Multi-agent elastic control method based on virtual network three-dimensional extension under DoS attack

Abstract

The present invention discloses a multi-agent elastic control method based on a three-dimensional extension of a virtual network under DoS attacks, which belongs to the technical field of multi-agent security control and comprises the following steps: step 1, performing dynamic modeling on a multi-agent system and a virtual network layer, and converting the dynamic equations based on a distributed control protocol of each agent; step 2, designing a fully distributed control protocol according to the DoS attack to represent the influence of the attack on the system communication topology and the system state; step 3, designing the interaction parameters between the virtual network layer and the multi-agent system, and adjusting the communication weight; step 4, designing a control protocol for the multi-agent system to achieve consistency under DoS attacks of different degrees; the multi-agent elastic control method based on a three-dimensional extension of a virtual network under DoS attacks provided by the present invention significantly enhances the robustness of the multi-agent system and effectively resists the negative influence of DoS attacks on system performance.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-agent security control, and in particular relates to a multi-agent elastic control method based on three-dimensional expansion of a virtual network under DoS attacks. Background Art

[0002] With the rapid development of the control field, the research on multi-agent systems has received more and more attention. Especially in the consistency control protocol. The communication network serves as a medium for information exchange between agents, and any two agents can be identified through this communication network. However, in the case of DoS attacks, the communication network of the multi-agent system will be affected, which will affect the system from reaching consistency. Therefore, it is very important to protect the signal channel from malicious attacks. At present, there are many methods to solve network attacks, and resilient cooperative control is one of them. The concept of resilient control is given in the literature (see Wei D, Ji K. Resilient industrial control system (rics): Concepts, formulation, metrics, and insights. 2010 3rd International Symposium on Resilient Control Systems, 2010. 15–22.), and the system can be effectively controlled even if unexpected failures occur, which may have catastrophic consequences. In addition, DoS attacks can be regarded as one of the unexpected failures.

[0003] Through DoS attacks, attackers can send a large number of data packets to the target to prevent the system from transmitting and exchanging normal data. At present, most defense strategies are based on estimated dynamic compensators to design resilient control protocols. However, this will also cause overcompensation to the system, thereby affecting the nominal performance of the system. Now a new network defense strategy based on a secure communication network of a virtual system is proposed, such as (see Gusrialdi A, Qu Z, Simaan M A. Competitive interaction design of cooperative systems against attacks. IEEE Transactions on Automatic Control, 2018, 63(9):3159–3166.). It achieves resilient control by introducing a second network to reduce the impact of the attack. The advantage of this strategy is that, under normal circumstances, it does not interfere with the control of the multi-agent system. The robustness of the system is guaranteed by the design of the virtual system. Therefore, this application proposes a multi-agent resilient control method based on three-dimensional expansion of a virtual network under DoS attacks. Summary of the invention

[0004] The purpose of the present invention is to provide a multi-agent elastic control method based on three-dimensional expansion of virtual network under DoS attack, design a collaborative elastic control protocol for multi-agent system, utilize the virtual network layer to effectively deal with the denial of service (DoS) attack on the system, and realize the consistency control of the multi-agent system.

[0005] To achieve the above object, the present invention provides a multi-agent elastic control method based on virtual network three-dimensional expansion under DoS attack, comprising the following steps:

[0006] Step 1: Dynamically model the multi-agent system and the virtual network layer, and transform the dynamic equations based on the distributed control protocol of each agent;

[0007] Step 2: Based on the DoS attack, a fully distributed control protocol is designed to represent the impact of the attack on the system communication topology and system status, ensuring that the model can accurately describe the system status when attacked;

[0008] Step 3: Design the interaction parameters between the virtual network layer and the multi-agent system and adjust the communication weight so that it can maintain stable operation when attacked;

[0009] Step 4: Design a control protocol for the multi-agent system to achieve consensus under different degrees of DoS attacks.

[0010] Preferably, in step 1, the multi-agent system and the virtual network layer are dynamically modeled, and the specific process of converting the dynamic equations based on the distributed control protocol of each agent is as follows:

[0011] Step 101: Establish a multi-agent system consisting of N agents and a linear system. The dynamics formula of the i-th agent is as follows:

[0012] ;

[0013] in, Representing an Agent status, Representing an Agent The control input, and are two constant matrices of appropriate dimensions, represents a real vector space of dimension n, represents a real vector space of dimension m, represents an n×n square matrix whose elements are real numbers, represents an m×m square matrix whose elements are real numbers, express The time derivative of

[0014] Step 102, using a diagram to describe the network communication topology in the multi-agent system;

[0015] Step 103: Consider each agent The distributed control protocol of step 101 The dynamic equation of each intelligent agent is transformed and expressed as follows:

[0016] ;

[0017] ;

[0018] In the formula, is the coupling gain, is the feedback gain, represents the elements of the graph adjacency matrix, Representing an Agent The coupling gain is selected as , represents the smallest non-zero eigenvalue of the Laplacian matrix, is the Laplace matrix, K is selected ,in In order to obtain a positive value by solving the algebraic Riccati equation to ensure the stability of the system, the details are as follows:

[0019] ;

[0020] In the formula, Represents the identity matrix.

[0021] Preferably, the specific content of describing the network communication topology in the multi-agent system by using a graph in step 102 is as follows: each agent is represented by each node of the communication topology graph. ,in and denote the node set and edge set respectively, It represents agent 1 to agent , for each node in the topology graph; in the communication topology graph In one side Representing an Agent and Mutual information acquisition, communication topology The Laplace matrix of Defined as , is a non-negative element and an adjacency matrix with zero diagonal elements, is the degree matrix, which is a square matrix whose elements are all zero except the main diagonal. Represents the specific values ​​of the main diagonal elements, which are arranged on the main diagonal in sequence; Laplace matrix has an eigenvalue of zero and the corresponding eigenvector is a vector of 1 if and only if the communication topology is connected, represents the Laplacian matrix of element, Represents an N×N square matrix whose elements are real numbers.

[0022] Preferably, in step 2, according to the DoS attack, a fully distributed control protocol is designed to represent the impact of the attack on the system communication topology and system status. The specific process is as follows:

[0023] Step 201: Construct a mathematical model of periodic DoS attacks:

[0024] ;

[0025] n is a positive integer representing the number of cycles, T is the duration of a DoS attack, Indicates the time period during which the system is not attacked by DoS (Denial of Service), and t indicates the time variable; when When , it means that the system is not under DoS attack and the system communication is normal; when , indicating that the system is under DoS attack and the system communication is abnormal, which may cause data packet loss;

[0026] Step 202: Design elastic control based on virtual system. The specific expression is as follows:

[0027] ;

[0028] ;

[0029] in, represents the state of the virtual node, H is the dynamic matrix inside the virtual system, , and constant It is a parameter that needs to be designed. is the interaction parameter between the multi-agent system and the virtual system, Represents a virtual node status, Represents a virtual node status, express The time derivative of Represents the weight of the communication channels between virtual nodes, Representing an Agent status, and is the weight of the communication path between the agent and the virtual node, and the matrix and are interaction matrices, which depend on the attacker's strategy. Their purpose is to eliminate the impact of the attack on the multi-agent system. It is necessary to choose a suitable dynamic matrix and To build a stable virtual network. Represents the Laplace matrix corresponding to the communication topology between virtual nodes. These designed parameters are related to the attack, and different attacks require different parameters.

[0030] Preferably, the interaction parameters between the virtual network layer and the multi-agent system in step 3 include , , M, G, H and , weight and is the weight of the communication path between the agent and the virtual node, and its value is , represents the Laplacian matrix of element, is the interaction parameter between the multi-agent system and the virtual system, the matrices M and G are the interaction matrices, and H is the dynamic matrix inside the virtual system, where the H matrix selects a Hurwitz matrix, the M matrix is ​​designed to be equal to the feedback gain matrix, and the G matrix is ​​designed to be , is the positive solution of the algebraic Riccati equation, and its specific expression is as follows:

[0031] .

[0032] Preferably, the different degrees of DoS attacks in step 4 include two situations: the DoS attack only acts on the communication channel between two adjacent intelligent agents and the DoS attack destroys the entire communication channel.

[0033] Preferably, considering that the DoS attack only acts on the communication channel between two adjacent agents, the designed control protocol is as follows:

[0034] ;

[0035] , ;

[0036] in, when When When , it means that no attack occurs in the system; is the Laplace matrix when there is no attack, is the Laplace matrix when there is an attack.

[0037] Preferably, considering the situation where a DoS attack destroys the entire communication channel, the designed control protocol is as follows:

[0038] ;

[0039] in, ,when When , indicating that no attack has occurred within the system.

[0040] Therefore, the present invention adopts the multi-agent elastic control method based on virtual network three-dimensional expansion under the above-mentioned DoS attack, which has the following beneficial effects:

[0041] (1) Under normal operation, the present invention will not interfere with the control process of the multi-agent system and will not affect the nominal performance of the system.

[0042] (2) The present invention considers and designs a fully distributed elastic network control strategy that does not rely on global information. The operation of each agent in the system is based on its own local information and the information of its neighbors, and does not rely on global information.

[0043] (3) The fully distributed control algorithm adopted in the present invention is based on the virtual network layer. Compared with the existing algorithms, this method can ensure the robustness of the system regardless of whether the attack signal is correctly identified.

[0044] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is an overall flow chart of the multi-agent elastic control method based on three-dimensional expansion of virtual network under DoS attack of the present invention;

[0046] Figure 2 It is a schematic diagram of the communication topology of the multi-agent system and the virtual network layer in the simulation experiment of the present invention;

[0047] Figure 3 It is a DoS attack signal diagram in the simulation experiment of the present invention;

[0048] Figure 4 It is a consistency error diagram of the multi-agent system under DoS attack that destroys part of the communication topology in the simulation experiment of the present invention;

[0049] Figure 5 It is a consistency error diagram of a multi-agent system with a virtual network layer under a DoS attack that destroys part of the communication topology in the simulation experiment of the present invention;

[0050] Figure 6 It is a consistency error diagram of the multi-agent system under DoS attack that destroys the complete communication topology in the simulation experiment of the present invention;

[0051] Figure 7 It is a consistency error diagram of a multi-agent system with a virtual network layer under a DoS attack that destroys the complete communication topology in the simulation experiment of the present invention. DETAILED DESCRIPTION

[0052] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0053] See also Figure 1-7 , a multi-agent elastic control method based on virtual network stereo expansion under DoS attack, comprising the following steps:

[0054] Step 1: Perform dynamic modeling on the multi-agent system and virtual network layer, and transform the dynamic equations based on the distributed control protocol of each agent. The specific process is as follows:

[0055] Step 101: Establish a multi-agent system consisting of N agents and a linear system. The dynamics formula of the i-th agent is as follows:

[0056] ;

[0057] in, Representing an Agent status, Representing an Agent The control input, and are two constant matrices of appropriate dimensions, represents a real vector space of dimension n, represents a real vector space of dimension m, represents an n×n square matrix whose elements are real numbers, represents an m×m square matrix whose elements are real numbers, express The time derivative of

[0058] Step 102: Use a graph to describe the network communication topology in the multi-agent system. The specific content is as follows: Each agent is represented by each node of the communication topology graph. ,in and denote the node set and edge set respectively, It represents agent 1 to agent , for each node in the topology graph; in the communication topology graph In one side Representing an Agent and Mutual information acquisition, communication topology The Laplace matrix of Defined as , is a non-negative element and an adjacency matrix with zero diagonal elements, is the degree matrix, which is a square matrix whose elements are all zero except the main diagonal. Represents the specific values ​​of the main diagonal elements, which are arranged on the main diagonal in sequence; Laplace matrix has an eigenvalue of zero and the corresponding eigenvector is a vector of 1 if and only if the communication topology is connected, represents the Laplacian matrix of element, Represents an N×N square matrix whose elements are real numbers;

[0059] Step 103: Considering the distributed control protocol of each agent i, the dynamic equation of the i-th agent in step 101 is transformed and expressed as follows:

[0060] ;

[0061] ;

[0062] In the formula, is the coupling gain, is the feedback gain, represents the elements of the graph adjacency matrix, Representing an Agent The coupling gain is selected as , represents the smallest non-zero eigenvalue of the Laplacian matrix, is the Laplace matrix, K is selected ,in In order to obtain a positive value by solving the algebraic Riccati equation to ensure the stability of the system, the details are as follows:

[0063] ;

[0064] In the formula, Represents the identity matrix.

[0065] Step 2: Based on the DoS attack, a fully distributed control protocol is designed to represent the impact of the attack on the system communication topology and system status, ensuring that the model can accurately describe the system status when attacked; the specific process is as follows:

[0066] Step 201: Construct a mathematical model of periodic DoS attacks:

[0067] ;

[0068] n is a positive integer representing the number of cycles, T is the duration of a DoS attack, Indicates the time period during which the system is not attacked by DoS (Denial of Service), and t indicates the time variable; when When , it means that the system is not under DoS attack and the system communication is normal; when , indicating that the system is under DoS attack and the system communication is abnormal, which may cause data packet loss;

[0069] Step 202: Design elastic control based on virtual system. The specific expression is as follows:

[0070] ;

[0071] ;

[0072] in, represents the state of the virtual node, H is the dynamic matrix inside the virtual system, , and constant It is a parameter that needs to be designed. is the interaction parameter between the multi-agent system and the virtual system, Represents a virtual node status, represents the state of virtual node i, express The time derivative of Represents the weight of the communication channels between virtual nodes, Representing an Agent status, and is the weight of the communication path between the agent and the virtual node, and the matrix and are interaction matrices, which depend on the attacker's strategy. Their purpose is to eliminate the impact of the attack on the multi-agent system. It is necessary to choose a suitable dynamic matrix and To build a stable virtual network. Represents the Laplace matrix corresponding to the communication topology between virtual nodes. These designed parameters are related to the attack, and different attacks require different parameters.

[0073] Step 3: Design the interaction parameters between the virtual network layer and the multi-agent system, and adjust the communication weight so that it can maintain stable operation when attacked; the interaction parameters between the virtual network layer and the multi-agent system include , , M, G, H and , weight and is the weight of the communication path between the agent and the virtual node, and its value is , represents the Laplacian matrix of element, is the interaction parameter between the multi-agent system and the virtual system, the matrices M and G are the interaction matrices, and H is the dynamic matrix inside the virtual system, where the H matrix selects a Hurwitz matrix, the M matrix is ​​designed to be equal to the feedback gain matrix, and the G matrix is ​​designed to be , is the positive solution of the algebraic Riccati equation, and its specific expression is as follows:

[0074] .

[0075] Step 4: Design a control protocol for the multi-agent system to reach consensus under different degrees of DoS attacks; different degrees of DoS attacks include two situations: the DoS attack only acts on the communication channel between two adjacent agents and the DoS attack destroys the entire communication channel, as follows:

[0076] Considering that the DoS attack only acts on the communication channel between two adjacent agents, the designed control protocol is as follows:

[0077] ;

[0078] , ;

[0079] in, when When When , it means that no attack occurs in the system; is the Laplace matrix when there is no attack, is the Laplace matrix when there is an attack.

[0080] Considering the situation where DoS attack destroys the entire communication channel, the designed control protocol is as follows:

[0081] ;

[0082] in, ,when When , indicating that no attack has occurred within the system.

[0083] Example

[0084] Simulation verification experiments were conducted for the case where the DoS attack only acts on the communication channel between two adjacent agents and the case where the DoS attack destroys the entire communication channel, as follows:

[0085] 1. Consider a DoS attack that only acts on the communication channel between two adjacent agents, where the communication channel between agent 1 and agent 2 is destroyed:

[0086] The dynamic matrix of the system is as follows:

[0087] ;

[0088] A sinusoidal signal with a frequency of 1 Hz is selected to simulate the active and inactive effects of a DoS attack. When the value of the sinusoidal signal is greater than 0, the attack is activated; when the value is less than or equal to zero, the attack is stopped.

[0089] When there is no attack, the coupling gain is chosen to be At the same time, since the Laplace matrix has changed, the coupling gain also needs to change. The new coupling gain is . The value of is chosen to be 10.

[0090] Can get And K matrix:

[0091] ;

[0092] The H matrix and The matrix is ​​as follows:

[0093] , ;

[0094] Choose M=K. Therefore, we can get the G matrix:

[0095] ;

[0096] from Figure 4 and Figure 5As can be seen in the figure, the error converges slowly. This is because the attack does not completely destroy the communication channel. However, with the design of the virtual layer, it can be clearly seen that the designed resilient cooperative control makes the error converge faster. In addition, the final consistent error is within a small range.

[0097] 2. Consider the case where a DoS attack destroys the entire communication channel:

[0098] The dynamic matrix of the system is as follows:

[0099] ;

[0100] The coupling gain is chosen to be .

[0101] When not attacking, you can get And K matrix:

[0102] ;

[0103] The H matrix and The matrix is ​​as follows:

[0104] , ;

[0105] Choose M=K. Therefore, we can get the G matrix:

[0106] ;

[0107] When the system is attacked, And the K matrix is ​​as follows:

[0108] ;

[0109] Get the G matrix:

[0110] ;

[0111] Can be obtained from Figure 6 and Figure 7 It is clearly seen that after adding the designed virtual layer, the system error can converge to a small range.

[0112] Therefore, the present invention adopts the multi-agent elastic control method based on three-dimensional expansion of virtual network under the above-mentioned DoS attack, which significantly enhances the robustness of the multi-agent system, effectively resists the negative impact of DoS attacks on system performance, and ensures the stability of the system under attack environment.

[0113] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A multi-agent elastic control method based on virtual network stereo expansion under DoS attack, characterized in that: The following steps are involved: Step 1: Dynamically model the multi-agent system and the virtual network layer, and transform the dynamic equations based on the distributed control protocol of each agent; Step 2: Based on the DoS attack, a fully distributed control protocol is designed to represent the impact of the attack on the system communication topology and system status; Step 3: Design the interaction parameters between the virtual network layer and the multi-agent system and adjust the communication weight; Step 4: Design a control protocol for the multi-agent system to reach consensus under different degrees of DoS attacks; In step 2, based on the DoS attack, a fully distributed control protocol is designed to represent the impact of the attack on the system communication topology and system status. The specific process is as follows: Step 201: Construct a mathematical model of periodic DoS attacks: ； n is a positive integer representing the number of cycles, T is the duration of a DoS attack, represents the time period during which the system is not attacked by DoS, and t represents the time variable; when When , it means that the system is not under DoS attack and the system communication is normal; when , indicating that the system is under DoS attack and the system communication is abnormal, resulting in data packet loss; Step 202: Design elastic control based on virtual system. The specific expression is as follows: ， ； in, represents the state of the virtual node, H is the dynamic matrix inside the virtual system, , and constant It is a parameter that needs to be designed. is the interaction parameter between the multi-agent system and the virtual system, represents the state of virtual node j, represents the state of virtual node i, express The time derivative of Represents the weight of the communication channels between virtual nodes, represents the state of agent j, and is the weight of the communication path between the agent and the virtual node, and the matrix and is the interaction matrix; The different degrees of DoS attacks in step 4 include two situations: the DoS attack only acts on the communication channel between two adjacent intelligent agents and the DoS attack destroys the entire communication channel.

2. The multi-agent elastic control method based on virtual network three-dimensional expansion under DoS attack according to claim 1 is characterized in that: In step 1, the multi-agent system and the virtual network layer are dynamically modeled. The specific process of converting the dynamic equations based on the distributed control protocol of each agent is as follows: Step 101: Establish a multi-agent system consisting of N agents and a linear system. The dynamics formula of the i-th agent is as follows: ； in, represents the state of agent i, represents the control input of agent i, and are all constant matrices, represents a real vector space of dimension n, represents a real vector space of dimension m, represents an n×n square matrix whose elements are real numbers, represents an m×m square matrix whose elements are real numbers, express The time derivative of Step 102, using a diagram to describe the network communication topology in the multi-agent system; Step 103: Considering the distributed control protocol of each agent i, the dynamic equation of the i-th agent in step 101 is transformed and expressed as follows: ； ； In the formula, is the coupling gain, is the feedback gain, represents the elements of the graph adjacency matrix, represents the state of agent j; where the coupling gain is selected , represents the smallest non-zero eigenvalue of the Laplacian matrix, is the Laplace matrix, K is selected ,in To obtain a positive definite value by solving the algebraic Riccati equation, as follows: ； In the formula, Represents the identity matrix.

3. The multi-agent elastic control method based on virtual network three-dimensional expansion under DoS attack according to claim 2 is characterized in that: The specific contents of describing the network communication topology in the multi-agent system by using a graph in step 102 are as follows: Each agent is represented by each node of the communication topology graph. ,in and denote the node set and edge set respectively, It represents agent 1 to agent , for each node in the topology graph; in the communication topology graph In one side Indicates that agents i and j obtain information from each other, communication topology diagram The Laplace matrix of Defined as , is a non-negative element and an adjacency matrix with zero diagonal elements, is the degree matrix, Represents the specific values ​​of the main diagonal elements, which are arranged on the main diagonal in sequence; Laplace matrix has an eigenvalue of zero and the corresponding eigenvector is a vector of 1 if and only if the communication topology is connected, represents the Laplacian matrix of element, Represents an N×N square matrix whose elements are real numbers.

4. The multi-agent elastic control method based on three-dimensional expansion of virtual network under DoS attack according to claim 3 is characterized by: The interaction parameters between the virtual network layer and the multi-agent system in step 3 include , , M, G, H and , weight and is the weight of the communication path between the agent and the virtual node, and its value is , represents the Laplacian matrix of element, is the interaction parameter between the multi-agent system and the virtual system, the matrices M and G are the interaction matrices, and H is the dynamic matrix inside the virtual system, where the H matrix selects a Hurwitz matrix, the M matrix is ​​designed to be equal to the feedback gain matrix, and the G matrix is ​​designed to be , is the positive solution of the algebraic Riccati equation, and its specific expression is as follows: 。 5. The multi-agent elastic control method based on three-dimensional expansion of virtual network under DoS attack according to claim 4 is characterized in that: Considering that the DoS attack only acts on the communication channel between two adjacent agents, the designed control protocol is as follows: ； ， ； in, when When When , it means that no attack occurs in the system; is the Laplace matrix when there is no attack, is the Laplace matrix when there is an attack.

6. The multi-agent elastic control method based on three-dimensional expansion of virtual network under DoS attack according to claim 5 is characterized by: Considering the situation where DoS attack destroys the entire communication channel, the designed control protocol is as follows: ； in, ,when When , indicating that no attack has occurred within the system.

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