Adaptive Event-Triggered Security Control Method for Multi-Agent Systems Under Deception Attacks

Abstract

An adaptive event-triggered security control method for multi-agent systems under deception attacks is proposed, involving event-triggered control of multi-agent systems. Based on graph theory, the communication topology graph, adjacency matrix, and Laplace matrix of the system are defined. It is assumed that the communication topology between multi-agent systems is randomly switched, and the switching process follows a continuous-time Markov process. The assumptions about the communication topology graph are relaxed, requiring that the union of all possible communication topologies be undirected and connected, without requiring each switching subgraph to be connected. A deception attack is modeled, an upper bound on the attack signal is set, and the objective function for system security control under deception attacks is defined. An event-triggered distributed adaptive security control strategy is designed, and the state of neighboring agents is estimated using observer techniques. The effectiveness of the control strategy in ensuring system security under Markov random switching of communication topologies is verified through simulation using Lyapunov stability theory, stochastic analysis, and linear matrix inequality methods.

Description

Technical Field

[0001] This invention belongs to the field of event-triggered control of multi-agent systems, and in particular relates to an adaptive event-triggered security control method for multi-agent systems under deception attacks and observer-based deception attacks under Markov random switching communication topologies. Background Technology

[0002] With the widespread application of networked control systems, the theory of Multi-Agent Systems (MAS) has been widely applied in engineering fields such as power networks, multiprocessor networks, autonomous vehicles, and intelligent transportation. The control problem of MAS has attracted widespread attention from researchers. In real-world network environments, continuous communication can lead to congestion, resulting in longer communication delays and increased packet loss. Furthermore, the limited energy of agents and the limited network bandwidth are also issues that must be considered in practical applications. The purpose of designing event-triggered security controls is to solve the problem of network congestion, thereby effectively reducing the number of control tasks executed and saving communication and computing resources.

[0003] Multi-agent systems rely heavily on network communication. While the development of network communication and information technology facilitates system functional expansion, it also presents greater security challenges. Network security control for multi-agent systems primarily addresses potential security issues, such as defending against common network attacks.

[0004] Security control for multi-agent systems includes any means specifically designed to prevent data attacks, such as denial-of-service attacks and spoofing attacks. Reference 1 (He, Wangli and Mo, Zekun. Secure Event-Triggered Consensus Control of Linear Multiagent Systems Subject to Sequential Scaling Attacks. IEEE Transactions on Cybernetics, 2022, 52(10): 10314-10327.) proposes a security control protocol against sequence scaling attacks. Reference 2 (Liu, Jinliang and Wang, Yuda and Cao, Jinde and Yue, Dong and Xie, Xiangpeng, Jianlong. Secure Adaptive-Event-Triggered Filter Design With Input Constraint and Hybrid CyberAttack. IEEE Transactions on Cybernetics, 2021, 51(8), 4000-4010.) proposes a security control protocol to protect against various network attacks.

[0005] In multi-agent systems, agents collaborate through a communication network to complete predetermined tasks. However, the random switching characteristics of communication networks and the potential risk of spoofing attacks pose significant challenges to the system's security control. Factors such as packet loss can temporarily disrupt communication between neighboring agents, altering the communication topology. Furthermore, the openness and shared nature of wireless communication technologies make multi-agent systems vulnerable to network attacks, and not all real-time information is observable during communication within such systems. Summary of the Invention

[0006] The purpose of this invention is to address the aforementioned difficulties in the prior art by providing an adaptive event-triggered security control method for multi-agent systems under deception attacks, based on observer technology and event-triggered strategies, thus overcoming the impact of random topology switching and deception attacks on multi-agent systems. This invention proposes an observer-based event-triggered adaptive gain security control protocol to solve the adaptive event-triggered security control problem of multi-agent systems with general linear dynamics under randomly switching communication topologies when subjected to deception attacks.

[0007] First, based on graph theory and Markov processes, a stochastic switching communication topology for the multi-agent system is given. Relative observation information between the system and its neighboring agents is obtained through observers. Next, a dynamic model of the multi-agent system is established, along with an objective function for its security control. Finally, a distributed adaptive security control method is presented to defend against deception attacks under the Markov stochastic switching communication topology. An event-triggered mechanism is used to update the control signal, and the proposed adaptive security control method is verified to ensure the multi-agent system can achieve tracking control tasks.

[0008] The adaptive event-triggered security control method for multi-agent systems under deception attacks described in this invention includes the following steps:

[0009] Step 1: Without loss of generality, assume that the multi-agent system consists of N agents, numbered 1,...,N; define the system's communication topology graph, adjacency matrix, and Laplace matrix based on graph theory; secondly, assume that the communication topology between the multi-agent system is randomly switched, and that this switching process can be described by an traversed continuous-time Markov random process.

[0010] The first step is to define the communication topology graph of the multi-agent system based on graph theory. Its edge set represents the communication relationships between agents;

[0011] The second step is to provide the adjacency matrix of the communication topology graph. and Laplace matrix

[0012] Third, assume that the communication topology between the multi-agent system switches randomly, and this switching process is described by a continuous-time Markov random process. The communication graph of N agents switches across s graphs, represented as follows:

[0013] Step 2: Assume the communication topology of the multi-agent system; assume the union of all possible communication topologies between agents. It is undirected and connected, and it is not required that every switching subgraph is connected, thus relaxing the assumptions about the communication topology graph. The corresponding adjacency matrix and Laplace matrix are respectively and

[0014] Step 3: Model the deception attack hypothetically. Based on the stealth nature of the deception attack, assume an upper bound for the deception attack signal.

[0015] The first step is to establish a deception attack model for a multi-agent system, where the probability of an agent being attacked follows a Bernoulli random distribution.

[0016] The second step is to assume that the upper bound of the attack energy is assumed because the energy injected into the agent by the attack is generally limited, given that the amplitude or energy of the attack signal does not exceed a given threshold τ.

[0017] Step 4: Observe the state of neighboring agents using observer technology, design an event-triggered distributed adaptive security control method for multi-agent systems to defend against deception attacks under Markov random switching communication topology, and use Lyapunov stability theory, stochastic analysis method and linear matrix inequality method to verify that the proposed adaptive security control can ensure that the multi-agent system achieves the security control goal. Finally, simulation verification is performed.

[0018] The first step is to design an observer model based on relative output information and give an event triggering strategy, whose event triggering function only needs to use its own output information and observer information to make judgments.

[0019] The second step is to consider the impact of random and energy-limited deception attacks, design a distributed feedback controller based on observer information, and establish a corresponding multi-agent system closed-loop error model.

[0020] The third step is to verify the effectiveness of the control method based on Lyapunov stability theory and the linear matrix inequality method.

[0021] The fourth step is to verify that the designed event triggering strategy will not trigger an unlimited number of times within a finite time, thereby eliminating Zeno behavior caused by event triggering.

[0022] The fifth step, based on Schul's lemma, proposes a method for solving the controller gain matrix and the observer gain matrix;

[0023] The sixth step is to perform simulation in Simulink to verify whether the designed event triggering strategy and controller can meet the control objectives.

[0024] The beneficial effects of this invention are as follows:

[0025] This invention designs a distributed adaptive tracking control method for multi-agent systems under Markov random switching communication topologies. Combining an event-triggered strategy and observer technology, the method enables each agent in the multi-agent system to automatically update its coupling gain using only local information from its neighbors under random topology switching, thereby designing a secure control method for multi-agent systems to counter spoofing attacks. This method can guarantee the performance and security of multi-agent systems in environments with uncertainty and attack threats, and is characterized by its distributed and adaptive nature, effectively handling the problems of random topology switching and spoofing attacks. Furthermore, since agents only update their control gains when necessary, this method can also reduce the communication and computational burden of the system. This invention provides an effective solution suitable for multi-agent systems operating in complex environments. By combining observer technology and an event-triggered strategy, this invention improves the robustness and security of the system, and has broad application prospects. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of the architecture of an embodiment of the present invention.

[0027] Figure 2 This represents the communication topology switching subgraph and the parallel graph.

[0028] Figure 3 This refers to the communication topology switching process.

[0029] Figure 4 This is the tracking trajectory along the X-axis.

[0030] Figure 5 The tracking trajectory is along the Y-axis.

[0031] Figure 6 The tracking trajectory error is denoted by X.

[0032] Figure 7 This represents the tracking trajectory error along the Y-axis.

[0033] Figure 8 This is the controller gain curve.

[0034] Figure 9 These are the trigger times for four aircraft events. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of this invention clearer, the following embodiments will be used in conjunction with the accompanying drawings to further illustrate the invention. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0036] Figure 1This paper presents an architecture diagram of an embodiment of the invention, illustrating a distributed security control protocol framework for a multi-agent system under deception attacks and Markov random switching communication topologies. The embodiment first defines a random switching communication topology for the multi-agent system based on graph theory and Markov processes. It then acquires relative observation information between itself and its neighboring agents through an observer. Next, it establishes a dynamic model of the multi-agent system and a target function for security control. Finally, it presents a distributed adaptive security control method for defending against deception attacks under a Markov random switching communication topology. This method uses an event-triggered mechanism to update control signals and verifies that the proposed adaptive security control method can ensure the multi-agent system achieves tracking and control tasks.

[0037] Step 1: Without loss of generality, assume that the multi-agent system consists of N agents, numbered 1,...,N. Define the system's communication topology graph, adjacency matrix, and Laplace matrix based on graph theory. Next, assume that the communication topology between the multi-agent systems switches randomly, and that this switching process can be described by an iterative continuous-time Markov random process.

[0038] Step 1.1: Define the communication topology of the multi-agent system based on graph theory. in Let E represent the set of agents in the network, and let E represent the set of edges that interact between agents. A directed edge (i,j)∈E starts from node i and ends at node j, indicating that agent j can receive information from agent i.

[0039] Step 1.2: Communication Topology Diagram adjacency matrix The definition is as follows:

[0040]

[0041] Its Laplace matrix Defined as:

[0042]

[0043] Step 1.3: Define a random switching communication topology based on Markov random processes. The communication graph represents time t. Randomly switch between s different graphs, that is and The distribution of the Markov process σ(t) is unique and invariant, i.e., π = [π1, ..., π]. s ] T satisfy And π p ≥0, p=1,...,s, when When σ(t) is distributed as π, where It is the set of positive real numbers.

[0044] Step 2: Give a general dynamic model of multi-agent systems, and design a corresponding observer model to observe the output state of the system for multi-agent systems under deception attack.

[0045] Step 2.1: When the information transmission process between intelligent agents is subjected to a deception attack, normal data will be injected with an attack signal ε. i Using Bernoulli random variable α i Describe a random deception attack, assuming the probability of the attack succeeding is... Considering the possibility of a deception attack, agent j receives the following information from agent i:

[0046]

[0047] Among them, y i (t) represents the output of agent i. α represents the output received by the neighboring agent after being attacked. i (t) represents the probability that the agent is attacked.

[0048] Assume the deception attack signal satisfies the following conditions:

[0049] ||ε i (t)‖ 2 ≤τ (2)

[0050] Where, ε i (t) represents the injected signal of the attack, and τ represents the upper bound of the injected signal.

[0051] Step 2.2: Establish a general linear dynamic model for multi-agent systems:

[0052]

[0053] Where, x i (t) represents the state of the agent, u i (t) is the input, y i (t) represents the output, A is the transition matrix, B is the input matrix, and C is the output matrix. The matrix pair (A,B) is stable, and the matrix pair (A,C) is observable.

[0054] In real-world systems, not all states are measurable; therefore, an observer is introduced.

[0055]

[0056] Where F is the observer gain matrix to be designed. For observation status, This is the output of the observation.

[0057] Step 3: Design an adaptive event-triggered strategy based on relative observers, provide a distributed adaptive controller based on event-triggered information, and establish a security control objective function for the multi-agent system.

[0058] Step 3.1: First, define the measurement error of agent i as: The initial time when the event is triggered is Design an observation-based adaptive event triggering strategy:

[0059]

[0060] Among them, ο i ∈(0,1), υ i It is a constant, ι i It is a positive constant, Γ = PBB T P,m i (t) is the defined measurement error. Undefined consistency error. It is an auxiliary variable and satisfies:

[0061]

[0062] in, η i >0,

[0063] Step 3.2: Define Consistency Error At the moment of two adjacent event triggering Design a distributed adaptive event-triggered control protocol:

[0064]

[0065] Where, d i (t) represents the adaptive gain, and the constant gain matrix is ​​K = B. T P, For time-varying weights, Let d be the estimated state of agent i at the trigger time. i For adaptive coupling gain and satisfying:

[0066]

[0067] Where, β i and It is a predefined constant, and d i The initial conditions of (t) are satisfied

[0068] Step 3.3: Define the mean state error make Based on stochastic analysis theory, an objective function for the security control of multi-agent systems under stochastically switched communication topologies is proposed. That is, for any initial state x(0), there exists a scalar e and a compact set. This allows the expectation of the consistency error δ(t) to converge to the compact set. In, that is:

[0069]

[0070] Where E is the expected value and t0 is the initial time.

[0071] Step 4: For multi-agent systems under Markov random communication topology switching and spoofing attacks, a distributed event-triggered adaptive security control method is proposed. Using Lyapunov stability theory, the proposed adaptive security control method is verified to ensure the multi-agent system achieves its control objective. The proposed event-triggered strategy is verified not to trigger an unlimited number of times within a finite time. Finally, the gain matrices of the observer and controller are given.

[0072] Step 4.1: Define the estimation error of agent i as... From the dynamic equations of the multi-agent system, the form of the deception attack, the designed observer and control protocol, and the variables defined above, we can obtain:

[0073]

[0074]

[0075] in, Therefore, we can obtain The matrix variables in the formula are defined as follows:

[0076] α(t)=diag{α1(t),α2(t),...,α N (t)}. To simplify the notation, the variable t will be omitted below.

[0077] Step 4.2: Construct the Lyapunov function:

[0078]

[0079] Among them, V 1p =E[Z T Θ p Z1 {σ(t)＝p} ], Z = [δ] T ,q T ] T , The multi-agent closed-loop system (11) can converge exponentially to a compact set. The conditions are:

[0080] For a given upper bound of attack τ, ο i ∈(0,1), κ>0, χ>0, probability matrix F, if there exists a positive scalar c, η i , ι i , ρ i And positive definite matrices P and Q such that:

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087] Established.

[0088] in,

[0089]

[0090] yes The smallest non-zero eigenvalue.

[0091] verify:

[0092] For a connected graph, according to:

[0093]

[0094] We can obtain V > 0. Differentiating the first term V1 of the Lyapunov function, we get:

[0095]

[0096] definition in The vector form can be: Combining Young's inequalities, we can obtain the following two inequalities:

[0097]

[0098]

[0099] The first equation holds because each subgraph is assumed to be undirected, therefore... And it uses equations

[0100] Depend on have We can obtain:

[0101]

[0102] From equation (20), combined with equations (21) and (22), we can obtain:

[0103]

[0104] Among them, the use

[0105] Consider the following formula:

[0106]

[0107] It uses formulas. And Young's inequality. At the same time, according to... The definition and some mathematical calculations yield the following results. for have:

[0108]

[0109] Depend on We can obtain:

[0110]

[0111] From the first term of (25), we can obtain:

[0112]

[0113] in,

[0114] Calculate the remaining terms of formula (20):

[0115]

[0116] Differentiating V2, we get:

[0117]

[0118] Combining (24), (25), (28)-(30), we can obtain:

[0119]

[0120] Based on the update law, the following analysis is made:

[0121] 1) If have:

[0122]

[0123] 2) If have:

[0124]

[0125] according to and Substituting (32) and (33) into (31) yields:

[0126]

[0127] From the adaptive event triggering strategy (5), we can obtain:

[0128]

[0129] make Substituting (35) into (34) and finally combining (13), we get:

[0130]

[0131] From V = V1 + V2, according to the complementarity lemma, we have:

[0132]

[0133] Then we have:

[0134]

[0135] According to inequality (14), we have:

[0136]

[0137] As t→∞, we have:

[0138]

[0139] That is, as t→∞, system (11) is asymptotically stable, and the error variable δ(t) converges to the compact set l. Verification complete.

[0140] Step 4.3: Exclude Zeno behavior of the event triggering strategy, i.e., it will not trigger an unlimited number of times within a finite time, to verify the feasibility of the event triggering strategy.

[0141] verify:

[0142] for From the dynamic event triggering condition (5), we get:

[0143]

[0144] Assumption For any two consecutive sampling times in [t0, t), for Differentiation yields:

[0145]

[0146] in, Ω i =GCq i -GFε i .

[0147] Integral both sides of (38):

[0148]

[0149] We can obtain:

[0150]

[0151] As can be seen from the definition Then we have:

[0152]

[0153] From step 4.2, we know that there exist positive constants θ1, θ2, ν such that the expectation of q is in The inner convergence rate ν converges to θ1, i.e. Therefore, there exists a positive constant. Makes the following inequalities true:

[0154]

[0155] in,

[0156] If ||A||≠0, then we have:

[0157]

[0158] Based on the dynamic event triggering strategy, we can obtain:

[0159]

[0160] Combining equation (47), we can obtain:

[0161]

[0162] Then we have:

[0163]

[0164] Verification has any finite interval

[0165] Next, verification As k approaches infinity. Assume the opposite corollary, i.e. It will not tend towards infinity. (Introducing the concept) and Then you can export and In equation (46) The value is a constant. Positive correlation, therefore it can be deduced that Therefore, from equation (50), we can obtain the following when k→∞:

[0166]

[0167] This is a contradiction. Therefore, the assumption is false, meaning that as k approaches infinity... It tends towards infinity. Zeno behavior can be excluded.

[0168] If ||A||=0, then The same logic applies.

[0169] In conclusion, Zeno behavior of agent i can be excluded.

[0170] Step 4.4: Based on Shure's lemma and linear matrix inequalities, simplify the inequality conditions in Step 4.2, and give the solution expressions for the gain matrices of the controller and observer. At this point, the multi-agent closed-loop system (11) can converge exponentially to a compact set. The conditions are:

[0171] If there exist positive definite matrices P and Q such that:

[0172]

[0173]

[0174]

[0175] χI n -Q<0 (55)

[0176] Established, among which Then the controller feedback gain matrix is ​​K = B T P, the observer gain matrix is ​​G = Q -1 X.

[0177] verify:

[0178] Substituting the parameters into equation (13), we get:

[0179]

[0180] Therefore:

[0181]

[0182] Ψ+κQ<0 (58)

[0183] Define X = QG, and by Schuler's complement lemma, we can obtain:

[0184]

[0185] Substituting the parameters into equation (14) yields:

[0186]

[0187] Clearly, equation (60) is equivalent to:

[0188]

[0189] χI n -Q<0 (62)

[0190] When equations (57), (58), (61), and (62) hold, equations (13) and (14) also hold. Furthermore, according to the definitions of X and K, the controller gain and observer gain can be calculated as K = B. T P and G=Q -1 X. Verification complete.

[0191] Step 4.5: Based on the designed observer, event triggering strategy and control protocol, conduct simulation verification under the scenarios of Markov topology switching and spoofing attacks.

[0192] Ten spacecraft examples are used for verification. The relative dynamic equations of the i-th spacecraft and the reference point can be described as follows:

[0193]

[0194] Where x i y i and z i The relative position of the i-th spacecraft and the reference point is represented by ω, the orbital angular velocity of the reference point is represented by μ, the Earth's lexical coefficient is represented by r, and the distance between the reference point and the Earth's center of gravity is represented by a; ix a iy and a iz This indicates the control input for the three axes.

[0195] The dynamic model (63) can be rewritten using the state-space model (3) as follows:

[0196]

[0197] in, The matrix pair (A, B) is stabilized, and the matrix pair (A, C) is observable. The controller gain matrix and observer gain matrix are calculated according to step 4.4.

[0198] Considering the scenarios of multi-space vehicles under Markov topology switching and deception attacks, Figure 2 The topology switching subgraph and merge graph are shown for topology switching caused by random communication failures of multiple spacecraft. The communication topology switching process is as follows: Figure 3 As shown.

[0199] The spacecraft flies in the same plane; draw the tracking trajectories along the X and Y axes, respectively, as follows: Figure 4 and 5 As shown. From Figure 4 and Figure 5 The tracking trajectory shows that the aircraft's position trajectory on the X and Y axes quickly converges to the desired trajectory, indicating that the control strategy can effectively guide the aircraft's motion.

[0200] Plot the tracking error on the X-axis and Y-axis respectively, as follows: Figure 6 and 7 As shown in the figure, the error can be converged over a large range within 10 seconds, and the final stable error can be within 0.5 meters, verifying that the controller designed according to the present invention can achieve the control objective.

[0201] Figure 8 The gain curve of the controller is represented by... Figure 8 It can be seen that the controller gain eventually converges to a stable value. This indicates that the controller parameter adjustment is effective and the system has good robustness. Figure 9 The event trigger times for the 1st, 4th, 7th, and 10th aircraft are indicated. It can be seen that the designed event triggering strategy will not trigger an unlimited number of times within a finite time, and can effectively reduce unnecessary communication and save communication resources.

[0202] Experiments show that the multi-agent system and its control strategy designed in this invention can still achieve accurate trajectory tracking and effectively save communication resources even when faced with uncertainties such as random communication failures and Markov topology switching. This fully verifies the effectiveness and practicality of the method of this invention.

[0203] This invention can be applied to, but is not limited to, the following fields: In the field of network security, this method can be used to design more secure network protocols and defense mechanisms to resist network attacks such as man-in-the-middle attacks, phishing attacks, and DDoS attacks. In drone swarm flight, this method can help ensure the security of communication between drones to maintain swarm stability and complete predetermined tasks. In intelligent transportation systems, this method can be applied to vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communication to improve traffic safety and flow management. In industrial automation and remote monitoring systems, this method can be applied to ensure the continuity and security of production processes, especially in the face of malicious attacks. In smart grids, this method can be applied to ensure the stable supply and effective distribution of power systems and prevent power outages caused by malicious attacks. In financial markets, this method can be applied to design more robust algorithmic trading strategies and improve the regulatory capabilities of financial markets to prevent fraud and market manipulation. In the field of emergency response, such as fire fighting and earthquake rescue, this method can be applied to establish reliable communication networks to effectively coordinate actions in emergency situations. Through the above applications, this method can improve the security and reliability of systems at multiple levels, especially in the face of uncertainty and malicious attacks.

[0204] The above embodiments are merely preferred embodiments of the present invention and should not be considered as limiting the scope of the present invention. All equivalent variations and improvements made within the scope of the present invention should still fall within the patent coverage of the present invention.

Claims

1. An adaptive event-triggered security control method for multi-agent systems under deception attacks, characterized in that... Includes the following steps: Step 1: Assume the multi-agent system consists of... It consists of 1 intelligent agent, numbered as ; Based on graph theory, we define the system communication topology graph, adjacency matrix, and Laplace matrix. Secondly, we assume that the communication topology between multi-agent systems is randomly switched, and this switching process can be described by a continuous-time Markov random process. Finally, we assume that the union graph of all possible communication topologies between agents is undirected and connected. The specific steps are as follows: Step 1.1: Define the communication topology of the multi-agent system based on graph theory. ,in Represents the set of intelligent agents in the network. A directed edge represents the set of edges representing interactions between agents. From node Start to node End, indicating the intelligent agent Can receive intelligent agents Information; Step 1.2: Communication Topology Diagram adjacency matrix The definition is as follows: Its Laplace matrix Defined as: Step 1.3: Define a random switching communication topology based on Markov random processes. represent Communication diagram at any time, exist Randomly switch between different graphs, that is and Among them, Markov processes The distribution of is unique and invariant, that is... satisfy and ,when hour, The distribution is ,in It is the set of positive real numbers; Step 1.4: Assume that the union graph of all possible communication topologies between agents is undirected and connected, without requiring that each switching subgraph is connected, thus relaxing the assumptions about the communication topology graph; agents obtain relative information between themselves and their neighboring agents in real time through randomly switched communication topologies. Step 2: Provide a multi-agent dynamics model, and design a corresponding observer model to observe the output state of the multi-agent system under deception attack. Step 2.1: When the information transmission process between intelligent agents is subjected to a deception attack, normal data will be injected with attack signals. Using Bernoulli random variables Describe a random deception attack, assuming the probability of the attack succeeding is... Considering the possibility of a deception attack, the information received by agent j from agent i is: in, For intelligent agents The output, The output received by the neighboring agent after being attacked. The probability that the agent is attacked; Assume the deception attack signal satisfies the following conditions: in, Injecting signals for the attack, This is the upper bound of the injected signal; Step 2.2: Establish a multi-agent linear dynamics model: in, The state of the agent. For input, For output, The transition matrix, For the input matrix, To output the matrix, matrix pairs It is calm, matrix pair It is observable; In real-world systems, not all states are measurable; therefore, an observer is introduced. in, For observation status, For observation output, Here is the gain matrix of the observer to be designed; Step 3: Design an adaptive event-triggered strategy based on relative observers, provide a distributed adaptive controller based on event-triggered information, and establish a security control objective function for the multi-agent system; Step 3.1: First, define the intelligent agent. The measurement error is: The initial time when the event is triggered is Design an observation-based adaptive event triggering strategy: in, , It is a constant. It is a positive constant. , For the defined measurement error, Undefined consistency error; It is an auxiliary variable and satisfies: in, , , ; Step 3.2: Define Consistency Error At the moment of two adjacent event triggering Design a distributed adaptive event-triggered control protocol: in, For adaptive gain, constant gain matrix , For time-varying weights, For intelligent agents The estimated state at the trigger time. For adaptive coupling gain and satisfying: in, and It is a predefined constant, and The initial conditions are satisfied ; Step 3.3: Define the mean state error ,make Based on stochastic analysis theory, an objective function for the secure control of multi-agent systems under stochastically switched communication topologies is proposed, namely, for any initial state... There exists a scalar and a compact set This leads to consistency error The expectation is that it can converge to compact set. In, that is: in, As expected, This is the initial time; Step 4: For multi-agent systems under Markov random topology switching and spoofing attacks, a distributed event-triggered adaptive security control method is proposed. Using Lyapunov stability theory, it is verified that the proposed adaptive security control method can guarantee that the multi-agent system achieves the control objective, and that the proposed event-triggered strategy will not trigger an unlimited number of times within a finite time. Based on Schur's lemma, the gain matrices of the observer and controller are given. According to the designed observer, event-triggered strategy and control protocol, simulation verification is carried out under the scenarios of Markov topology switching and spoofing attacks.

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