A Secure Group Consensus Control Method for Heterogeneous Unmanned Systems under DoS Attacks

Abstract

The present invention claims protection for a secure grouping consensus control method for heterogeneous unmanned systems under DoS attacks. The cluster control of unmanned systems is a typical application of the consensus collaborative control of multi-agent systems, and the multi-agent system is specifically elaborated in the content of this patent. It includes using matrix knowledge to transform the dynamic models of second-order agents and first-order agents to obtain the dynamic equations of an equivalent homogeneous system; considering that project engineering is generally deployed in an open environment, introducing more complex and variable multi-channel independent DoS attacks to enhance the robustness of the system; introducing an estimator to eliminate the adverse effects brought by multi-channel independent DoS attacks and accelerate the convergence of the system; agents and their estimators need to distinguish the information transmitted by neighbor nodes and process the information separately according to the secure consensus protocol; the control protocol for agent state update additionally considers the case of different state dimensions in heterogeneous systems, which can ensure the ultimate realization of secure grouping consensus of multi-agent systems.

Description

Technical Field

[0001] The present invention relates to the field of multi-agent system control. Unmanned system cluster control is a typical application of consistent collaborative control of multi-agent systems. The multi-agent system is used for specific description in this patent content. Background Art

[0002] Multi-agent distributed systems, due to their unique advantages such as high efficiency, scalability, and robustness, are widely used in smart grids, intelligent decision-making, and expert systems. While robustness and fault tolerance are inherent in multi-agent systems, their purpose is merely to ensure a certain degree of resilience against internal disturbances and errors. Once malicious attacks intrude from the outside, the system's fault tolerance mechanisms often become ineffective, severely impacting performance and even causing it to diverge. For a securely controllable distributed multi-agent system, not only must fault tolerance be designed within the system, but external malicious attacks must also be considered. Therefore, the security of multi-agent systems has become a critical issue that needs to be addressed urgently.

[0003] An analysis of existing research reveals the following: First, DoS attack modeling is relatively simple. The periodic and aperiodic DoS attacks involved are mostly synchronized DoS attacks on the channel, making their control protocols inapplicable to systems subject to more flexible, independent DoS attacks on multiple channels. Second, existing research primarily focuses on homogeneous systems, with limited attention paid to heterogeneous systems, which are more realistic. Third, while existing security control protocols ultimately achieve system consensus, they lack effective solutions for the problem of slowed convergence caused by communication interruptions during DoS attacks. Furthermore, for a resource-limited system, the relationships between agents are not limited to the simple cooperative or competitive relationships described in existing literature; more complex cooperative-competitive relationships are more suitable for practical engineering applications. Based on the above analysis, this paper designs a controller with a novel estimator to mitigate the impact of DoS attacks and accelerate system convergence. Compared to similar work, during a DoS attack, our estimator iteratively simulates the states of neighboring agents based on the last communication information before the communication interruption and the information of the agent using our estimator, effectively preventing excessive deviations in the agent states. In addition, the cooperation-competition relationship between intelligent agents is fully considered when designing the controller, making it more suitable for real-world applications.

[0004] After searching, the application publication number CN111934917A is a group consistency control method for a heterogeneous multi-agent system based on trust nodes, which includes: any agent undergoing state convergence receives state values from neighboring agents and sorts the received state values in descending order; performs information value processing, selectively removes nodes, and represents the removed nodes as a set Ri, represents the set of trusted nodes in the removed nodes as Ti, and sets the edge weights of the remaining removed nodes and node i to 0; obtains the position and speed information of normal nodes according to the dynamic equation, sets a consistency control protocol based on the position and speed information of normal nodes, and processes the normal nodes using the consistency control protocol to achieve node group consistency in the heterogeneous multi-agent system. The present invention expands the system structure to a heterogeneous multi-agent system, adds a trust node mechanism and grouping, and enhances the robustness of the multi-agent system.

[0005] 1. The malicious attacks considered in the above patents are a type of node attack. Although malicious nodes will introduce some irrelevant data into the system, there is always data available for system updates, and the data introduced by malicious nodes does not always have a bad effect. At certain moments, it may even be beneficial to system convergence. The DoS attack model considered in this article is to maliciously occupy the communication network, resulting in a lack of necessary interactive information between nodes. However, the control protocol of the multi-agent system is designed based on the interactive information between nodes, so DoS attacks will cause greater damage to the multi-agent system. The control protocol designed in this article based on the DoS attack model has higher security.

[0006] Second, the core concept of the control protocol design in the aforementioned patent is to filter received data through sorting, eliminating marginal data at both ends and retaining central data to ensure system security and consistency. However, the attack model in this article results in a lack of interactive information available to nodes. Therefore, the control protocol in the aforementioned patent is not suitable for multi-agent systems subjected to DoS attacks.

[0007] Third, the communication topology used in the aforementioned patents is fixed, but in real applications, communication topologies are easily changed by interference or malicious attacks. Therefore, the control protocol designed in this paper fully considers various situations of system topology switching, making it more applicable. Summary of the Invention

[0008] The present invention aims to solve the above problems in the prior art. It proposes a method for secure group consensus control of heterogeneous unmanned systems under DoS attacks. Unmanned system cluster control is a typical application of consensus collaborative control of multi-agent systems. This patent content uses a multi-agent system to specifically illustrate the application. The technical solution of the present invention is as follows:

[0009] A security grouping consensus control method for heterogeneous unmanned systems under DoS attacks, which includes the following steps:

[0010] S1. Use matrix knowledge to transform the dynamic model of a heterogeneous system with second-order agents and first-order agents to obtain the dynamic equation of an equivalent homogeneous system;

[0011] S2. Introduce a multi-channel independent DoS attack model;

[0012] S3. Introduce an estimator that can be iteratively updated; the estimator is enabled when a DoS attack occurs and is used to estimate the states of neighboring agents during the DoS attack;

[0013] S4. Agents and their estimators distinguish the information transmitted by neighboring nodes, and process the information of agents in the same group and agents in different groups separately according to the security consensus protocol;

[0014] S5. Set the control protocol for agent state update. The control protocol takes into account the different state dimensions in the heterogeneous system. Each agent continuously updates its own state information according to its corresponding control strategy, and finally realizes the secure grouping consensus of the multi-agent system.

[0015] Furthermore, the dynamic model of the heterogeneous system of second-order agents and first-order agents transformed by using matrix knowledge is as follows:

[0016]

[0017] where, x i (t) represents the position information of agent i at time t, denotes the derivative of x i (t), v i (t) represents the velocity information of agent i at time t, denotes the derivative of v i (t), u i (t) represents the control input of agent i at time t; r1 represents the set of first-order agents, and r2 represents the set of second-order agents;

[0018] The transformed agent dynamic equation includes:

[0019]

[0020] where, the system matrix the input matrix u i (t) represents the control input of agent i at time t; the transformation vector W i (t) can be expressed according to different agents as:

[0021]

[0022] Furthermore, the step S2 also has the following constraints on DoS attacks:

[0023]

[0024] where, Λ ij (t1, t2) represents the set of time periods during which the channel (i, j) ∈ ε suffers from DoS attacks within the time period [t1, t2), ε represents the initial edge set of the system, and (i, j) represents the edge through which the agent i transmits information to the agent j; len(Λ ij (t1, t2)) represents the total time of DoS attacks suffered by the channel (i, j) ∈ ε within the time period [t1, t2); represents the magnitude of the attack intensity, and γ ij > 0 is the base time for each channel to suffer from DoS attacks;

[0025] For different attack modes, define ζ(t) = {(i, j) ∈ ε \ ε(t)|t ∈ len(Λ ij (0, ∞))} as the set of channels suffering from attacks at time t, where ε \ ε(t) means belonging to the set ε but not belonging to the set ε(t).

[0026] Furthermore, the dynamic equation of the S3 estimator is as follows:

[0027]

[0028] where, represents the estimated value of the position of the neighbor agent by the agent i at time t, represents the estimated value of the velocity of the neighbor agent by the agent i at time t, represents the control input of the estimator at time t;

[0029] The control protocol of the estimator is as follows:

[0030]

[0031] where, c1 and c2 are the coupling strengths regarding position and velocity respectively, and N Si represents the set of agents in the same group as the agent i, and N Di represents the set of agents not in the same group as the agent i.

[0032] Furthermore, the S4, the agent and its estimator need to distinguish the information transmitted by the neighbor nodes, and process the information of the agents in the same group and the information of the agents in different groups respectively according to the security consistency protocol, specifically including:

[0033] Establish a cooperation-competition interaction mechanism. The cooperation-competition interaction mechanism means that there is a cooperation relationship among the agents in the same group, and a competition relationship among the agents in different groups. The adjacent nodes of agent i can only be in N Si and N Di So N i = N Si ∪N Di ; Considering the two-group situation, the first M nodes are in one group, and the last N - M nodes are in another group. The two-group mechanism and the cooperation-competition interaction relationship are considered simultaneously in the control protocol.

[0034] Furthermore, the specific steps of step S5 include:

[0035] For a heterogeneous multi-agent system, when the following conditions are met, it is said that the multi-agent system based on cooperation-competition can asymptotically achieve two-group consensus:

[0036]

[0037]

[0038] Among them, means that agent i and agent j are in the same group, means that agent i and agent j are in different groups.

[0039] Furthermore, assume that the multi-agent system consists of N agents, and its topological relationship can be represented by a time-varying undirected graph where represents the node set, represents the edge set at time t. In an undirected graph, the edge (i, j) ∈ ε(t) for information transmission from agent i to agent j is equivalent to the edge (j, i) ∈ ε(t) for information transmission from agent j to i, that is, (i, j) = (j, i); the set of adjacent nodes of node i can be expressed as [[ID=From here, it seems there is some text missing in your input. Please check and provide the complete content for accurate translation.]] For the adjacency matrix representing the connection relationship between nodes at time t, where a ij (t) > 0 is the weight of the edge (i, j). If (i, j) ∈ ε(t), then a ij (t) = 1; otherwise, a ij (t) = 0; it is stipulated that a ii (t) = 0, that is, there is no self-loop in the system topology; the Laplacian matrix of the undirected graph at time t is defined as where and when i ≠ j, l ij (t) = -a ij (t); Considering that the system topology is time-varying, the initial Laplacian matrix is defined as L = {L(t)|t = 0}, and the initial graph is defined as Among them represents the initial edge set.

[0040] Furthermore, the security control protocol based on the estimator is designed as follows:

[0041]

[0042] where c1 and c2 are the coupling strengths regarding position and velocity respectively, and N Si represents the set of agents in the same group as agent i, and N Di represents the set of agents in different groups from agent i, and ζ(t) represents the set of edges suffering from DoS attacks.

[0043] The advantages and beneficial effects of the present invention are as follows:

[0044] 1. The system model of the present invention is a heterogeneous multi-agent system with different dynamic models in Claim 2. There are both first-order agents and second-order agents in the system. Compared with the homogeneous systems that only have first-order agents or second-order agents in similar work, the agents with different dynamic models in this system model can cooperate with each other and collaborate to complete complex tasks. Therefore, the heterogeneous system can more accurately describe the actual engineering.

[0045] 2. The present invention introduces the DoS attack model described in Claim 3 into the system, and it is a multi-channel independent DoS attack where multiple communication links are independently attacked. Periodic DoS attacks and non-periodic DoS attacks in similar work are essentially multi-channel synchronous attacks, which are special cases of multi-channel independent DoS attacks. In addition, the control protocol designed by the present invention for multi-channel independent DoS attacks in Claim 3 is also applicable to heterogeneous systems suffering from multi-channel synchronous DoS attacks, but not vice versa. Therefore, the control protocol of the present invention is more universal and the applicability of the system is very wide.

[0046] 3. The present invention introduces the estimator designed in Claim 4 in the design of the controller. The estimator is enabled when a DoS attack occurs and is used to estimate the states of neighboring agents during the DoS attack. Therefore, the controller proposed by the present invention can effectively avoid the excessive deviation of the states of agents during the DoS attack, thereby effectively weakening the adverse effects of the DoS attack on the system and accelerating the convergence of the system.

[0047] 4. The present invention introduces the two-group mechanism and the cooperation-competition interaction mechanism described in Claim 5 and Claim 6 into the control protocol of the heterogeneous multi-agent system. This protocol divides the agents in the system into two groups. Compared with a single cooperation or competition interaction relationship, the cooperation-competition interaction is more in line with the interaction relationship of each unit in the realistic complex system, which is beneficial to the execution of complex tasks in the heterogeneous system. Finally, it can achieve that the agents in the same group converge to the same state value, and the convergence state values of the agents in different groups are opposite as described in Claim 6. In addition, the two-group mechanism is also more conducive to the decomposition of large tasks in the complex system and improves the execution efficiency of the heterogeneous system. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 is the system control flowchart of the preferred embodiment provided by the present invention;

[0049] Figure 2 is the system topology diagram of the embodiment of the present invention;

[0050] Figure 3 is the agent position evolution diagram of the embodiment of the present invention;

[0051] Figure 4 is the agent speed evolution diagram of the embodiment of the present invention.

[0052] Figure 5 is the DoS attack signal diagram of the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0053] The control of unmanned system clusters is a typical application of the consensus cooperative control of multi-agent systems. The content of this patent uses multi-agent systems for specific elaboration. The technical solutions in the embodiments of the present invention will be clearly and detailedly described below with reference to the accompanying drawings in the embodiments of the present invention. The described embodiments are only part of the embodiments of the present invention.

[0054] The technical solution of the present invention to solve the above technical problems is:

[0055] As Figure 1 shown, a secure grouping consensus control method for a heterogeneous unmanned system under DoS attacks, the method includes but is not limited to the following steps:

[0056] S1. Use matrix knowledge to transform the dynamic model of the heterogeneous system with second-order agents and first-order agents to obtain the dynamic equation of the equivalent homogeneous system.

[0057] The dynamic model of the heterogeneous system is as follows:

[0058]

[0059] Among them, x i(t) represents the position information of agent i at time t, v i (t) represents the velocity information of agent i at time t, u i (t) represents the control input of agent i at time t. r1 represents the set of first-order agents, and r2 represents the set of second-order agents.

[0060] The converted agent dynamics equation includes:

[0061]

[0062] Among them, the system matrix The input matrix u i (t) represents the control input of agent i at time t. The conversion vector W i (t) can be expressed according to different agents as:

[0063]

[0064] Among them, x i (t) represents the position information of agent i at time t, v i (t) represents the velocity information of agent i at time t. r1 represents the set of first-order agents, and r2 represents the set of second-order agents.

[0065] S2. Considering that project engineering is generally deployed in an open environment, more complex and changeable multi-channel independent DoS attacks are introduced to enhance the system robustness.

[0066] The DoS attacks generated in the DoS attack model are restricted and cannot continue indefinitely. It needs to terminate the attack activity and sleep for a period of time when the resources are exhausted to provide energy for the next attack. Therefore, the following constraints are imposed on the DoS attack:

[0067]

[0068] Among them, Λ ij (t1,t2) represents the set of time periods of DoS attacks suffered by the channel (i,j)∈ε during the time period [t1,t2), and len(Λ ij (t1,t2)) represents the total time of DoS attacks suffered by the channel (i,j)∈ε during the time period [t1,t2). Represents the magnitude of the attack intensity, γ ij >0 is the basic time for each channel to suffer DoS attacks.

[0069] In similar work, generally, two situations are discussed: all channels are under attack or all channels are in normal communication. The multi-channel independent DoS attack model considers various attack patterns. Such multi-channel independent DoS attacks are more flexible, which increases the difficulty in system security control. For different attack patterns, define ζ(t) = {(i, j) ∈ ε \ ε(t)|t ∈ len(Λ ij (0, ∞))}, as the set of channels under attack at time t, where ε \ ε(t) means belonging to the set ε but not belonging to the set ε(t).

[0070] S3. Introduce an estimator that can be iteratively updated to eliminate the adverse effects brought by multi-channel independent DoS attacks and accelerate system convergence.

[0071] The dynamic equation of the estimator is as follows:

[0072]

[0073] where, represents the estimated value of the position of agent i for its neighbor agents at time t, represents the estimated value of the velocity of agent i for its neighbor agents at time t, represents the control input of the estimator at time t.

[0074] The control protocol of the estimator is as follows:

[0075]

[0076] where, c1 and c2 are the coupling strengths regarding position and velocity respectively, N Si represents the set of agents in the same group as agent i, N Di represents the set of agents not in the same group as agent i.

[0077] S4. Agents and their estimators need to distinguish the information transmitted by neighbor nodes and process the information of agents in the same group and agents in different groups respectively according to the security consistency protocol.

[0078] The cooperation-competition interaction mechanism means that there is a cooperation relationship among agents in the same group, and a competition relationship among agents in different groups. The adjacent nodes of agent i can only be in N Si and N Di , so N i = N Si ∪N Di . In addition, to reduce the analysis difficulty, temporarily consider the two-group situation. The first M nodes are in one group, and the last N - M nodes are in another group. Since the two-group mechanism and the cooperation-competition interaction relationship are considered simultaneously in the control protocol, this control protocol is more general than similar work.

[0079] S5. The control protocol for agent state update additionally considers the case of different state dimensions in heterogeneous systems. Each agent continuously updates its own state information according to its corresponding control strategy, and finally realizes the secure grouping consensus of the multi-agent system.

[0080] For a heterogeneous multi-agent system, if the following conditions are satisfied, the multi-agent system based on cooperation-competition can asymptotically achieve bipartite consensus:

[0081]

[0082]

[0083] where indicates that agent i and agent j are in the same group, indicates that agent i and agent j are in different groups.

[0084] Suppose the multi-agent system consists of N agents, and its topological relationship can be represented by a time-varying undirected graph where represents the node set, represents the edge set at time t. In an undirected graph, the edge (i, j) ∈ ε(t) for information transmission from agent i to agent j is equivalent to the edge (j, i) ∈ ε(t) for information transmission from agent j to i, that is, (i, j) = (j, i). The set of adjacent nodes of node i can be represented as is the adjacency matrix representing the connection relationship between nodes at time t, where a ij (t) > 0 is the weight of the edge (i, j). If (i, j) ∈ ε(t), then a ij (t) = 1; otherwise, a ij (t) = 0. It is stipulated that a ii (t) = 0, that is, there is no self-loop in the system topology. The Laplacian matrix of the undirected graph at time t is defined as where and when i ≠ j, l ij (t) = -a ij (t). Considering that the system topology is time-varying, the initial Laplacian matrix is defined as L = {L(t)|t = 0}, and the initial graph is defined as where represents the initial edge set.

[0085] To verify the effectiveness of the proposed secure consensus control protocol, MATLAB is used for simulation verification. In the description of this specification, one node represents one agent.

[0086] Consider a multi-agent system with 6 agents, and the communication topology is as Figure 2 shown. Among them, nodes v1, v3, v4 and nodes v2, v5, v6 belong to two groups respectively. Without loss of generality, the initial states of each agent are selected as follows: x(0) = [-1, -2, -4, 6, 8, 10] T , v(0) = [0.7, 0.3, -0.66, -0.5] T . From Figure 2 it can be seen that the communication topology graph has 8 edges. Therefore, there are a total of 2 8 = 256 attack patterns, which will not be listed one by one here. Set the attack intensity of each channel's DoS attack as i, j = 1, 2, 3, 4, 5, 6, i ≠ j.

[0087] From the simulation results, as Figure 3 and Figure 4 respectively show the evolution processes of the position states and velocity states of all agents. At 20.84 unit time, the velocities of the second-order agent nodes 3, 4, 5, 6 converge to 0, and at 22.64 unit time, the positions of all agents converge to ±2.4. Figure 5 shows the step diagram of the DoS signal, and it can be seen that the DoS attacks suffered by each channel are different.

[0088] It should also be noted that the term "including", "comprising" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed, or also includes elements inherent in such a process, method, commodity or device. Without more limitations, an element defined by the statement "including a..." does not exclude the existence of another identical element in the process, method, commodity or device including the said element.

[0089] The above embodiments should be understood as only for illustrating the present invention and not for limiting the protection scope of the present invention. After reading the content recorded in the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A secure grouping consensus control method for heterogeneous unmanned systems under DoS attacks. The cluster control of unmanned systems is a typical application of the consensus collaborative control of multi-agent systems. It is specifically described using multi-agent systems, and is characterized in that, Including the following steps: S1. Use matrix knowledge to transform the dynamic model of a heterogeneous system with second-order agents and first-order agents to obtain the dynamic equation of an equivalent homogeneous system; S2. Introduce a multi-channel independent DoS attack model; S3. Introduce an estimator that can be iteratively updated. The estimator is enabled when a DoS attack occurs and is used to estimate the states of neighbor agents during the DoS attack; S4. The agents and their estimators need to distinguish the information transmitted by neighbor nodes and process the information of agents in the same group and agents in different groups separately according to the security consensus protocol; S5. Set the control protocol for agent state update. The control protocol takes into account the different state dimensions in the heterogeneous system. Each agent continuously updates its own state information according to its corresponding control strategy, and finally realizes the secure grouping consensus of the multi-agent system; The dynamic model of the heterogeneous system of second-order agents and first-order agents transformed using matrix knowledge is as follows: where x i (t) represents the position information of agent i at time t, denotes the derivative of x i (t), and v i (t) represents the velocity information of agent i at time t, denotes the derivative of v i (t), and u i (t) represents the control input of agent i at time t; r1 represents the set of first-order agents, and r2 represents the set of second-order agents; The dynamic equation of the transformed agent includes: Among them, the system matrix input matrix u i (t) represents the control input of agent i at time t; the transformation vector W i (t) can be expressed according to different agents as follows: Step S2 also has the following constraints on the DoS attack: Among them, Λ ij (t1, t2) represents the set of time periods during which the channel (i, j) ∈ ε is under a DoS attack within the time period [t1, t2). ε represents the initial set of edges in the system, and (i, j) represents the edge through which information is transmitted from agent i to agent j; len(Λ ij (t1, t2)) represents the total time of the DoS attack suffered by the channel (i, j) ∈ ε within the time period [t1, t2); represents the magnitude of the attack intensity, γ ij > 0 is the base time for each channel to suffer a DoS attack; For different attack patterns, define ζ(t) = {(i, j) ∈ ε \ ε(t) | t ∈ len(Λ ij (0, ∞))}, as the set of channels under attack at time t, where ε \ ε(t) means belonging to set ε but not belonging to set ε(t); The dynamic equation of the estimator in S3 is as follows: Among them, represents the estimated position of agent i for its neighbor agents at time t, represents the estimated velocity of agent i for its neighbor agents at time t, represents the control input of the estimator at time t; The control protocol of the estimator is as follows: where c1 and c2 are the coupling strengths regarding position and velocity respectively, N Si denotes the set of agents in the same group as agent i, N Di denotes the set of agents not in the same group as agent i.

2. The security grouping consensus control method for heterogeneous unmanned systems under DoS attacks according to claim 1, wherein In S4, the agents and their estimators need to distinguish the information transmitted by neighbor nodes and process the information of agents in the same group and agents in different groups separately according to the security consensus protocol. Specifically, it includes: Establish a cooperation-competition interaction mechanism. The cooperation-competition interaction mechanism means that there is a cooperation relationship among the agents in the same group, and a competition relationship among the agents in different groups. The adjacent nodes of agent i can only be in N Si and N Di So N i = N Si ∪ N Di ; Considering the two-group case, the first M nodes are in one group, and the last N - M nodes are in another group. The two-group mechanism and the cooperation-competition interaction relationship are considered simultaneously in the control protocol.

3. The secure grouping consensus control method for heterogeneous unmanned systems under DoS attacks according to claim 2, characterized in that Step S5 specifically includes: For a heterogeneous multi-agent system, when the following conditions are met, it is said that the multi-agent system based on cooperation-competition can asymptotically achieve two-group consensus: Among them, indicates that agent i and agent j are in the same group, indicates that agent i and agent j are in different groups.

4. A security grouping consistent control method for heterogeneous unmanned systems under DoS attacks according to claim 3, characterized in that, Suppose the multi-agent system consists of N agents, and its topological relationship can be represented by a time-varying undirected graph denoted as, where represents the node set, represents the edge set at time t. In an undirected graph, the edge (i, j) ∈ ε(t) for information transmission between agents i and j is equivalent to the edge (j, i) ∈ ε(t) for information transmission from agent j to i, that is, (i, j) = (j, i); the set of adjacent nodes of node i can be expressed as is the adjacency matrix representing the connection relationship between nodes at time t, where a ij (t) > 0 is the weight of the edge (i, j). If (i, j) ∈ ε(t), then a ij (t) = 1; Otherwise , a ij \(a(t)=0\); It is stipulated that a ii \(a(t)=0\), that is, there is no self-loop in the system topology; at time \(t\), the undirected graph The Laplacian matrix of is defined as where and when \(i\neq j\), \(l\) ij (t)= -a ij (t); Considering that the system topology is time-varying, the initial Laplacian matrix is defined as \(L = \{L(t)|t = 0\}\), and the initial graph is defined as where represents the initial edge set.

5. The secure grouping consensus control method for heterogeneous unmanned systems under DoS attacks according to claim 4, characterized in that The design of the security control protocol based on the estimator is as follows: where $c_1$ and $c_2$ are the coupling strengths regarding position and velocity respectively, $N$ Si denotes the set of agents in the same group as agent $i$, $N$ Di denotes the set of agents in different groups from agent $i$, and $\zeta(t)$ represents the set of edges suffering from DoS attacks.

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