative system model in Step 1 can be described as:

[0030]

[0031] Among them, e(t) = col(e 1 (t) e 2 (t)... e N (t)), L is the Laplacian matrix. Combining the unmanned vehicle cooperative system with graph theory, L = [l ij , L Γ(t) is the Laplacian matrix determined by Γ(t) given in the switching method proposed in Step 2. i and j are the numbers of unmanned vehicles. When i = j, l ij = -a ij , when i ≠ j, l ij = -a ij , a ij is the weight coefficient.

[0032] The tracking error can be described as:

[0033]

[0034] Among them, δ(t) = col(δ 1 (t) δ 2 (t)... δ N (t)), is the average value of the instantaneous states of each unmanned vehicle at time t, that is

[0035] Considering the unmanned vehicle cooperative system model proposed in Step 1, a description method for the tracking error can be obtained:

[0036]

[0037] Based on the Lyapunov stability theory, sufficient conditions for the unmanned vehicle cooperative system to achieve consensus under the event-triggered mechanism are obtained;

[0038] Obtaining the sufficient conditions for the consensus of the unmanned vehicle cooperative system under asynchronous DoS attacks includes the following steps:

[0039] Construct the Lyapunov function as:

[0040]

[0041] where, V 1 (t) = x T (t)Px(t), x(t) = col(x 1 (t) x 2 (t)... x N (t)), P ∈ R n×n is a positive definite matrix;

[0042] Taking the derivatives of V 1 (t) and in the Lyapunov function respectively, we can obtain:

[0043]

[0044] where is the observation error;

[0045] Using Young's inequality, for the perform scaling, we can obtain:

[0046]

[0047] Using Young's inequality, for the perform scaling, we can obtain:

[0048]

[0049] From the above, the derivative of the Lyapunov function can be obtained as:

[0050]

[0051] where, ρ * = min(ρ1 ρ 2 ... ρ N ),ρ * =max(ρ 1 ρ 2 ... ρ N ),θ * =min(θ 1 θ 2 ... θ N ),ξ * =min(ξ 1 ξ 2 ... ξ N );

[0052] Based on the above process, the sufficient conditions for the unmanned vehicle cooperative system to reach consistency under the event-triggering mechanism are as follows:

[0053] Set the scalar ξ i >0. If the unmanned vehicle cooperative system can reach consistency, then there exist a positive definite matrix P ∈ R n×n and a positive definite matrix Φ i ∈ R n×n such that the following linear matrix inequality holds:

[0054]

[0055] Solve the linear matrix inequality in the above sufficient conditions to obtain the controller gain and the design parameters of the observer-based event-triggering mechanism.

[0056] Step 5. Design a method for equivalent decay rate to effectively obtain the relationship between the network attack intensity and the dynamic event-triggering mechanism parameters. In actual production, the event-triggering design can be carried out according to the actual network environment and production requirements;

[0057] Considering that the subsystem decay rate α σ(t) in Step 5 cannot accurately match the dynamic performance of a single unmanned vehicle, to more accurately describe the internal relationship between network attacks and design parameters, the following method for equivalent decay rate is proposed:

[0058] Integrate within each subsystem switching moment for the situation described in Step 5, and use the recursive idea to convert the integration from within the subsystem switching moment to the entire time interval:

[0059]

[0060] where,

[0061] Design the equivalent decay rate ​where \(m = \{1, 2\}\), representing the transmission channel between the autonomous vehicle \(i\) and the autonomous vehicle \(j\) being in a safe state and an attacked state, respectively;

[0062] From the definition of the equivalent attenuation rate it can be known that the relationship between it and the subsystem attenuation rate is:

[0063]

[0064] Subsequently, when holds, the value range of \(p(0, t)\) can be obtained as:

[0065]

[0066] Considering the asynchronous DoS attack model described in Step 2, it can be obtained that:

[0067]

[0068] Based on the above process, the relationship between the system attack strength and the parameters of the dynamic event-triggering mechanism can be obtained as follows:

[0069] If the autonomous vehicle cooperation system can maintain consistency under asynchronous denial-of-service attacks, then there exist constants and such that the following inequalities hold:

[0070]

[0071] where can represent the attack strength of the asynchronous denial-of-service attack.

[0072] The method for controlling the consistency of the autonomous vehicle cooperation system based on event triggering under asynchronous denial-of-service attacks of the present invention has the following advantages:

[0073] 1. The present invention fully applies graph theory and set knowledge to vividly and intuitively express the network topology relationship formed among individuals in the autonomous vehicle cooperation system.

[0074] 2. The present invention applies denial-of-service attacks to the autonomous vehicle cooperation system, solving the problem that information cannot be transmitted between autonomous vehicles when the communication network of the system is attacked. And considering the problem that the denial-of-service attacks suffered by multiple transmission channels are asynchronous due to the wide geographical distribution of large-scale autonomous vehicle cooperation systems in the real situation, it is more in line with general practical applications.

[0075] 3. The present invention designs a dynamic event-triggering mechanism applicable to the autonomous vehicle cooperation system, ensuring more effective signal transmission between autonomous vehicles and reducing the dependence on the actual state during the system control process.

[0076] 4. By means of the equivalent attenuation rate method, the present invention obtains the relationship between the system consistency and the intensity of the denial-of-service attack. In actual production, the design parameters can be adjusted to balance the working efficiency and system resilience to meet the production requirements and efficiency requirements.

[0077] 5. The present invention proposes a sufficient condition for the realization of consistency in an unmanned vehicle cooperative system suffering from a denial-of-service attack, provides a judgment criterion for the realization of fixed-time consistency in this type of system, and gives a design method for an event-triggered scheme for a class of asynchronous denial-of-service attacks. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 It is a flowchart of the event-triggered control method for the unmanned vehicle cooperative system under a denial-of-service attack according to an embodiment of the present invention;

[0079] Figure 2 It is a topology diagram of the unmanned vehicle cooperative system according to an embodiment of the present invention;

[0080] Figure 3 It is a schematic diagram of the position consistency of the nonlinear unmanned vehicle cooperative system under a denial-of-service attack according to an embodiment of the present invention;

[0081] Figure 4 It is a triggering moment diagram of the event trigger according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0082] In order to better understand the purpose, structure and function of the present invention, the following further describes in detail the design method of the dynamic event-triggered mechanism in an unmanned vehicle cooperative system under an asynchronous denial-of-service attack with reference to the accompanying drawings.

[0083] As Figure 1 shown, the design method of the dynamic event-triggered mechanism in an unmanned vehicle cooperative system under an asynchronous denial-of-service attack includes the following steps:

[0084] Step 1. Establish a model of a leaderless linear unmanned vehicle cooperative system:

[0085] Specifically, the unmanned vehicle cooperative system model is as follows:

[0086]

[0087] y i (t) = Cx i (t)

[0088] where N is the set of natural numbers, i ∈ N is the unmanned vehicle number, x i (t) is the state of the i-th unmanned vehicle, u i (t) is the input of the i-th unmanned vehicle, y i(t) is the output of the i-th driverless vehicle, and A, B, and C are matrices of appropriate dimensions.

[0089] Step 2. Construct an asynchronous denial-of-service attack model. According to the network states (secure state and attacked state) among driverless vehicles, divide the time interval into multiple sub-intervals with the same state, and establish a switched system model;

[0090] Specifically, the present invention considers asynchronous denial-of-service attacks. Denial-of-service attacks can cause transmission channel blockages and signal transmission failures. Considering that the network attacker has limited energy, the method for establishing an attack model with limited attacks in the duration dimension is as follows:

[0091]

[0092] Among them, |D ij (t 1 ,t 2 )| is the total duration of the DoS attack on the ij channel within the time interval (t 1 ,t 2 ); is a positive real number, 0 < μ ij < 1;

[0093] The method for establishing the switched system model in step (2) includes:

[0094] Γ(t) = {(i, j) ∈ ε | t ∈ D ij (0, ∞)};

[0095] Among them, Γ(t) is the set of transmission channels in the denial-of-service attack interval at time t;

[0096] Under asynchronous denial-of-service attacks, the switching vector of the switched system is described as:

[0097]

[0098] Among them, Ε Γ(t) (t 1 ,t 2 ) represents the set of time intervals divided by Γ(t), and then different Ε Γ(t) (t 1 ,t 2 ) are used as switching vectors to further establish a switched system model.

[0099] Step 3. Construct a dynamic event-triggered mechanism under asynchronous denial-of-service attacks;

[0100] Specifically, the present invention introduces a dynamic event-triggering mechanism to alleviate the problems of communication resource constraints and control dependence on real-time state information. Packets that do not meet the following conditions are considered unnecessary data and will be discarded by the triggering mechanism; when the following conditions are met, the sampled data is released into the network and transmitted to its own controller and neighboring unmanned vehicles.

[0101] The method for designing the event-triggering function of the event-triggering mechanism is as follows:

[0102]

[0103] where η i (t) is a dynamic variable related to the internal information of the dynamic event-triggering mechanism and the system, is the system error, ξ i , θ i are positive real numbers, and Φ i is a symmetric positive definite matrix of appropriate dimension;

[0104] Step 4. Based on the Lyapunov stability theory and the idea of switched systems, using linear matrix inequality tools, obtain the sufficient conditions for the unmanned vehicle cooperative system to maintain consistency under asynchronous denial-of-service attacks and the design method of each parameter of the dynamic event-triggering mechanism;

[0105] Specifically, considering the effective tool of the Lyapunov stability theory, using the tracking error, transform the consistency problem into a stability problem, and then based on the Lyapunov stability theory, obtain the sufficient conditions for the unmanned vehicle cooperative system to maintain consistency under asynchronous denial-of-service attacks.

[0106] Step 4.1. Based on the event-triggering mechanism, construct a tracking error model of the unmanned vehicle cooperative system, and transform the consistency problem into a stability problem;

[0107] The method for constructing the tracking error model includes:

[0108] The unmanned vehicle cooperative system model in Step 1 can be described as:

[0109]

[0110] where e(t) = col(e 1 (t) e 2 (t)... e N (t)), L is the Laplacian matrix, combining the unmanned vehicle cooperative system with graph theory, L = [l ij , and L Γ(t) is the Laplacian matrix determined by Γ(t) given in the switching method proposed in Step 2, and i, j are the numbers of unmanned vehicles. When i = j, l ij=-a ij , when \(i\neq j\), \(l\) ij =-a ij , \(a\) ij is the weight coefficient.

[0111] The tracking error can be described as:

[0112]

[0113] where \(\delta(t)=\text{col}(\delta\) 1 (t)\(\delta\) 2 (t)\(\cdots\delta\) N (t)) is the average value of the instantaneous states of each autonomous vehicle at time \(t\), that is

[0114] Considering the autonomous vehicle cooperative system model proposed in Step 1, a description method of the tracking error can be obtained:

[0115]

[0116] Step 4.2. Based on the Lyapunov stability theory, obtain the sufficient conditions for the autonomous vehicle cooperative system to reach consensus under the event-triggered mechanism;

[0117] Obtaining the sufficient conditions for the consensus of the autonomous vehicle cooperative system under asynchronous DoS attacks includes the following steps:

[0118] Construct the Lyapunov function as:

[0119]

[0120] where \(V\) 1 (t)=x T (t)Px(t), \(x(t)=\text{col}(x\) 1 (t)x 2 (t)\(\cdots x\) N (t)), \(P\in R\) n×n is a positive definite matrix;

[0121] Take the derivatives of \(V\) 1 (t) and respectively, and we can obtain:

[0122]

[0123] where is the observation error;

[0124] Using Young's inequality for the Scaling can be performed to obtain:

[0125]

[0126] Using Young's inequality for the said Scaling can be performed to obtain:

[0127]

[0128] As described above, the derivative of the Lyapunov function can be obtained as:

[0129]

[0130] where ρ * = min(ρ 1 ρ 2 ... ρ N ), ρ * = max(ρ 1 ρ 2 ... ρ N ), θ * = min(θ 1 θ 2 ... θ N ), ξ * = min(ξ 1 ξ 2 ... ξ N );

[0131] Based on the said process, the sufficient conditions for the unmanned vehicle cooperative system to achieve consistency under the event-triggering mechanism are as follows:

[0132] Set the scalar ξ i > 0. If the unmanned vehicle cooperative system can achieve consistency, then there exist a positive definite matrix P ∈ R n×n and a positive definite matrix Φ i ∈ R n×n , such that the following linear matrix inequality holds:

[0133]

[0134] Solve the linear matrix inequality in the said sufficient conditions to obtain the controller gain and the design parameters of the observer-based event-triggering mechanism.

[0135] Step 5. Design a method for equivalent attenuation rate to effectively obtain the relationship between the network attack intensity and the parameters of the dynamic event-triggering mechanism. In actual production, the event-triggering design can be carried out according to the actual network environment and production requirements;

[0136] Specifically, considering the subsystem attenuation rate α described in step 5 σ(t) which cannot precisely match the dynamic performance of a single unmanned vehicle, to more accurately describe the internal relationship between cyber attacks and design parameters, an equivalent attenuation rate method is proposed as follows:

[0137] For the one described in step 4 Integrate within each subsystem switching moment, and using the recursive idea, convert the integration from within the subsystem switching moment to the entire time interval:

[0138]

[0139] where

[0140] Design the equivalent attenuation rate where m = {1, 2}, representing the transmission channels between unmanned vehicle i and unmanned vehicle j being in a safe state and an attacked state respectively;

[0141] From the definition of the said equivalent attenuation rate it can be known that the relationship between it and the subsystem attenuation rate is:

[0142]

[0143] Subsequently, when holds, the value range of the said p(0, t) can be obtained as:

[0144]

[0145] Considering the asynchronous DoS attack model described in step 2, it can be obtained that:

[0146]

[0147] Based on the said process, the relationship between the system attack strength and the dynamic event triggering mechanism parameters can be obtained as follows:

[0148] If the unmanned vehicle collaborative system can maintain consistency under asynchronous denial-of-service attacks, then there exist constants and such that the following inequality holds:

[0149]

[0150] where can express the attack strength of asynchronous denial-of-service attacks.

[0151] Step 6. Simulation example analysis

[0152] The following provides a specific embodiment by using the method of simulation analysis. By writing a Matlab program to solve the linear matrix inequality to obtain the design parameters of the dynamic event-triggering mechanism and draw the simulation curves, the effectiveness of the present invention is proved by simulation examples:

[0153] Consider an unmanned vehicle cooperative system consisting of 4 unmanned vehicles, each unmanned vehicle has 4-dimensional state information, and the system parameters are:

[0154]

[0155] Set the initial state values of each unmanned vehicle as:

[0156] x 1 (0) = (3.2 1.2 0 0.8), x 2 (0) = (-1.4 1.1 2.7 1.5), x 3 (0) = (4.6 -1.8 -2.3 1.2), x 4 (0) = (-2.7 -0.3 4 1);

[0157] Design the topological structure diagram of the unmanned vehicle cooperative system as shown in Figure 2 As shown, it can be seen that there are a total of 6 data transmission channels;

[0158] Set the time interval as t ∈ [0, 10], and the attack intervals of asynchronous denial-of-service attacks are as follows:

[0159] D 1,2 = {t | [1, 1.5] [5.5, 6] [8, 9.3]};

[0160] D 2,4 = {t | [2, 2.3] [2.8, 3.5] [6, 6.5]};

[0161] D 3,4 = {t | [0.5, 0.9] [4, 4.3] [6.2, 7]};

[0162] D 1,3 = {t | [3, 3.6] [6.5, 7.3]};

[0163] D 2,3 = {t | [4.1, 5] [9, 9.3]};

[0164] D 1,4 = {t | [1.6, 2] [2.2, 3] [8.2, 8.8]};

[0165] Considering that the calculation amount of the linear matrix inequality described in step 4 is huge, the present invention gives the following algorithm to simplify the operation:

[0166] 1). Set a suitable subsystem attenuation rate α σ(t) , solve the linear matrix inequality described in step 4 to obtain a positive definite matrix P and an event-triggering parameter Φ i ;

[0167] 2). Substitute the positive definite matrix P obtained in step 1) into the linear matrix inequalities related to other subsystems to obtain the results.

[0168] Based on the above method, using Matlab, it can be obtained that:

[0169]

[0170] Furthermore, the parameters of the dynamic event-triggering mechanism can be designed as:

[0171] ρ i = 1, θ i = 0.6, ξ i = 0.1;

[0172] Figure 3 - Figure 4 The simulation results are given. The state trajectories of the unmanned vehicles are as Figure 3 shown. It can be seen that each unmanned vehicle maintains consistency; the triggering moments of each unmanned vehicle are as Figure 4 shown. It can be seen that the event-triggering mechanism proposed in the present invention significantly reduces the signal transmission frequency and effectively alleviates the problem of limited communication resources.

[0173] From the above simulation results, it can be seen that: the design method of the dynamic event-triggering mechanism in the unmanned vehicle cooperative system under asynchronous denial-of-service attacks disclosed in the present invention can ensure the consistency of the unmanned vehicle cooperative system under asynchronous denial-of-service attacks, and through the described dynamic event-triggering mechanism, effectively reduces the communication frequency and alleviates the problem of limited communication resources.

[0174] It can be understood that the present invention is described through some embodiments. Those skilled in the art know that without departing from the spirit and scope of the present invention, various changes or equivalent replacements can be made to these features and embodiments. In addition, under the teaching of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application belong to the scope protected by the present invention.

Claims

1. A dynamic event triggering design method for an unmanned vehicle cooperative system under asynchronous denial of service attacks, characterized in that: The steps include: (1) Establish a model of unmanned vehicle collaborative system; (2) Construct an asynchronous denial of service attack model. According to the communication status (safe state and attacked state) between unmanned vehicles, divide the time interval into multiple sub-intervals with the same state and establish a switching system model. (3) Build a dynamic event triggering mechanism under asynchronous denial of service attacks; (4) Based on Lyapunov stability theory and switching system ideas, linear matrix inequality tools are used to obtain sufficient conditions for the unmanned vehicle cooperative system to maintain consistency under asynchronous denial of service attacks and the design method of various parameters of the dynamic event trigger mechanism; (5) Design a method for equivalent attenuation rate to effectively obtain the relationship between network attack intensity and dynamic event trigger mechanism parameters. In actual production, event triggering can be designed according to the actual network environment and production needs.

2. The design method of dynamic event triggering mechanism in unmanned vehicle cooperative system under asynchronous denial of service attack according to claim 1 is characterized by: The model of the unmanned vehicle cooperative system in step (1) is defined as follows: Where i∈N is the number of the unmanned vehicle, x i (t) is the state of the ith unmanned vehicle. Its dimension is related to the type of unmanned vehicle in reality and usually includes parameter variables such as position, speed, angular velocity, acceleration, etc. i (t) is the input of the i-th unmanned vehicle, y i (t) is the output of the i-th unmanned vehicle, and A, B, and C are matrices of appropriate dimensions.

3. The design method of dynamic event triggering mechanism in unmanned vehicle cooperative system under asynchronous denial of service attack according to claim 1, characterized in that: The model of the asynchronous denial of service attack in step (2) is defined as follows: Denial of service attacks can cause transmission channel blockage, resulting in signal transmission failure. Considering the limited energy of network attackers, the method of establishing an attack model limited in duration dimension is as follows: Among them, |D ij (t1, t2)| is the sum of the duration of the DoS attack on the ij channel in the time interval (t1, t2), is a positive real number, 0<μ ij <1; The method for establishing the switching system model in step (2) includes: Γ(t)={(i,j)∈ε|t∈D ij (0,∞)}; Among them, Γ(t) is the set of transmission channels in the denial of service attack interval at time t; Among them, Γ(t) (t1, t2) represents the set of time intervals divided by Γ(t), and then by different E Γ(t) (t1, t2) is used as the switching vector to establish the switching system model.

4. The design method of dynamic event triggering mechanism in unmanned vehicle cooperative system under asynchronous denial of service attack according to claim 1, characterized in that: The design method of the dynamic event triggering mechanism in step (3) is as follows: The method for designing the event trigger function of the event trigger mechanism is: Among them, η i (t) is a dynamic variable related to the dynamic event triggering mechanism and the internal information of the system, is the observation error, ξ i ,θ i is a positive real number, Φ i is a symmetric positive definite matrix of appropriate dimension.

5. The design method of dynamic event triggering mechanism in unmanned vehicle cooperative system under asynchronous denial of service attack according to claim 1, characterized in that: The sufficient conditions for the unmanned vehicle cooperative system to maintain consistency under asynchronous denial of service attacks and the design method of each parameter of the dynamic event trigger mechanism in step (3) are as follows: Set scalar ξ i > 0, if the unmanned vehicle cooperative system can achieve consistency, then there exists a positive definite matrix P∈R n×n and the positive definite matrix Φ i ∈R n×n , so that the following linear matrix inequality holds: where K = B T P, Φ are symmetric positive definite matrices and satisfy: ρ * = min(ρ1ρ2...ρ N ), ρ * = max(ρ1ρ2...ρ N ), θ * = min(θ1θ2...θ N ), ξ * = min(ξ1ξ2...ξ N ).

6. The design method of dynamic event triggering mechanism in unmanned vehicle cooperative system under asynchronous denial of service attack according to claim 1, characterized in that: The method for effectively obtaining the relationship between the network attack intensity and the dynamic event triggering mechanism parameters in step (5) is as follows: The design method of the equivalent attenuation rate includes: If the unmanned vehicle cooperative system can maintain consistency under the attack of asynchronous denial of service attack, then there is a constant and So that the following inequality holds: in, and is the equivalent attenuation rate, which is the equivalent value of the attenuation rate of each subsystem of the unmanned vehicle cooperative system, The attack intensity of asynchronous denial of service attack.

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