Multi-agent control method for resisting data injection attack and communication range constraint

Abstract

The invention discloses a multi-agent control method for resisting data injection attack communication range constraints, and relates to the technical field of control. The method comprises the steps that S1, a security control strategy based on historical data is obtained, the security control strategy comprises the steps that a sender agent correspondingly sends # imgabs3 #, # imgabs4 # and # imgabs5 # data at three continuous moments # imgabs0 #, # imgabs1 # and # imgabs2 #, at the moment, corresponding information capable of being received by a receiver agent is # imgabs6 #, # imgabs7 # and # imgabs8 #, the receiver agent calculates the amount of approximate external attacker injection information based on the received data, and the amount of the external attacker injection information is calculated according to the amount of the external attacker injection information; obtaining data in an approximate neighbor state, wherein the data is discrete data; s2, carrying out serialization on the discrete data obtained in the step S1 to obtain smoothed data; s3, obtaining a distance-based communication weight strategy with a penalty factor to avoid an outlier phenomenon; s4, in combination with the communication weight strategy obtained in the step S3, a predetermined time control scheme is constructed and obtained based on backstepping control; under the attack of data injection, the controller of the intelligent agent can work normally.

Description

Technical Field

[0001] The present invention relates to the field of control technology, and in particular to a multi-agent control method for resisting data injection attacks and communication range constraints. Background Art

[0002] Multi-agent control technology, as the foundation for the control of multi-unmanned aerial vehicle (UAV) systems, multi-robot systems, and multi-unmanned vessel (UAV) systems, has been extensively researched and applied in recent years with the widespread deployment of these systems. Currently, two common control approaches are centralized and distributed. Centralized control uses individual agents as the central control center. Distributed control, in contrast, lacks a specific control center and instead relies on communication with neighboring agents. Its improved coordination and robustness have garnered widespread attention. The implementation of distributed control relies on good communication between agents and appropriate controller design. Therefore, when controlling multi-agent systems, one of the most important aspects is obtaining realistic neighbor states to design a suitable controller structure. Generally speaking, in most scenarios, communication between agents occurs by sending data packets over wireless networks. These packets contain the agent's state information, which neighboring agents use to design controllers.

[0003] like Figure 2 However, when multi-agent systems are deployed in real-world environments, data transmission is often subject to external malicious attacks. This requires agents to implement appropriate defenses to mitigate the effects of these attacks on control. Common attacks include spoofing, denial of service, replay, and false data injection. Because false data injection attacks modify data and resend it back to the receiving agent, resembling real information, they are difficult to detect and identify, significantly impacting system stability and even causing the task to fail. Designing appropriate control measures to recover information after an attack is crucial research.

[0004] like Figure 1 As shown, secondly, due to the limited power of the sensors equipped to the agents, they cannot support the transmission of information over long distances. Once an agent leaves the communication range of its neighbors, it will not be able to receive information, causing the agent to leave the group and the control task to fail. This is not allowed in the control process. It is very necessary to design an anti-loosening measure for multi-agent systems.

[0005] Furthermore, the system's convergence speed is another control performance metric worth focusing on. It's undeniable that for many scenarios, the system's convergence time must be deterministic or even pre-specified. Excessively long convergence times do not meet their actual control requirements. Therefore, building a control solution that can predict convergence time and ensure that the system converges within the predetermined timeframe is of great practical engineering significance.

[0006] Therefore, the inability of the intelligent agent's controller to work properly under data injection attacks has become a technical problem that needs to be solved urgently. Summary of the Invention

[0007] The present invention provides a multi-agent control method for resisting data injection attack and communication range constraint, solving the technical problem that the controller of the agent cannot work normally under the data injection attack.

[0008] In order to solve the above technical problems, the technical solutions adopted by the present invention are as follows: A multi-agent control method for resisting data injection attacks and communication range constraints includes the following steps: Step S1: Design and obtain a security control strategy based on historical data. The security control strategy includes the sender agent at three consecutive moments 、 、 Send accordingly 、 、 data, is a predetermined amount, , is the sender agent in status, is the sender agent in , the corresponding information that the receiver agent can receive is 、 、 , It's a multiplicative attack. It is an additive attack. The receiver agent calculates the approximate amount of information injected by the external attacker based on the received data, thereby obtaining the approximate neighbor state data, which is discrete data. Step S2: Continuize the discrete data obtained in step S1 to obtain smoothed data; Step S3: Design a distance-based communication weight strategy with a penalty factor to avoid outliers; Step S4: Combining the communication weight strategy obtained in step S3, based on backstepping control, a predetermined time control scheme is constructed.

[0009] A further technical solution is: in step S1, the attack form is: (1) In formula (1), It is the information that the receiver agent can receive and utilize. is the information sent by the sender agent; Will 、 、 The three data are operated as follows: ① ② ③ yes The estimated value of yes Estimated value of assuming the attack signal 、 、 , if the calculated result is Substitute a smaller constant to calculate the approximate amount of information injected by an external attacker; According to formula (2), the approximate neighbor state is calculated. (2) In formula (2), is the approximate neighbor state; Select three consecutive pieces of information as 、 、 , The estimated error is: (3) In formula (3), for estimated value of; The following inequalities are satisfied: yes The upper bound of the rate of change, , , , rewrite formula (3) as: (4) In formula (4), ; According to formula (4), as long as the time interval Select a small enough value so that the strategy can guarantee The accuracy of the estimate, The estimated error is: (5) In formula (5), yes The upper bound of the rate of change, ; Time interval 、 The selected value is small enough so that the security control strategy can ensure Accuracy of estimates.

[0010] A further technical solution is: in step S2, (6) In formula (6), is the smoothed data, as estimated value of; , , yes The moment after for Estimates, for Estimates.

[0011] A further technical solution is that: in step S3, the communication weight for: (7) In formula (7), is the communication weight between the ith agent and the lth agent, is the connection weight between the ith agent and the lth agent based on graph theory, is the penalty factor, represents the vector distance between agents, represents the distance between agents, is the first-order state of the ith agent, To estimate the first-order state of the neighbor l-th agent, is the upper bound of the distance between agents allowed; the estimated value of the neighboring agent l is calculated according to formula (6) , due to the estimated With actual There is a certain error between The choice of needs to take this part of the error into account, namely: (8) In formula (8), is the upper bound of the error, is the maximum communication range of the agent; Combining Equations (7) and (8), we obtain a distance-based communication weight strategy with a penalty factor. When the distance between agents gradually approaches the communication boundary, the communication weight between agents will gradually increase, making the agents more closely connected in the topology, thus staying away from the communication boundary, preventing the occurrence of outliers, and maintaining the connectivity of the communication topology.

[0012] A further technical solution is that: step S4 specifically includes the following steps: Depend on Agents form a multi-agent system, The dynamic equation of an agent is: (9) In formula (9), Representative The first Stage state, 、 Representing the The input and output of an agent, the output is the data sent through the network, represents an unknown nonlinear function, , Represents the order, , represent The derivative of For the The first Stage state, represent The derivative of Representative The first Stage state, For the The first-order state of each agent; Predefined time scale functions for: (10) In formula (10), is the time scale function, For time, For the scheduled time, , is the design parameter, ; Based on the communication weights in step S3, the distributed error is: (11) In formula (11), For the The distributed error of each agent, Represents the number of agents; By taking the derivative of formula (11), we can get: (12) In formula (12), represent The derivative of , Representative The second-order state of an agent, represents a nonlinear function, for The derivative of , ; Coordinate transformation: (13) In formula (13), It is The first-order error variable of each agent, It is The first The error variable, It is The first First-order virtual controller; Combined with the coordinate transformation of formula (13), the virtual controller designed based on the backstepping method includes formulas (14), (15) and (16), the controller is formula (17), and the adaptive law is formula (18), as follows: (14) In formula (14), It is The second-order virtual controller of each agent, yes The derivative of yes Estimates, , is the square of the fuzzy weight modulus, 、 All are design parameters; (15) In formula (15), It is The third-order virtual controller of each agent, For the The second-order error variable of each agent, is a design parameter; (16) In formula (16), is the k+1th order virtual controller, For the The first The error variable, is a design parameter; (17) In formula (17), For the The first The error variable, is a design parameter; (18) In formula (18), for The derivative of is a design parameter; The predetermined time control scheme includes a virtual controller, a controller and an adaptive law, and an RBF neural network is used to approximate the unknown nonlinear function, that is: (19) In formula (19), is a nonlinear function. When k=1, ,when hour, , is an unknown nonlinear function, is the ideal weight vector, is the radial basis function vector, is the approximation error, is the upper bound of the approximation error, , .

[0013] A further technical solution is: further comprising step S5 after step S4, Step S5: Using the Lyapunov function stability definition, prove that the predetermined time control scheme obtained in step S4 is effective.

[0014] A further technical solution is that: step S5 specifically includes the following steps: Lyapunov function: (20) In formula (20), is the Lyapunov function, Represents the estimation error of the unknown weight vector; By deriving Equation (20) and substituting it into the corresponding virtual controllers (14), (15), and (16), the controller (17), and the adaptive law (18), we can obtain: (twenty one) In formula (21), yes The derivative of , , is the upper bound of the approximation error; Solving equation (21) yields: (twenty two) In formula (22), yes exist The value at time , that is, the initial value of the Lyapunov function; According to formula (22), when time When , the Lyapunov function is a bounded quantity, which means that the elements that constitute the Lyapunov function It is also a bounded quantity, that is, there is a constant 、 ,satisfy ; Combined with formula (13), we can get , , obviously , which means that the system achieves consistency at a predetermined time, and in addition, all states are bounded; Next, we will explain that any agents will not be far away from each other. Any smart neighbor , energy function: (twenty three) In formula (23), is the energy function, , To estimate the neighbor The first-order state of each agent is calculated according to formula (6); By taking the derivative of formula (23), we can get: (twenty four) In formula (24), yes The derivative of yes The derivative of Substituting formula (14) into formula (24) yields: (25) In formula (25), is bounded, the following inequality holds: (26) at this time , will decrease, which means that the distance between agents is decreasing; , inequality (26) will be Therefore, it can be ensured that the distance between agents is always smaller than the communication range of each other, and there will be no outliers.

[0015] A further technical solution is: further comprising step S6 located after step S4, Step S6: Verify the feasibility of the predetermined time control scheme obtained in step S4 through a numerical simulation example.

[0016] The beneficial effects of adopting the above technical solution are: A multi-agent control method for resisting data injection attack and communication range constraint includes step S1: designing and obtaining a security control strategy based on historical data, the security control strategy includes the sender agent at three consecutive moments 、 、 Send accordingly 、 、 data, is a predetermined amount, , is the sender agent in status, is the sender agent in , the corresponding information that the receiver agent can receive is 、 、 , It's a multiplicative attack. This is an additive attack. The receiving agent calculates the approximate amount of information injected by the external attacker based on the received data, thereby obtaining approximate neighbor state data, which is discrete data. Step S2: The discrete data obtained in step S1 is continuousized to obtain smoothed data. Step S3: A distance-based communication weight strategy with a penalty factor is designed to avoid outliers. Step S4: Combining the communication weight strategy obtained in step S3 with a backstepping control scheme to construct a predetermined time control scheme. Under the data injection attack, the agent's controller can function normally. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a distribution map of the communication range in this application; Figure 2This is the data flow diagram of the data injection attack in this application; Figure 3 is the topological graph between the agents in step S6 of this application; Figure 4 is a graph of the absolute error of consistency between agents in step S6 of the present application; Figure 5 is a graph of the estimated strategy error in step S6 of the present application; Figure 6 is a graph of the distance between agents when the penalty factor is included in step S6 of the present application; Figure 7 is a graph of the distance between agents when the penalty factor is not included in step S6 of the present application; Figure 8 It is a flowchart of this application. DETAILED DESCRIPTION

[0018] The purpose of this application is to provide a method for controlling the time consistency of a multi-agent system under data injection attacks and limited communication range. First, considering that the multi-agent system may be subject to data injection attacks during communication, this application designs a security estimation strategy based on historical data. By using the currently transmitted data and the data transmitted from the previous two moments, the information received after the attack can be parsed into an approximate true information. Secondly, to address the problem of limited communication range between agents, this application designs a distance-based communication weight scheme. By adding a distance penalty factor to the normal weight, the distributed error increases as the distance between agents increases, thereby enhancing the control effect and enabling the multi-agent system to maintain connectivity. Then, based on the backstepping method and a preset time scale function, a control scheme is designed to ensure that the multi-agent system can achieve consistency under data injection attacks and limited communication range. Finally, the rationality of the proposed control algorithm is verified through simulation examples.

[0019] In order to make the purpose, technical solutions and advantages of this application clearer, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the drawings in the embodiments of this application. Obviously, the described embodiments are only part of the embodiments of this application, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is in no way intended to limit the present application and its application or use. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0020] In the following description, many specific details are set forth to facilitate a full understanding of the present application. However, the present application may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without violating the connotation of the present application. Therefore, the present application is not limited to the specific embodiments disclosed below.

[0021] like Figure 8 As shown, the present invention discloses a multi-agent control method for resisting data injection attacks and communication range constraints, which includes the following steps.

[0022] Step S1: In order to solve the problem of data injection attacks during data transmission between intelligent agents, a security control strategy based on historical data is designed.

[0023] In multi-agent communication, data is often sent to neighboring agents over wireless networks. During this process, the transmitted data may be vulnerable to external attackers who can inject carefully disguised data into real information to confuse the multi-agent system. This situation can significantly affect the stability of the system, making it unable to complete the required tasks. In this application, the following attack forms are considered: (1) In formula (1), It is the information that the receiver agent can receive and utilize. is the information sent by the sender agent.

[0024] Since the agent can only receive information after being attacked, this application designs a security estimation strategy based on historical data, specifically: the sender agent receives information at three consecutive moments. 、 、 Send accordingly 、 、 data, is a predetermined amount, , is the sender agent in status, is the sender agent in , the corresponding information that the receiver agent can receive is 、 、 , It's a multiplicative attack. It is an additive attack.

[0025] Will 、 、 The three data are operated as follows: ① ② ③ yes The estimated value of yes Estimated value of assuming the attack signal 、 、 , if the calculated result is Substitute a smaller constant to calculate the approximate amount of information injected by an external attacker.

[0026] Through the above three calculation steps, we can calculate the approximate amount of information injected by the external attacker, and thus get the approximate real state, that is, (2) In formula (2), It is an approximate neighbor state.

[0027] From formula (2), we can see that the accuracy of state estimation is closely related to the injected data. 、 If the above strategy can accurately estimate the injected data, then the approximate neighbor state can be obtained.

[0028] Without loss of generality, we select three consecutive pieces of information as 、 、 , The estimated error is: (3) In formula (3), for estimated value.

[0029] The following inequalities are satisfied:

[0030]

[0031]

[0032] yes The upper bound of the rate of change, , , , rewrite formula (3) as: (4) In formula (4), .

[0033] According to formula (4), as long as the time interval Select a small enough value so that the strategy can guarantee The accuracy of the estimate, The estimated error is: (5) In formula (5), yes The upper bound of the rate of change, ; Time interval 、 The selected value is small enough so that the security control strategy can ensure Accuracy of estimates.

[0034] Step S2: A discrete data continuity scheme is constructed to ensure that the continuous information is continuous and differentiable.

[0035] Since the communication between agents is in the form of discrete data packets, and the controller design is based on continuous states, the data obtained through step S1 cannot be directly used in the controller design. Therefore, a solution to make the data continuous is needed, namely: (6) In formula (6), is the smoothed data, as estimated value of; , , yes After the moment, for Estimates, for Estimates.

[0036] From equation (6), we can see that the signal is monotonic within an interval, which means that within the sampling interval Inside, , indicating that the signal is smoother.

[0037] Step S3: To prevent possible outliers, a distance-based communication weight design with a penalty factor is proposed.

[0038] Consider using a communication topology connection graph to represent the communication between agents. If the agents Can receive intelligent agents The information communication weight ,otherwise In this application, it is considered that if the distance between agents is too large, the communication connection will be disconnected, that is, , so the communication weight To redesign: (7) In formula (7), is the communication weight between the ith agent and the lth agent, is the connection weight between the ith agent and the lth agent based on graph theory, is the penalty factor, represents the vector distance between agents, represents the distance between agents, is the first-order state of the ith agent, To estimate the first-order state of the neighbor l-th agent, is the upper bound of the allowed distance between agents.

[0039] According to formula (6), the estimated value of the neighboring agent l is calculated , due to the estimated With actual There is a certain error between The choice of needs to take this part of the error into account, namely: (8) In formula (8), is the upper bound of the error, is the maximum communication range of the agent.

[0040] Combining Equations (7) and (8), we obtain a distance-based communication weight strategy with a penalty factor. When the distance between agents gradually approaches the communication boundary, the communication weight between agents will gradually increase, making the agents more closely connected in the topology, thus staying away from the communication boundary, preventing the occurrence of outliers, and maintaining the connectivity of the communication topology.

[0041] Step S4: In combination with the communication weights redesigned in step S3, a predetermined time control scheme is constructed based on backstepping control.

[0042] In this application, Agents form a multi-agent system, The dynamic equation of an agent is: (9) In formula (9), Representative The first Stage state, 、 Representing the The input and output of an agent, the output is the data sent through the network, represents an unknown nonlinear function, , Represents the order, , represent The derivative of For the The first Stage state, represent The derivative of Representative The first Stage state, For the The first-order state of an agent.

[0043] Design a predefined time scale function for: (10) In formula (10), is the time scale function, For time, For the scheduled time, , is the design parameter, .

[0044] Based on the newly designed communication weights in step S3, the distributed error is considered to be: (11) In formula (11), For the The distributed error of each agent, Represents the number of agents.

[0045] By taking the derivative of formula (11), we can get: (12) In formula (12), represent The derivative of , Representative The second-order state of an agent, represents a nonlinear function, for The derivative of , .

[0046] Consider the following coordinate transformation: (13) In formula (13), It is The first-order error variable of each agent, It is The first The error variable, It is The first Virtual controller.

[0047] Combined with the coordinate transformation of formula (13), the virtual controller designed based on the backstepping method includes formulas (14), (15) and (16), the controller is formula (17), and the adaptive law is formula (18), as follows: (14) In formula (14), It is The second-order virtual controller of each agent, yes The derivative of yes Estimates, , is the square of the fuzzy weight modulus, 、 These are all design parameters.

[0048] (15) In formula (15), It is The third-order virtual controller of the agent, For the The second-order error variable of each agent, is a design parameter.

[0049] (16) In formula (16), is the k+1th order virtual controller, For the The first The error variable, is a design parameter.

[0050] (17) In formula (17), For the The first The error variable, is a design parameter.

[0051] (18) In formula (18), for The derivative of is a design parameter.

[0052] In addition, the RBF neural network is used to approximate the unknown nonlinear function, namely: (19) In formula (19), is a nonlinear function. When k=1, ,when hour, , is an unknown nonlinear function, is the ideal weight vector, is the radial basis function vector, is the approximation error, is the upper bound of the approximation error, , .

[0053] Step S5: Using the Lyapunov function stability definition, prove that the controller given in step S4 is effective.

[0054] The designed predetermined time control scheme can ensure that the multi-agent system (Equation (9)) converges within the predetermined time, and all agents will not have outliers during the control process.

[0055] Consider the following Lyapunov function: (20) In formula (20), is the Lyapunov function, Represents the estimation error of the unknown weight vector.

[0056] By deriving Equation (20) and substituting it into the corresponding virtual controllers (14), (15), and (16), the controller (17), and the adaptive law (18), we can obtain: (twenty one) In formula (21), yes The derivative of , , is the upper bound of the approximation error.

[0057] Solving equation (21) yields: (twenty two) In formula (22), yes exist The value at time , that is, the initial value of the Lyapunov function.

[0058] According to formula (22), when time When , the Lyapunov function is a bounded quantity, which means that the elements that constitute the Lyapunov function It is also a bounded quantity, that is, there is a constant 、 ,satisfy ; Combined with formula (13), we can get , , obviously , which means that the system achieves consistency at a predetermined time and, in addition, all states are bounded.

[0059] Next, we will explain that any agents will not be far away from each other. Any smart neighbor , energy function: (twenty three) In formula (23), is the energy function, , To estimate the neighbor The first-order state of each agent is calculated according to formula (6).

[0060] By taking the derivative of formula (23), we can get: (twenty four) In formula (24), yes The derivative of yes The derivative of .

[0061] Substituting formula (14) into formula (24) yields: (25) In formula (25), is bounded, the following inequality holds: (26) at this time , will decrease, which means that the distance between agents is decreasing; , inequality (26) will be Therefore, it can be ensured that the distance between agents is always smaller than the communication range of each other, and there will be no outliers.

[0062] Step S6: According to the predetermined time control scheme given in step S4, the feasibility of the proposed algorithm is verified through a numerical simulation example.

[0063] like Figure 3 As shown, consider a multi-agent system consisting of four agents, as its topological structure, the dynamic equation of the agent is: (27) In formula (27), represents the first-order state of the follower agent, i.e., its position, represents the second-order state of the follower agent, i.e., speed, represents the input of the follower agent, represents the number of the agent, , The data injection attack takes the form of: The initial state of the agent system is: 、 、 、 ; 、 、 、 .

[0064] The remaining control parameters are: , in formula (15) , in formula (18) , in formula (10) , in formula (14) , in formula (7) .

[0065] like Figure 4 As shown in the simulation image of the system, the horizontal axis is time in seconds and the vertical axis is consistency error In order to more intuitively show the consistency error of the agent, this application defines a consistency absolute error, namely It can be seen that the absolute error of consistency converges to a sufficiently small area within the predetermined time.

[0066] like Figure 5 As shown, the horizontal axis is time in seconds, and the vertical axis is the estimation error, which shows that the designed estimation strategy based on historical information can estimate the true state of neighbor information at the cost of smaller error.

[0067] like Figure 6 and Figure 7 As shown, in order to demonstrate that the weight design with penalty factors in the algorithm of this application can ensure the constraint effect on the distance between intelligent agents, weight schemes with or without penalty factors are designed.

[0068] like Figure 6As shown, the horizontal axis is time in seconds, and the vertical axis is the distance between agents when the penalty factor is included , it can be seen that when achieving consistency control, the agents are always within the communication range of each other, that is, .

[0069] like Figure 7 As shown, the horizontal axis is time in seconds, and the vertical axis is the distance between agents when the penalty factor is not included. , it can be shown that if the distance between agents quickly exceeds their communication range without adding a penalty factor, information exchange and consistent control cannot be achieved, and the distributed control strategy fails. Through comparative experiments, it can be concluded that the distance-based penalty factor designed in this paper is effective.

[0070] In order to facilitate the overall understanding of the technical solution of the present application, the technical concept is summarized and briefly described as follows. Based on background knowledge, the present application proposes an anti-outlier predetermined time control scheme with a security mechanism to ensure that the multi-agent system can separate the real and usable information from the attacked signal, and at the same time achieve predetermined time convergence control of the system under the premise of ensuring that outliers do not occur. In order to avoid the impact of data injection attacks, a security estimation strategy based on historical data is proposed, which can effectively parse the valid neighbor state. At the same time, since the communication between agents is discrete, a state retainer is designed to make discrete information continuous. In addition, due to the limited communication range, a topological weight design scheme is designed based on distance and with a penalty factor. On this basis, combined with adaptive and backstepping techniques, a security control scheme that converges at a predetermined time and maintains connectivity is constructed. This scheme not only solves the problem of data injection attacks, but also ensures that the system reaches a consensus within the predetermined time and no agent exceeds the communication range.

[0071] The improvements of this application include: a security estimation strategy based on historical data; a communication weight design scheme based on the distance between intelligent agents; and a predefined time control scheme for data injection attacks and bounded communication range.

[0072] Beneficial technical effects: This application proposes a multi-agent control strategy that can resist data injection attacks and has communication range constraints, achieving predetermined time consistency control of the multi-agent system. To address malicious data injection attacks by external attackers on data transmitted between agents, this application proposes a security estimation strategy based on historical data, which can estimate the approximate value of the state of neighboring agents through historical data. To address the situation where the communication range between agents is limited, this application proposes a distance-based weight design scheme that can ensure that the agents do not exceed each other's communication range during the control process.

[0073] In summary, this application proposes a multi-agent control scheme that is resistant to data injection attacks and constrained by communication range. This scheme ensures that the group of agents can achieve consistency even when subjected to data injection attacks and under limited communication range, while also ensuring that the time required to execute tasks can be specified. The proposed control scheme consists of a security estimation scheme based on historical data, a discrete information continuity scheme, a weight design scheme based on a penalty factor, and a predetermined time control scheme based on backstepping. First, using the post-attack information sent by neighboring agents, a security estimation scheme is employed to extract true state information from this post-attack information. The discrete information continuity scheme allows the extracted correct information to be continuous, thus enabling subsequent controller design. Second, to prevent drones from straying from the group due to out-of-range communication, a weight design scheme based on a penalty factor is employed. Finally, based on the security estimation strategy, continuity scheme, and novel weight design, a predetermined time control scheme is proposed to ensure system convergence within a predetermined time. This application is primarily applicable to multi-agent control scenarios subject to data injection attacks and constrained by communication range.

[0074] The intelligent agent is a drone, robot, unmanned ship, robot dog or robot wolf.

Claims

1. A multi-agent control method for resisting data injection attacks with communication range constraints, characterized by: The following steps are included: Step S1: Design and obtain a security control strategy based on historical data. The security control strategy includes the sender agent at three consecutive moments 、 、 Send accordingly 、 、 data, is a predetermined amount, , is the sender agent in status, is the sender agent in , the corresponding information that the receiver agent can receive is 、 、 , It's a multiplicative attack. It is an additive attack. The receiver agent calculates the approximate amount of information injected by the external attacker based on the received data, thereby obtaining the approximate neighbor state data, which is discrete data. Step S2: Continuize the discrete data obtained in step S1 to obtain smoothed data; Step S3: Design a distance-based communication weight strategy with a penalty factor to avoid outliers; Step S4: Combining the communication weight strategy obtained in step S3, based on backstepping control, a predetermined time control scheme is constructed.

2. A multi-agent control method for resisting data injection attacks with communication range constraints according to claim 1, characterized in that: In step S1, the attack form is: (1) In formula (1), It is the information that the receiver agent can receive and utilize. is the information sent by the sender agent; Will 、 、 The three data are operated as follows: ① ② ③ yes The estimated value of yes Estimated value of assuming the attack signal 、 、 , if the calculated result is Substitute a smaller constant to calculate the approximate amount of information injected by an external attacker; According to formula (2), the approximate neighbor state is calculated. (2) In formula (2), is the approximate neighbor state; Select three consecutive pieces of information as 、 、 , The estimated error is: (3) In formula (3), for estimated value of; The following inequalities are satisfied: yes The upper bound of the rate of change, , , , rewrite formula (3) as: (4) In formula (4), ; According to formula (4), as long as the time interval Select a small enough value so that the strategy can guarantee The accuracy of the estimate, The estimated error is: (5) In formula (5), yes The upper bound of the rate of change, ; Time interval 、 The selected value is small enough so that the security control strategy can ensure Accuracy of estimates.

3. The multi-agent control method for resisting data injection attacks with communication range constraints according to claim 2, characterized in that: In the step S2, (6) In formula (6), is the smoothed data, as estimated value of; , , yes After the moment, for Estimates, for Estimates.

4. The multi-agent control method for resisting data injection attacks with communication range constraints according to claim 3 is characterized by: In step S3, the communication weight for: (7) In formula (7), is the communication weight between the ith agent and the lth agent, is the connection weight between the ith agent and the lth agent based on graph theory, is the penalty factor, represents the vector distance between agents, represents the distance between agents, is the first-order state of the ith agent, To estimate the first-order state of the neighbor l-th agent, is the upper bound of the distance between agents allowed; the estimated value of the neighboring agent l is calculated according to formula (6) , due to the estimated With actual There is a certain error between The choice of needs to take this part of the error into account, namely: (8) In formula (8), is the upper bound of the error, is the maximum communication range of the agent; Combining Equations (7) and (8), we obtain a distance-based communication weight strategy with a penalty factor. When the distance between agents gradually approaches the communication boundary, the communication weight between agents will gradually increase, making the agents more closely connected in the topology, thus staying away from the communication boundary, preventing the occurrence of outliers, and maintaining the connectivity of the communication topology.

5. The multi-agent control method for resisting data injection attacks with communication range constraints according to claim 4 is characterized in that: The step S4 specifically includes the following steps: Depend on Agents form a multi-agent system, The dynamic equation of an agent is: (9) In formula (9), Representative The first Stage state, 、 Representing the The input and output of an agent, the output is the data sent through the network, represents an unknown nonlinear function, , Represents the order, , represent The derivative of For the The first Stage state, represent The derivative of Representative The first Stage state, For the The first-order state of each agent; Predefined time scale functions for: (10) In formula (10), is the time scale function, For time, For the scheduled time, , is the design parameter, ; Based on the communication weights in step S3, the distributed error is: (11) In formula (11), For the The distributed error of each agent, Represents the number of agents; By taking the derivative of formula (11), we can get: (12) In formula (12), represent The derivative of , Representative The second-order state of an agent, represents a nonlinear function, for The derivative of , ; Coordinate transformation: (13) In formula (13), It is The first-order error variable of each agent, It is The first The error variable, It is The first First-order virtual controller; Combined with the coordinate transformation of formula (13), the virtual controller designed based on the backstepping method includes formulas (14), (15) and (16), the controller is formula (17), and the adaptive law is formula (18), as follows: (14) In formula (14), It is The second-order virtual controller of each agent, yes The derivative of yes Estimates, , is the square of the fuzzy weight modulus, 、 All are design parameters; (15) In formula (15), It is The third-order virtual controller of the agent, For the The second-order error variable of each agent, is a design parameter; (16) In formula (16), is the k+1th order virtual controller, For the The first The error variable, is a design parameter; (17) In formula (17), For the The first The error variable, is a design parameter; (18) In formula (18), for The derivative of is a design parameter; The predetermined time control scheme includes a virtual controller, a controller and an adaptive law, and an RBF neural network is used to approximate the unknown nonlinear function, that is: (19) In formula (19), is a nonlinear function. When k=1, ,when hour, , is an unknown nonlinear function, is the ideal weight vector, is the radial basis function vector, is the approximation error, is the upper bound of the approximation error, , .

6. The multi-agent control method for resisting data injection attacks with communication range constraints according to claim 1, characterized in that: The method further comprises step S5 after step S4, Step S5: Using the Lyapunov function stability definition, prove that the predetermined time control scheme obtained in step S4 is effective.

7. The multi-agent control method for resisting data injection attacks with communication range constraints according to claim 6, characterized in that: The step S5 specifically includes the following steps: Lyapunov function: (20) In formula (20), is the Lyapunov function, Represents the estimation error of the unknown weight vector; By deriving Equation (20) and substituting it into the corresponding virtual controllers (14), (15), and (16), the controller (17), and the adaptive law (18), we can obtain: (21) In formula (21), yes The derivative of , , is the upper bound of the approximation error; Solving equation (21) yields: (22) In formula (22), yes exist The value at time , that is, the initial value of the Lyapunov function; According to formula (22), when time When , the Lyapunov function is a bounded quantity, which means that the elements that constitute the Lyapunov function It is also a bounded quantity, that is, there is a constant 、 ,satisfy ; Combined with formula (13), we can get , , obviously , which means that the system achieves consistency at a predetermined time, and in addition, all states are bounded; Next, we will explain that any agents will not be far away from each other. Any smart neighbor , energy function: (23) In formula (23), is the energy function, , To estimate the neighbor The first-order state of each agent is calculated according to formula (6); By taking the derivative of formula (23), we can get: (24) In formula (24), yes The derivative of yes The derivative of Substituting formula (14) into formula (24) yields: (25) In formula (25), is bounded, the following inequality holds: (26) at this time , will decrease, which means that the distance between agents is decreasing; , inequality (26) will be Therefore, it can be ensured that the distance between agents is always smaller than the communication range of each other, and there will be no outliers.

8. The multi-agent control method for resisting data injection attacks with communication range constraints according to claim 1, characterized in that: The method further comprises step S6 after step S4, Step S6: Verify the feasibility of the predetermined time control scheme obtained in step S4 through a numerical simulation example.

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