Self-adaptive event triggering safety control method for multi-agent system under spoofing attack

Abstract

The invention discloses a self-adaptive event triggering safety control method of a multi-agent system under spoofing attack, and relates to event triggering control of the multi-agent system. A communication topological graph, an adjacent matrix and a Laplacian matrix of the system are defined based on a graph theory, it is assumed that communication topology between multi-agent systems is randomly switched, and the switching process follows a continuous time Markov process; assumptions on the communication topological graphs are relaxed, it is required that the combined graph of all possible communication topological graphs is undirected connected, and it is not required that each switching sub-graph is connected; modeling a spoofing attack, setting an attack signal upper bound, and defining a system security control objective function under the spoofing attack; an event-triggered distributed adaptive security control strategy is designed, the state of a neighbor agent is estimated by using an observer technology, it is verified that the control strategy can ensure the system security under the Markov random switching communication topology, and the effectiveness of the method is verified by using a Lyapunov stability theory, a stochastic analysis and linear matrix inequality method and simulation.

Description

Technical Field

[0001] The present invention belongs to the field of event triggering control of multi-agent systems, and in particular to an adaptive event triggering safety control method for multi-agent systems under deception attacks and observer-based deception attacks under Markov random switching communication topologies. Background Art

[0002] With the widespread application of networked control systems, theories related to multi-agent systems (MAS) have been widely used in engineering fields such as power networks, multi-processor networks, driverless cars, and intelligent transportation. The control problem of multi-agent systems has attracted widespread attention from scientific researchers. In actual network environments, continuous communication can lead to communication congestion, which in turn leads to longer communication delays and increased packet loss. In addition, the limited energy of agents and limited network bandwidth are also issues that must be considered in practical applications. The purpose of designing event-triggered safety control is to solve the problem of network congestion, thereby effectively reducing the number of executions of control tasks and saving communication and computing resources.

[0003] Multi-agent systems cannot do without network communication. With the development of network communication and information technology, while it facilitates the expansion of system functions, it also makes the system face more security challenges. Network security control of multi-agent systems is mainly used to solve security problems that the system may face, such as defending against common network attacks.

[0004] The security control of multi-agent systems includes any means specifically designed to prevent data attacks, defending against common network attacks such as denial of service attacks and deception 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 for sequential 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 for protecting against multiple network attacks.

[0005] In a multi-agent system, each agent collaborates with each other through a communication network to complete a predetermined task. However, the random switching characteristics of the communication network and the potential risk of deception attacks pose a huge challenge to the security control of the system. Due to factors such as packet loss, the communication between adjacent agents may be temporarily interrupted, thereby changing the communication topology between agents. At the same time, due to the openness and sharing of wireless communication technology, multi-agent systems are vulnerable to network attacks, and not all real-time information is observable during the communication process of the multi-agent system. Summary of the invention

[0006] The purpose of the present invention is to solve the above-mentioned difficult problems in the prior art, and to provide an adaptive event-triggered safety control method for a multi-agent system under deception attacks based on observer technology and event triggering strategy, so as to overcome the influence of random switching topology and deception attacks on the multi-agent system. The present invention proposes an observer-based event-triggered adaptive gain safety control protocol to solve the adaptive event-triggered safety control problem of a multi-agent system with general linear dynamics under random switching communication topology under deception attacks.

[0007] Firstly, according to graph theory and Markov process, a random switching communication topology of a multi-agent system is given. The relative observation information between itself and its neighboring agents is obtained through the observer. Then, the dynamic model of the multi-agent is established, and the objective function of the security control of the multi-agent system is established. Finally, a distributed adaptive security control method for the multi-agent system to defend against deception attacks under the Markov random switching communication topology is given. The control signal is updated through the event trigger mechanism, and it is verified that the proposed adaptive security control method can ensure that the multi-agent system can achieve tracking control tasks.

[0008] The adaptive event-triggered security control method of a multi-agent system under a deception attack of the present invention comprises 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 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 the switching process can be described by a continuous-time Markov random process;

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

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

[0012] In the third step, we assume that the communication topology between multi-agent systems is switched randomly. The switching process is described by a continuous-time Markov random process. The communication graph of N agents switches between s graphs, which can be expressed as

[0013] Step 2: Give a hypothesis of the communication topology of the multi-agent system; assume that the union of all possible communication topologies between agents It is undirected and connected, without requiring every switching subgraph to be connected, relaxing the assumption on the communication topology graph; The corresponding adjacency matrix and Laplacian matrix are and

[0014] Step 3: Hypothetically model the deception attack. Based on the concealment characteristics of deception attacks, assume an upper bound of the deception attack signal.

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

[0016] The second step is to assume that the upper bound of the attack energy is assumed to be limited, given the concealed nature of deception attacks. That is, the amplitude or energy of the attack signal does not exceed a given threshold τ.

[0017] Step 4: Observe the state of neighboring agents through observer technology, design a multi-agent system event-triggered distributed adaptive security control method to defend against deception attacks under Markov random switching communication topology, apply 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 can achieve the goal of security control, and finally conduct simulation verification;

[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 for judgment;

[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 closed-loop error model for the multi-agent system;

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

[0021] The fourth step is to verify that the designed event triggering strategy will not be triggered infinitely within a limited time, thereby eliminating the event-triggered Zeno behavior;

[0022] The fifth step is to propose a solution method for the controller gain matrix and the observer gain matrix based on Schur's lemma.

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

[0024] The beneficial effects of the present invention are:

[0025] The present invention designs a distributed adaptive tracking control method for a multi-agent system under a Markov random switching communication topology, combines an event triggering strategy and an observer observation technology, so that each agent in the multi-agent system automatically updates its coupling gain using only the local information between its neighbors under the random switching topology, and then designs a multi-agent system security control method to deal with deception attacks. The method of the present invention can ensure the performance and security of the multi-agent system in an environment of uncertainty and attack threats, and has the characteristics of being distributed and adaptive, and can effectively handle the problems of random switching topology and deception attacks. In addition, since the agent only updates the control gain when necessary, the method can also reduce the communication and computing burden of the system. The present invention provides an effective solution, which is suitable for multi-agent systems working in complex environments. By combining observer technology and event triggering strategies, the present invention can improve the robustness and security of the system and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 FIG. 4 is a schematic diagram of the architecture of an embodiment of the present invention.

[0027] Figure 2 Switch between subgraphs and union graphs for communication topology.

[0028] Figure 3 It is the communication topology switching process.

[0029] Figure 4 is the tracking trajectory of the X axis.

[0030] Figure 5 is the tracking trajectory of the Y axis.

[0031] Figure 6 is the tracking error of the X-axis.

[0032] Figure 7 is the tracking error of the Y axis.

[0033] Figure 8 is the controller gain curve.

[0034] Fig. 9 The aircraft event triggering moments for the four aircraft. DETAILED DESCRIPTION

[0035] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the following embodiments will further illustrate the present invention in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0036] Figure 1The architecture diagram of an embodiment of the present invention is given, that is, a schematic diagram of the framework of a distributed security control protocol for a multi-agent system under deception attacks and Markov random switching communication topologies. The embodiment of the present invention first gives a random switching communication topology for a multi-agent system based on graph theory and Markov processes, obtains relative observation information between itself and neighboring agents through an observer, then establishes a dynamic model of the multi-agent, establishes an objective function for the security control of the multi-agent system, and finally gives a distributed adaptive security control method for the multi-agent system to defend against deception attacks under the Markov random switching communication topology, updates the control signal through an event trigger mechanism, and verifies that the proposed adaptive security control method can ensure that the multi-agent system can achieve tracking 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 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 the switching process can be described by a continuous-time Markov random process.

[0038] Step 1.1: Define the communication topology of the multi-agent system based on graph theory in Represents the set of agents in the network, E represents the set of edges that interact between agents, and 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 The adjacency matrix of 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 a Markov random process. represents the communication graph at time t, Randomly switch between s different graphs, that is, and Among them, the distribution of the Markov process σ(t) is unique and invariant, that is, π=[π1,...,π s ] T satisfy And π p ≥0,p=1,...,s, when When , the distribution of σ(t) is π, where is the set of positive real numbers.

[0044] Step 2: Given a general dynamic model of multi-agents, and targeting the multi-agent system under deception attacks, design a corresponding observer model to observe the output state of the system.

[0045] Step 2.1: When the information transmission process between agents is subjected to a deception attack, the normal data will be injected with the attack signal ε i . Using the Bernoulli random variable α i Describe the random deception attack behavior, and assume that the probability of a successful attack is Considering the existence of deception attacks, the information received by agent j from agent i is:

[0046]

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

[0048] Assume that the spoofing attack signal meets the following conditions:

[0049] ‖ε i (t)‖ 2 ≤τ (2)

[0050] Among them, ε i (t) is the injection signal of the attack, and τ is the upper bound of the injection signal.

[0051] Step 2.2: Establish a general linear dynamics model of multi-agents:

[0052]

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

[0054] In actual systems, not all states can be measured. Introduce observers:

[0055]

[0056] Where F is the observer gain matrix to be designed, is the observation state, The output is observation.

[0057] Step 3: Design an adaptive event triggering strategy based on relative observer, give a distributed adaptive controller based on event triggering information, and establish the safety control objective function of 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 adaptive event-triggering strategy based on observations:

[0059]

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

[0061]

[0062] in, η i >0,

[0063] Step 3.2: Define the consistency error At the moment when two adjacent events are triggered Design of a distributed adaptive event-triggered control protocol:

[0064]

[0065] Among them, d i (t) is the adaptive gain, the constant gain matrix K = B T P, is the time-varying weight, is the estimated state of agent i at the triggering moment, d i is the adaptive coupling gain and satisfies:

[0066]

[0067] Among them, β i and is a predefined constant, and d i The initial condition of (t) satisfies

[0068] Step 3.3: Define the mean state error make Based on the theory of stochastic analysis, the objective function of the safety control of multi-agent systems under random switching communication topology is proposed, that is, for any initial state x(0), there exists a scalar e and a compact set The expectation of the consistency error δ(t) can converge to a compact set In Chinese, that is:

[0069]

[0070] Among them, E is the expectation and t0 is the initial time.

[0071] Step 4: For the multi-agent system under Markov random switching communication topology and deception attack, a distributed event-triggered adaptive security control method is given. Using Lyapunov stability theory, it is verified that the proposed adaptive security control method can ensure that the multi-agent system achieves the control goal. It is verified that the proposed event triggering strategy will not be triggered infinitely in a finite time. Finally, the gain matrix of the observer and controller is given.

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

[0073]

[0074]

[0075] in, Thus we can get The matrix variables in the formula are defined as:

[0076] α(t)=diag{α1(t),α2(t),...,α N (t)}. To simplify the notation, the variable t is 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 , Then the multi-agent closed-loop system (11) can converge to the compact set exponentially The conditions are:

[0080] For a given attack upper bound τ, 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, Q such that:

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087] Established.

[0088] in,

[0089]

[0090] yes The smallest non-zero eigenvalue of .

[0091] verify:

[0092] For a connected graph, according to:

[0093]

[0094] It can be obtained that V>0. Taking the derivative of the first term V1 of the Lyapunov function, we can obtain:

[0095]

[0096] definition in Written as a vector: Combining Young's inequality, we can get the following two inequalities:

[0097]

[0098]

[0099] The first equality holds because each subgraph is assumed to be an undirected graph, so And the equation used is

[0100] Depend on have We can get:

[0101]

[0102] From formula (20), combined with (21) and (22), we can get:

[0103]

[0104] Among them, the use

[0105] Consider the following formula:

[0106]

[0107] The formula used and Young's inequality. At the same time, according to The definition and some mathematical calculations give for have:

[0108]

[0109] Depend on We can get:

[0110]

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

[0112]

[0113] in,

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

[0115]

[0116] Taking the derivative of V2, we get:

[0117]

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

[0119]

[0120] According to the updating 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), we obtain:

[0126]

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

[0128]

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

[0130]

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

[0132]

[0133] Then we have:

[0134]

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

[0136]

[0137] When t→∞, we have:

[0138]

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

[0140] Step 4.3: Eliminate the Zeno behavior of the event-triggered strategy, that is, it will not be triggered infinitely in a limited time, and verify the feasibility of the event-triggered strategy.

[0141] verify:

[0142] for According to the dynamic event trigger condition (5), we can get:

[0143]

[0144] Assumptions For any two consecutive sampling times in [t0, t), The derivative is:

[0145]

[0146] in, Ω i =GCq i -GFε i .

[0147] Integrate both sides of (38):

[0148]

[0149] We can get:

[0150]

[0151] From the definition, we know Then we have:

[0152]

[0153] From step 4.2, we know that there are positive constants θ1, θ2, ν such that the expectation of q is The convergence rate ν converges to θ1, that is, So there is a positive constant So that the following inequality holds:

[0154]

[0155] in,

[0156] If ||A||≠0, then:

[0157]

[0158] The dynamic event triggering strategy can be obtained:

[0159]

[0160] Combining formula (47), we can get:

[0161]

[0162] Then we have:

[0163]

[0164] Verify that in any finite interval

[0165] Next, verify As k approaches infinity, we assume the opposite conclusion, that is, Will not go to infinity. Introducing the concept and You can export and In formula (46) The value is the constant positively correlated, so it can be deduced that Therefore, from equation (50), we can get:

[0166]

[0167] is contradictory. Then the assumption is not true, which means that when k approaches infinity Goes to infinity. Zeno behavior can be excluded.

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

[0169] In summary, the Zeno behavior of agent i can be ruled out.

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

[0171] If there exists a positive definite matrix P,Q such that:

[0172]

[0173]

[0174]

[0175] χI n -Q<0 (55)

[0176] Established, of 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] Thus:

[0181]

[0182] Ψ+κQ<0 (58)

[0183] Define X = QG, and from Schur's complement lemma we can get:

[0184]

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

[0186]

[0187] Obviously, formula (60) is equivalent to:

[0188]

[0189] χI n -Q<0 (62)

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

[0191] Step 4.5: Based on the designed observer, event triggering strategy and control protocol, simulation verification is performed under the scenarios of Markov switching topology and deception attack.

[0192] An example of 10 spacecraft is used for verification. The relative dynamic equation between the ith spacecraft and the reference point can be described as:

[0193]

[0194] where x i ,y i and z i represents the relative position of the i-th spacecraft and the reference point, ω represents the orbital angular velocity of the reference point, μ represents the earth lemma coefficient, and r is the distance between the reference point and the center of gravity of the earth; a ix , a iy and a iz Represents the control input of the three axes.

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

[0196]

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

[0198] Consider multiple spacecraft under Markov switching topology and deception attack. Figure 2 The topology switching subgraph and the combined graph are caused by the random communication failure of multiple spacecraft. The communication topology switching process is as follows: Figure 3 shown.

[0199] The spacecraft flies in the same plane, and the tracking trajectories of the X-axis and Y-axis are drawn separately, such as Figure 4 and 5 As shown. Figure 4 and Figure 5 From the tracking trajectory in , we can see that the position trajectory of the aircraft on the X-axis and Y-axis quickly converges to the desired trajectory, indicating that the control strategy can effectively guide the movement of the aircraft.

[0200] Plot the tracking errors on the X-axis and Y-axis respectively, such as Figure 6 and 7 As shown in the figure, it can be seen that the error can complete a large range of convergence within 10s, 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 target.

[0201] Figure 8 The controller gain curve is represented by Figure 8 It can be seen that the controller gain can eventually converge to a stable value, which shows that the controller parameter adjustment is effective and the system has good robustness. Fig. 9 It represents the event triggering time of the 1st, 4th, 7th and 10th aircraft. It can be seen that the designed event triggering strategy will not be triggered infinitely within a limited time, and can effectively reduce unnecessary communications and save communication resources.

[0202] Experiments show that the multi-agent system and its control strategy designed by the present invention can still achieve accurate trajectory tracking and effectively save communication resources when facing random communication failures and the uncertainty of Markov switching topology. This fully verifies the effectiveness and practicality of the method of the present invention.

[0203] The method of the present invention can be applied to the following fields, including but not limited to: In the field of network security, the method can be applied 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 the formation flight of unmanned aerial vehicles, the method can help ensure the security of communication between unmanned aerial vehicles to maintain the stability of the formation and complete the predetermined tasks. In intelligent transportation systems, the method can be applied to vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communications to improve traffic safety and flow management. In industrial automation and remote monitoring systems, the method can be applied to ensure the continuity and safety of the production process, especially in the face of malicious attacks. In smart grids, the method can be applied to ensure the stable supply and effective distribution of power systems and prevent power failures caused by malicious attacks. In financial markets, the 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 firefighting, earthquake rescue, etc., the method can be applied to establish a reliable communication network to effectively coordinate actions in emergency situations. Through the above applications, the method can improve the security and reliability of the system at multiple levels, especially in the face of uncertainty and malicious attacks.

[0204] The above embodiments are only preferred embodiments of the present invention and cannot be considered to limit the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the present invention.

Claims

1. Adaptive event-triggered security control method for multi-agent systems under deception attacks, Features The following steps are involved: Step 1: Without loss of generality, assume that the multi-agent system consists of N agents, numbered 1,...,N; define the system 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 the switching process can be described by a continuous-time Markov random process; The first step is to define the communication topology of the multi-agent system based on graph theory; The second step is to give the adjacency matrix and Laplacian matrix of the communication topology graph; The third step is to describe the random switching communication topology of the system based on the continuous-time Markov random process; Step 2: Give an assumption about the communication topology of the multi-agent system; assume that the union of all possible communication topologies between agents is undirected and connected, without requiring that each switching subgraph is connected, and relax the assumption about the communication topology; In the first step, we assume that the union of all possible communication topology graphs of the agents is undirected and connected; In the second step, the agent obtains the relative information between itself and its neighboring agents in real time through randomly switched communication topologies; Step 3: Hypothetically model the deception attack. Based on the concealment of the deception attack, assume the upper bound of the deception attack signal. The first step is to establish a deception attack model for the multi-agent system, that is, the probability of the agent being attacked satisfies the Bernoulli random distribution; The second step is to assume that the upper bound of the attack energy is assumed to be limited, given the concealed nature of deception attacks. That is, the amplitude or energy of the attack signal does not exceed a given threshold τ. Step 4: Observe the state of neighboring agents through observer technology, design a multi-agent system event-triggered distributed adaptive security control method to defend against deception attacks under Markov random switching communication topology, apply 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 can achieve the goal of security control, and finally conduct simulation verification; 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 for judgment; 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 closed-loop error model for the multi-agent system; The third step is to verify the effectiveness of the control method based on Lyapunov stability theory and linear matrix inequality method; The fourth step is to verify that the designed event triggering strategy will not be triggered infinitely within a limited time, and exclude the Zeno behavior of event triggering; The fifth step is to propose a solution method for the controller gain matrix and the observer gain matrix based on Schur's lemma. The sixth step is to perform simulation in Simulink to verify whether the designed event trigger strategy and controller can meet the control objectives.

2. The adaptive event-triggered security control method for a multi-agent system under a deception attack as claimed in claim 1, Features In step 1, the specific steps are: Step 1.1: Define the communication topology of the multi-agent system based on graph theory in represents the set of agents in the network, E represents the set of edges that interact between agents, and 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; Step 1.2: Communication topology diagram The adjacency matrix of The definition is as follows: Its Laplace matrix Defined as: Step 1.3: Define a random switching communication topology based on a Markov random process. represents the communication graph at time t, Randomly switch between s different graphs, that is, and Among them, the distribution of the Markov process σ(t) is unique and invariant, that is, π=[π 1 ,...,π s ] T satisfy And π p ≥0,p=1,...,s, when When , the distribution of σ(t) is π, where is the set of positive real numbers.

3. The adaptive event-triggered security control method for a multi-agent system under a deception attack as claimed in claim 1, Features In step 2, a hypothesis of the communication topology of the multi-agent system is given; it is assumed that the union of all possible communication topologies between agents is undirectedly connected. When the information transmission process between agents is subjected to a deception attack, the normal data will be injected with the attack signal ε i ; Using Bernoulli random variable α i Describe the random deception attack behavior, and assume that the probability of a successful attack is Considering the existence of deception attacks, the information received by agent j from agent i is: Assume that the spoofing attack signal meets the following conditions: ‖e i (t)‖ 2 ≤τ (2) Build a general linear dynamics model for multi-agents: Among them, the matrix pair (A, B) is stable, and the matrix pair (A, C) is observable; In actual systems, not all states can be measured. Introduce observers: Where F is the observer gain matrix to be designed.

4. The adaptive event-triggered security control method for a multi-agent system under a deception attack as claimed in claim 1, Features In step 3, the deception attack is modeled hypothetically. According to the concealment characteristic of the deception attack, the upper bound of the deception attack signal is assumed, and the specific steps of establishing the objective function of the multi-intelligence system security control under the deception attack are as follows: Step 3.1: First, define the measurement error of agent i as: The initial time when the event is triggered is Design an adaptive event-triggering strategy based on observations: Among them, i ∈(0,1),υ i is a constant, ι i is a normal constant, Γ=PBB T P,m i (t) is the defined measurement error, is the defined consistency error; is an auxiliary variable and satisfies: in, η i >0, Step 3.2: At the moment when two adjacent events are triggered Design of a distributed adaptive event-triggered control protocol: Among them, d i (t) is the adaptive gain, the constant gain matrix K = B T P, is the time-varying weight, is the estimated state of agent i at the triggering moment, d i is the adaptive coupling gain and satisfies: Among them, β i and is a predefined constant, and d i The initial condition of (t) satisfies Step 3.3: Define the mean state error make Based on the theory of stochastic analysis, the objective function of the safety control of the multi-agent system under the random switching communication topology is proposed, that is, for any initial state x(0), there exists a scalar and a tight set The expectation of the consistency error δ(t) can converge to a compact set In Chinese, that is: Where E is the expectation, t 0 is the initial time.

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