Multi-agent sliding mode safety control method based on dynamic event triggering under hybrid network attack

Abstract

The invention discloses a multi-agent sliding mode safety control method based on dynamic event triggering under hybrid network attack, and the control method comprises the following steps: building a multi-agent system model comprising spoofing attack and DoS attack; in order to cope with hybrid network attacks, an integral sliding mode surface function is constructed, an online estimation method is provided, and an unknown network attack mode can be estimated in real time in the absence of prior information; a novel self-adaptive sliding mode controller is developed, and the accessibility of a preset sliding mode surface is ensured; by introducing an auxiliary variable, a dynamic and static event triggering mechanism in the framework is considered, so that the use of communication resources is minimized; a Lyapunov stability theory and a finite time method are utilized to analyze the convergence of the multi-agent system under the control strategy. According to the control method provided by the invention, the influence of spoofing attack and DoS attack on the system can be eliminated, so that the state of the multi-agent system is consistent within finite time.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-agent systems, and particularly to a multi-agent sliding mode security control method based on dynamic event triggering under hybrid cyber attacks. Background Art

[0002] In recent years, the research on multi-agent problems has received extensive attention in the field of control science and engineering. As the main problem of cooperative control of multi-agent systems, consensus control plays an important role in multi-agent cooperative control. It involves designing controllers that utilize local information while considering various initial conditions and network topology constraints to ensure the convergence of the states of all agents. The research results of consensus control have been widely applied in engineering fields such as unmanned aerial vehicle (UAV) development, sensor networks, multi-sensor information fusion, and satellite cluster attitude.

[0003] However, in practical engineering applications, since the hardware scale of multi-agents is a multiple of that of a single agent, the possibility of being attacked by a network is correspondingly multiplied. Taking the UAV cluster system as an example, during the process of UAV formation performing tasks, each UAV will be attacked by a network to varying degrees. These attacks will, on the one hand, affect the attitude of the individual itself, and on the other hand, affect the information interaction between it and other individuals, thereby affecting the control of the entire system. Network attacks are generally divided into denial-of-service (DoS) attacks and spoofing attacks. DoS attacks interrupt data transmission by blocking the communication network, and spoofing attacks deceive victims by tampering with the transmitted data packets.

[0004] Chinese Patent Application Publication No.: CN118760174A, discloses a sliding mode control method for multi-agents under DoS attacks; Chinese Patent Application Publication No.: CN119758851A, discloses a design method for an event-triggered consensus control protocol for an uncertain nonlinear multi-agent system under DoS attacks. However, there are still the following problems in the existing technologies. Although various control strategies have been proposed to achieve the consensus control of multi-agent systems, most of the existing methods rely on fixed triggering conditions and are difficult to adapt to dynamically changing environments and system states. In addition, the existing research mainly focuses on a single type of network attack, and the research on consensus control against hybrid cyber attacks is relatively less.

[0005] Therefore, it is of great significance to develop an event-triggered sliding mode control technology that can achieve consensus tracking of multi-agent systems under hybrid cyber attacks.

[0006] It should be noted that this part aims to provide background or context for the embodiments of the present invention stated in the claims. The description herein is not admitted to be prior art merely because it is included in this part. Summary of the Invention

[0007] In view of the above research background, the present invention provides a multi-agent sliding mode safety control method based on dynamic event triggering, thereby overcoming at least to some extent one or more problems caused by the limitations and deficiencies of the related art.

[0008] The present invention provides a multi-agent sliding mode safety control method based on dynamic event triggering, and the method includes the following steps:

[0009] Step S1: Establish a multi-agent system model including spoofing attacks and DoS attacks;

[0010] Step S2: Determine the communication topology structure of the multi-agent system;

[0011] Step S3: To cope with hybrid network attacks, an integral sliding mode surface function is constructed, and an integral term is introduced to compensate for the initial error of the system and the influence of network attacks;

[0012] Step S4: By introducing auxiliary variables, a dynamic event triggering mechanism is established;

[0013] Step S5: Develop a new type of adaptive dynamic event-triggered sliding mode controller, and according to the Lyapunov stability theory, verify that the multi-agent system achieves consensus tracking under the action of the designed consensus control method.

[0014] The further improvement of the solution of the present invention lies in: the implementation process of the step S1 is as follows:

[0015] Step S1.1: Determine the dynamic model of the leader as shown in (1):

[0016]

[0017] Where respectively represent the position state variable and the velocity state variable of the leader, u0(t) represents the control input, represents the nonlinear dynamics.

[0018] Step S1.2: Determine the dynamic model of the follower including hybrid network attacks as shown in (2):

[0019]

[0020] Where respectively represent the position state variable and the velocity variable of the i-th agent, represents the control input of the system, represents the nonlinear function of the system.

[0021] Step S1.3: Make assumptions for the inherent nonlinearity:

[0022] ||f(xi , v i , t) - f(x0, v0, t)|| ≤ h1||x i - x0|| + h2||v i - v0||,

[0023] where h1 and h2 are non - negative numbers.

[0024] Step S1.4: The deception attack against the controller is a typical attack form, which usually has the following characteristics: The enemy has complete knowledge of the system information, that is, the system state can be exploited by the attacker. And the enemy has the ability to inject false data on the communication channel between the controller and the actuator, thereby attacking the communication network between the agent i and its neighbor agent j. Under the false data injection attack, the control input received by the actuator is as follows:

[0025]

[0026] where u i (t) is the designed control input, W(t)Φ(x i (t), t) is the attack signal, that is, the false data injected by the attacker. The matrix W(t) represents the injection pattern of the false data, and Φ(x i (t), t) is a function of x i (t), that is, the false data generated by the state x i (t).

[0027] Step S1.5: The purpose of the DoS attack is to block the communication channel and make the target system unable to exchange information normally. Define the time interval set during which the communication is blocked (the interval time of the DoS attack) as

[0028]

[0029] Similarly, the time interval set without attack is

[0030] Ξ s (t1, t2) = [t1, t2]\Ξ a (t1, t2) (5)

[0031] A further improvement of the solution of the present invention lies in: The implementation process of the said step S2 is as follows:

[0032] Consider a directed graph G = (V, E, A), where the node set V = {1,..., N}, the edge set E = {(i, j), i, j ∈ V}, and the adjacency matrix A = [a ij N×N . If (j, i) ∈ E, then a ij > 0; otherwise a ij ​= 0. The Laplacian matrix of the directed graph G associated with the adjacency matrix A is denoted as L = [l ij N×N , and its elements are defined as follows:

[0033]

[0034] In a directed graph, a directed path from node i to node j is a series of edges (i, i1), (i, i2),..., (i k , j) ∈ E, where the nodes i l , l = 1,..., k are distinct. If there exists a root node in the directed graph G and there are directed paths from this node to any other node, then G is said to contain a directed spanning tree.

[0035] The communication topology among the followers is represented by a directed graph G, and its corresponding Laplacian matrix L is given by Equation (2.1). The communication topology between the leader and the followers is characterized by a diagonal matrix B = diag{b1,..., b N}. b i > 0 indicates that the ith follower can receive information sent by the leader, while b i = 0 indicates that the ith follower cannot obtain information from the leader. The communication topology of the entire system can be represented by an extended directed graph , which includes the connection relationships between the leader and all its followers.

[0036] A further improvement of the solution of the present invention lies in that the implementation process of step S3 is as follows:

[0037] Step S3.1: Define two consensus error functions as:

[0038]

[0039] For the convenience of studying multi-agent systems, the compact forms of the two consensus error functions can be expressed as:

[0040]

[0041] Step S3.2: Design the distributed integral sliding mode surface as:

[0042]

[0043] Next, Equation (9) is transformed into the following compact form:

[0044]

[0045] where S(t) = [S1(t), S2(t), …, S N (t)] T ,​ H = L + B.

[0046] A further improvement of the solution of the present invention lies in that the implementation process of step S4 is as follows:

[0047] Step S4: To further reduce the communication burden, the present invention proposes a dynamic event-triggering mechanism based on storing past states, current states, and dynamic parameters. Compared with the static event-triggering mechanism, it can better adapt to system changes and improve efficiency. The dynamic trigger function can be described as:

[0048]

[0049] where κ = γ2 - 1 / c, and c > 0, χ i (t) is an auxiliary variable satisfying the following conditions:

[0050]

[0051] where 0 < a i <ξ i <1, and the initial value χ i (0) > 0.

[0052] Each agent performs a triggering operation according to its independent event-triggering condition. During the interval between two triggers, the various parameters of the controller remain constant. The trigger moment can be represented by the following inequality:

[0053]

[0054] The above trigger condition satisfies the event-triggering protocol, ensuring that the system states can reach an agreement. At the same time, Zeno behavior can be excluded.

[0055] A further improvement of the solution of the present invention lies in that the implementation process of step S5 is as follows:

[0056] Step S5.1: Based on the distributed integral sliding mode surface in (9), a dynamic event-triggering sliding mode safety control protocol is designed:

[0057]

[0058] where and represent the last update times of the i-th agent and the j-th agent respectively, and is the estimated value of μ i (t),

[0059] Step S5.2: And to cope with hybrid network attacks, the following adaptation law is designed:

[0060]

[0061] where θ is a selected positive constant, and the auxiliary function σ i (t) is constructed as follows:

[0062]

[0063] where β > 0 represents the attenuation rate, and the auxiliary parameter According to the Lyapunov stability theory, it is verified that the multi-agent system achieves leader-following consensus tracking under the action of the designed consensus control method.

[0064] Beneficial effects: For a multi-agent system containing deception attacks and DoS attacks, the distributed integral sliding mode security consensus tracking control problem is studied. To cope with hybrid network attacks, the present invention constructs an integral sliding mode surface function and proposes an online estimation method, which can perform real-time estimation of unknown network attack patterns in the absence of prior information. Based on this, a novel adaptive sliding mode controller is developed to ensure the reachability of the preset sliding mode surface. Using the Lyapunov stability theory and the finite-time method, the convergence of the multi-agent system under this control strategy is analyzed. In addition, by introducing auxiliary variables, the dynamic and static event-triggering mechanisms within the framework are considered to minimize the use of communication resources. Generally speaking, the present invention has the following advantages:

[0065] (1) To describe the nonlinear multi-agent system under hybrid network attacks, a dynamic model is established to describe its quantitative relationship. The DoS attack destroys the connectivity of the communication topology, while the integrity of the data is destroyed by injecting false data into the control signal.

[0066] (2) Compared with the existing control strategies, the present invention takes into account the harmful effects of deception and DoS attacks. Combining the integral sliding mode control algorithm with dynamic triggering, a distributed sliding mode control scheme based on a dynamic triggering mechanism and an online evaluation strategy for false data injection attacks are proposed. The corresponding sufficient conditions are obtained through the Lyapunov stability and finite-time theory.

[0067] The multi-agent sliding mode security control method based on dynamic event triggering proposed by the present invention has high accuracy, strong security, high efficiency, not overly demanding hardware requirements, saves communication resources, has certain application significance, and can be applied to the consensus implementation problem of a class of multi-agents with hybrid network attacks. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 The flowchart of the present invention is shown.

[0069] Figure 2 Show the hybrid network attack signal diagram of the present invention.

[0070] Figure 3 Show the position state trajectory diagram of the system in the present invention.

[0071] Figure 4 Show the speed state trajectory diagram of the system in the present invention.

[0072] Figure 5 Show the representation diagram of the sliding mode trajectory in the present invention.

[0073] Figure 6 Show the internal dynamic variable evolution diagram in the present invention. Figure 7 Show the representation diagram of the triggering moment in the present invention. Detailed implementation manners

[0074] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the protection scope of the present invention.

[0075] In this exemplary embodiment, for a non-linear multi-agent with hybrid network attacks, a multi-agent sliding mode security control method based on dynamic event triggering is designed, including the following specific steps:

[0076] Step S1: Establish a multi-agent system model including spoofing attacks and DoS attacks, including the following specific steps:

[0077] Step S1.1: Determine the dynamic model of the leader as shown in (1):

[0078]

[0079] Where respectively represent the position state variable and speed state variable of the leader, u0(t) represents the control input, represents the non-linear dynamics.

[0080] Step S1.2: Determine the dynamic model of the follower including hybrid network attacks as shown in (2):

[0081]

[0082] Where respectively represent the position state variable and speed variable of the i-th agent, represents the control input of the system, Represents the non - linear function of the system.

[0083] Step S1.3: Make an assumption for the inherent non - linearity:

[0084] ||f(x i ,v i ,t)-f(x0,v0,t)||≤h1||x i -x0||+h2||v i -v0||,

[0085] where h1 and h2 are non - negative numbers.

[0086] Step S1.4: The deception attack on the controller is a typical form of attack, which usually has the following characteristics: The enemy has complete knowledge of the system information, that is, the system state can be exploited by the attacker. And the enemy has the ability to inject false data into the communication channel between the controller and the actuator, so as to attack the communication network between agent i and its neighbor agent j. Under the false data injection attack, the control input received by the actuator is as follows:

[0087]

[0088] where u i (t) is the designed control input, W(t)Φ(x i (t),t) is the attack signal, that is, the false data injected by the attacker. The matrix W(t) represents the injection pattern of the false data, and Φ(x i (t),t) is a function of x i (t), that is, the false data generated by the state x i (t).

[0089] Step S1.5: The purpose of the DoS attack is to block the communication channel and make the target system unable to exchange information normally. Define the set of time intervals during which the communication is blocked (the interval time of the DoS attack) as

[0090]

[0091] Similarly, the set of time intervals without attack is

[0092] Ξ s (t1,t2)=[t1,t2]\Ξ a (t1,t2) (5)

[0093] Step S2: Determine the communication topology of the multi - agent system, including the following steps:

[0094] Consider a directed graph \(G=(V, E, A)\), where the node set \(V = \{1,\ldots,N\}\), the edge set \(E=\{(i, j), i, j\in V\}\), and the adjacency matrix \(A = [a ij N×N \). If \((j, i)\in E\), then \(a ij > 0\); otherwise \(a ij = 0\). The Laplacian matrix of the directed graph \(G\) associated with the adjacency matrix \(A\) is denoted as \(L=[l ij N×N , and its elements are defined as follows:

[0095]

[0096] In a directed graph, a directed path from node \(i\) to node \(j\) is a series of edges \((i, i_1),(i, i_2),\ldots,(i k , j)\in E\), where the nodes \(i l , l = 1,\ldots,k\) are distinct. If there exists a root node in the directed graph \(G\) and there is a directed path from this node to any other node, then \(G\) is said to contain a directed spanning tree.

[0097] The communication topology among the followers is represented by a directed graph \(G\), and its corresponding Laplacian matrix \(L\) is given by Equation (2.1). The communication topology between the leader and the followers is characterized by a diagonal matrix \(B=\text{diag}\{b_1,\ldots,b N \}\). \(b i > 0\) indicates that the \(i\)-th follower can receive information sent by the leader, while \(b i = 0\) indicates that the \(i\)-th follower cannot obtain information from the leader. The communication topology of the entire system can be represented by an extended directed graph , which includes the connection relationships between the leader and all its followers.

[0098] Step S3: To cope with hybrid network attacks, an integral sliding mode surface function is constructed, including the following steps:

[0099] Step S3.1: Define two consensus error functions as:

[0100]

[0101] For the convenience of studying multi-agent systems, the compact forms of the two consensus error functions can be expressed as:

[0102]

[0103] According to the consensus error, we can obtain

[0104]

[0105] ​​Step S3.2: The distributed integral sliding mode surface is designed as:

[0106]

[0107] By introducing an integral term to compensate for the initial error of the system and the influence of cyber attacks, it is ensured that the system state converges to the sliding mode surface within a finite time.

[0108] Next, equation (10) is transformed into a compact form as follows:

[0109]

[0110] where S(t)=[S1(t),S2(t),…,S N (t)] T , H = L + B.

[0111] Step S4: To further reduce the communication burden, a dynamic event-triggering mechanism based on storing past states, current states, and dynamic parameters is proposed. Compared with the static event-triggering mechanism, it can better adapt to system changes and improve efficiency. The dynamic trigger function can be described as:

[0112]

[0113] where κ = γ2 - 1 / c, and c > 0, χ i (t) is an auxiliary variable that satisfies the following conditions:

[0114]

[0115] where 0 < a i < ξ i < 1, and the initial value χ i (0) > 0.

[0116] The measurement error of the event-triggering control strategy is designed as:

[0117]

[0118] Each agent performs a triggering operation according to its independent event-triggering condition. During the interval between two triggers, the various parameters of the controller remain constant. The trigger moment can be represented by the following inequality:

[0119]

[0120] The above trigger condition satisfies the event-triggering protocol, ensuring that the system states can reach an agreement. At the same time, Zeno behavior can be excluded.

[0121] Step S5: Develop a new type of adaptive sliding mode controller to ensure the reachability of the preset sliding mode surface, including the following steps:

[0122] Step S5.1: Based on the distributed integral sliding mode surface in (10), design a dynamic event-triggered sliding mode safety control protocol:

[0123]

[0124] where and represent the last update times of the i-th agent and the j-th agent respectively, and is the estimated value of μ i (t),

[0125] Step S5.2: And to cope with hybrid network attacks, design the following adaptation law:

[0126]

[0127] where θ is a selected positive constant, and The auxiliary function σ i (t) is constructed as follows:

[0128]

[0129] where β>0 represents the attenuation rate, and the auxiliary parameter

[0130] In adaptive control, the upper bound parameter μ i (t) of the unknown attack needs to be estimated online. If an unconstrained adaptation law is directly adopted, the parameter estimate value may grow infinitely (diverge) due to noise or interference, resulting in system instability. Ensure that the estimate value is always bounded. Therefore, a smooth projection function Proj is defined:

[0131]

[0132] Construct the following continuous function:

[0133]

[0134] where the real number 0<δ<1, is the upper bound of the given projection.

[0135] It should be noted that according to the embedded convex set hypothesis, we obtain the following useful properties:

[0136]

[0137] and

[0138]

[0139] According to Lyapunov stability theory, it is verified that the multi-agent system can achieve leader-follower consensus tracking under the action of the designed consensus control method.

[0140] Based on the above analysis, the main results of this embodiment are as follows:

[0141] First, consider the leader-follower nonlinear multi-agent system with deception attacks and Dos attacks. Under the action of the dynamic event-triggered sliding mode safety control protocol, the adaptation law, and the dynamic triggering condition, the states of the leader-follower nonlinear multi-agent system can be driven to the predefined distributed integral sliding mode surface (10) and remain on this surface thereafter.

[0142] Then, it can be obtained by using the Lyapunov stability theorem Therefore, despite the existence of hybrid cyber attacks, the positions and velocities of the multi-agents are forced to the distributed integral sliding mode surface and then remain on this surface, which means that the tracking error dynamics will persist on the surface of S i (t) = 0.

[0143] Once the tracking error dynamics reach the designed sliding surface, they will continue to slide along this sliding mode surface. Therefore, according to the sliding mode control theory, when the states of the multi-agents remain on the predefined integral sliding mode surface, there is It can be deduced that Combined with The following equation can be obtained:

[0144]

[0145] Combining (8) and (23), the sliding mode dynamics equation of the leader-follower nonlinear multi-agent is:

[0146]

[0147] Therefore, the adaptive sliding mode tracking control problem of the leader-follower continuous-time multi-agent with inherent nonlinear dynamics under hybrid cyber attacks is transformed into a sliding mode dynamic tracking control problem.

[0148] Considering the influence of hybrid cyber attacks on the multi-agent system, using the constructed dynamic event-triggered sliding mode safety control protocol (16), the states of the obtained sliding mode dynamics will reach leader-follower consensus.

[0149] It can be obtained by using the Lyapunov stability theorem At this time, the system (24) is globally asymptotically stable under the action of the controller, which means that the adaptive tracking performance of the leader-following continuous-time multi-agent system is guaranteed.

[0150] Compared with the traditional communication strategy that inefficiently utilizes communication resources, the present invention uses a dynamic event-triggered strategy, effectively saving resources, even when considering factors such as hybrid network attacks, system nonlinearity, and network transmission load. The sliding mode controller structure involved in the present invention is still simple and easy to implement.

[0151] The following combines specific simulation examples to further elaborate on this embodiment.

[0152] To prove the effectiveness of the proposed control strategy for leader-following multi-agents with hybrid network attacks, the present invention verifies the effectiveness of the proposed dynamic event-based adaptive sliding mode security control protocol through examples, which is applicable to leader-following consensus tracking under hybrid network attacks.

[0153] The simulation considers a multi-agent system composed of 5 agents. According to the leader-following topology, the adjacency matrix A, diagonal matrix D, and Laplacian matrix L of these multi-agents can be obtained as follows:

[0154] B = diag{1, 1, 0, 0}.

[0155] The dynamics of the leader are represented by the following model:

[0156]

[0157] The control input of the leader is u0 = 0.2sin(t).

[0158] The dynamics of the i-th follower are represented by the following model:

[0159]

[0160] In this simulation, the initial states of the leader's position and velocity are set as x0(0) = 0.1, v0(0) = 0, and the initial states of the followers' positions and velocities are x1(0) = 0.15, x2(0) = 0.1, x3(0) = 0.3, x4(0) = 0.12, v1(0) = -0.02, v2(0) = -0.02, v3(0) = -0.03, v4(0) = -0.01.

[0161] The hybrid network attack signal is as Figure 2 shown, and the false data W(t)Φ(x i (t), t) injected by the attacker is set as W(t) = [1, 1, 1, 1] and Φ a$\tau(t)=10x$ i $\sin(t)$. In this simulation, let $\eta_1 = 0.46$, $\eta_2 = 1.54$, $r = 2.664$, There are a total of 6 DoS attacks. The first DoS attack starts at $t = 3$ and ends at $t = 3.4$. The second DoS attack starts at $t = 6$ and ends at $t = 7$. The third DoS attack starts at $t = 9$ and ends at $t = 9.4$. The fourth DoS attack starts at $t = 12$ and ends at $t = 13$. The fifth DoS attack starts at $t = 15$ and ends at $t = 15.4$. The sixth DoS attack starts at $t = 18$ and ends at $t = 18.9$.

[0162] In addition, the parameters $\zeta_1 = 3$, $\zeta_2 = 0.1$ can be obtained. The coefficients $\alpha_1$, $\alpha_2$, $\gamma_1$, $\gamma_2$ of the dynamic event-triggered sliding mode safety control protocol are set to $\alpha_1 = 2$, $\alpha_2 = 0.75$, $\gamma_1 = 3.2$, $\gamma_2 = 0.1$ respectively. The coefficients in the dynamic trigger condition are designed as $\kappa = 0.5$, $a$ i $= 0.3$, $\xi$ i $= 0.3$. Figure 3-4 Shows the tracking trajectory of the multi-agent system under the dynamic event-triggered sliding mode control protocol proposed in the present invention. The results show that under the hybrid network attack, the closed-loop multi-agent system can achieve consensus tracking. It should be noted that the DoS attack interval is only effective when the topology becomes disconnected due to the DoS attack. During the effective DoS attack interval, the control input of each agent is set to 0 to save energy, and the auxiliary variable $\chi$ i $(t)$ evolves as Figure 6 shown, Figure 5 shows the sliding mode surface trajectory of the followers. Figure 7 Shows the triggering moments of four agents under the dynamic event-triggered control.

[0163] In summary, this case can show that the control method is effective.

[0164] This method designs a dynamic event-triggered sliding mode safety control method for dealing with second-order nonlinear multi-agent systems with hybrid network attacks. The characteristics of this method are that for nonlinear multi-agent systems with spoofing attacks and DoS attacks, a new type of adaptive sliding mode controller is developed based on adaptive control, dynamic event-triggered control, and integral sliding mode control algorithms, ensuring the reachability of the preset sliding mode surface. The dynamic variable $\chi$ in the dynamic event-triggered mechanism i can reduce the triggering times, save network resources, and avoid the occurrence of Zeno behavior. The integral sliding mode algorithm can effectively cope with the impact of hybrid network attacks on multi-agent systems. Compared with the conventional sliding mode control, this control law has a faster convergence speed, a limited convergence time, higher robustness, and more savings in network resources.

[0165] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A multi-agent sliding mode security control method based on dynamic event triggering under hybrid network attacks, characterized in that: It includes the following specific steps: Step S1: Establish a multi-agent system model including spoofing attacks and DoS attacks; Step S2:: Determine the communication topology of the multi-agent system; Step S3: To cope with hybrid cyber attacks, an integral sliding mode surface function is constructed, and an integral term is introduced to compensate for the initial error of the system and the impact of cyber attacks; Step S4: By introducing auxiliary variables, a dynamic event-triggering mechanism is established; Step S5: Develop a new type of adaptive dynamic event-triggering sliding mode controller. According to Lyapunov stability theory, it is verified that the multi-agent system achieves consensus tracking under the designed consensus control method.

2. The multi-agent sliding mode safety control method based on dynamic event triggering according to claim 1, wherein: The specific process of the said Step S1 is as follows: Step S1.1: Determine the dynamic model of the leader as shown in (1): where represent the position state variable and velocity state variable of the leader respectively, and u0(t) represents the control input, represents the nonlinear dynamics; Step S1.2: Determine the dynamic model of the follower including hybrid cyber attacks as shown in (2): wherein respectively represent the position state variable and velocity variable of the $i$-th agent, represents the control input of the system, represents the nonlinear function of the system; Step S1.3: Make assumptions about the inherent nonlinearity: ||f(x i ,v i ,t)-f(x0,v0,t)|| ≤ h1||x i -x0|| + h2||v i -v0||, where h1 and h2 are non-negative numbers; Step S1.4: The spoofing attack on the controller is a typical attack form, which usually has the following characteristics: The enemy has complete knowledge of the system information, that is, the system state can be exploited by the attacker, and the enemy has the ability to inject false data into the communication channel between the controller and the actuator, so as to attack the communication network between agent i and its neighbor agent j. Under the false data injection attack, the control input received by the actuator is as follows: where u i (t) is the designed control input, and W(t)Φ(x i (t),t) is the attack signal, that is, the false data injected by the attacker. The matrix W(t) represents the injection pattern of the false data, and Φ(x i (t),t) is a function of x i (t), that is, the false data generated by the state x i (t). Step S1.5: The purpose of the DoS attack is to block the communication channel and make the target system unable to exchange information normally. Define the time interval set during which the communication is blocked (the interval time of the DoS attack) as The time interval set without attack is Ξ s (t1, t2) = [t1, t2] \ Ξ a (t1, t2) (5).

3. The multi-agent sliding mode safety control method based on dynamic event triggering according to claim 1, characterized in that: The specific process of the said Step S2 is as follows: Consider a directed graph \(G=(V, E, A)\), where the node set \(V = \{1,\ldots,N\}\), the edge set \(E=\{(i, j), i, j\in V\}\), and the adjacency matrix \(A = [a ij N×N , if \((j, i)\in E\), then \(a ij > 0\); otherwise \(a ij = 0\). The Laplacian matrix of the directed graph \(G\) associated with the adjacency matrix \(A\) is denoted as \(L=[l ij N×N , and its elements are defined as follows:​​ In a directed graph, a directed path from node i to node j is a series of edges (i, i1), (i, i2),..., (i k , j) ∈ E, where the nodes i l , l = 1,..., k are all distinct. If there exists a root node in the directed graph G and there is a directed path from this node to any other node, then G is said to contain a directed spanning tree; The communication topology among the followers is represented by a directed graph $G$, and its corresponding Laplacian matrix $L$ is given by Eq. (2.1). The communication topology between the leader and the followers is characterized by a diagonal matrix $B = diag\{b_1,...,b N \}$, where $b i > 0$ indicates that the $i$-th follower can receive information sent by the leader, while $b i = 0$ indicates that the $i$-th follower cannot obtain information from the leader. The communication topology of the entire system can be represented by an extended directed graph , which includes the connection relationships between the leader and all its followers.

4. The multi-agent sliding mode safety control method based on dynamic event triggering according to claim 1, characterized in that, The specific process of the said Step S3 is as follows: Step S3.1: Define two consensus error functions as: For the convenience of studying the multi-agent system, the compact form of the two consensus error functions can be expressed as: Step S3.2: The distributed integral sliding mode surface is designed as: Next, convert Equation (9) into a compact form as follows: Among them 5. The multi-agent sliding mode safety control method based on dynamic event triggering according to claim 1, characterized in that: The specific process of the said Step S4 is as follows: Step S4: To further reduce the communication burden, the present invention proposes a dynamic event-triggering mechanism based on storing past states, current states, and dynamic parameters. Compared with the static event-triggering mechanism, it can better adapt to system changes and improve efficiency. The dynamic trigger function can be described as: f(ε i ,S i ,t) = F a (t)[||ε i (t)|| 2 -κ||S i (t)|| 2 -χ i (t) (11) where κ = γ2 - 1 / c, and c > 0, χ i (t) is an auxiliary variable satisfying the following conditions: where \(0 < a\) i <\xi i < 1, and the initial value \(\chi\) i (0)>0; Each agent performs a triggering operation according to its independent event triggering condition. During the interval between two triggerings, each parameter of the controller remains constant. The triggering moment can be represented by the following inequality: The above trigger condition satisfies the event-triggering protocol, ensuring that the system states can reach consensus and excluding Zeno behavior at the same time.

6. The multi-agent sliding mode safety control method based on dynamic event triggering according to claim 1, characterized in that: The specific process of the said Step S5 is as follows: Step S5.1: Based on the distributed integral sliding mode surface in (9), a dynamic event-triggering sliding mode safety control protocol is designed: Among them and respectively represent the last update times of the $i$-th agent and the $j$-th agent, and is the estimated value of $\mu$ i (t), Step S5.2: And to cope with hybrid cyber attacks, the following adaptive law is designed: where θ is a selected positive constant, and the auxiliary function σ i (t) is constructed as follows: where β > 0 represents the attenuation rate, and the auxiliary parameter τ = cò[ζ1||e1|| 2 + ζ2||e2|| 2 , ò = ||L + B||||(L + B) -1 ||. According to the Lyapunov stability theory, it is verified that the multi-agent system achieves leader-following consensus tracking under the action of the designed consensus control method.

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