CN114935915A - Security grouping consistency control method of heterogeneous unmanned system under DoS attack - Google Patents
Security grouping consistency control method of heterogeneous unmanned system under DoS attack Download PDFInfo
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Abstract
The invention relates to a security grouping consistency control method of a heterogeneous unmanned system under DoS attack, unmanned system cluster control is typical application of consistency cooperative control of a multi-agent system, and the multi-agent system is specifically explained in the patent content. Converting a kinetic model of a second-order agent and a first-order agent by using matrix knowledge to obtain a kinetic equation of an equivalent homogeneous system; project engineering is generally deployed in an open environment, more complex and variable multi-channel independent DoS attacks are introduced, and system robustness is enhanced; an estimator is introduced to eliminate adverse effects caused by multi-channel independent DoS attacks and accelerate system convergence; the intelligent agent and an estimator owned by the intelligent agent need to distinguish information transmitted by neighbor nodes, and the information is respectively processed according to a safety consistency protocol; the control protocol for updating the state of the intelligent agent additionally considers the condition of different state dimensions in the heterogeneous system, and can ensure that the safe grouping consistency of the multi-intelligent-agent system is finally realized.
Description
Technical Field
The invention relates to the field of multi-agent system control, and the cluster control of an unmanned system is a typical application of the consistency cooperative control of a multi-agent system, and is specifically described by using the multi-agent system in the patent content.
Background
Due to the characteristics of high efficiency, easy expandability, robustness and the like, the multi-agent distributed system is widely applied to the fields of intelligent power grids, intelligent decision making, expert systems and the like. Although there are robust and fault tolerant mechanisms in multi-agent systems, the purpose is only to ensure that the system has some resilience when it is subject to self-interference and errors. Once a malicious attack invades from the outside, the fault-tolerant mechanism of the system often loses effect, seriously affects the performance of the system, and even makes the system diverge. For a distributed multi-agent system capable of being safely controlled, not only a fault tolerance mechanism needs to be designed in the system, but also malicious attacks outside the system need to be considered additionally. Therefore, the security problem of the multi-agent system becomes an important problem to be solved urgently.
Through analysis of the existing research work, it can be easily found that: firstly, DoS attack modeling is simple, the related periodic and aperiodic DoS attacks are mostly synchronous DoS attacks on channels, and a control protocol of the DoS attack modeling is not applicable to a system under more flexible multi-channel independent DoS attacks; secondly, most of the existing work is based on a homogeneous system for research, and the heterogeneous system which is more in line with the reality is less involved; and thirdly, although the security control protocol in the existing document enables the system to finally reach the agreement, no better solution is provided for the problem that the convergence of the system is slowed down due to communication interruption during the DoS attack. In addition, for a system with limited resources, the relationship between the agents is not only a simple cooperation relationship or a competition relationship in the existing literature, but also a more complex cooperation-competition relationship is more suitable for application in practical engineering. Based on the above analysis, this chapter designs a controller with a novel estimator to eliminate the influence caused by DoS attack and accelerate the system convergence. Compared with the similar work, the estimator in the chapter continuously and iteratively simulates the state of a neighbor intelligent agent based on the information of the last communication before the communication interruption and the information of the intelligent agent using the estimator during the DoS attack, and can effectively avoid the excessive deviation of the state of the intelligent agent. In addition, the cooperation-competition relationship among the intelligent agents is fully considered when the controller is designed, so that the intelligent agent is more suitable for practical application.
Through retrieval, application publication No. CN111934917A, a heterogeneous multi-agent system grouping consistency control method based on trust nodes includes: any agent which performs state convergence receives state values from neighbor agents, and performs descending sorting on the received state values; carrying out information value processing, selectively removing nodes, representing the removed nodes by using a set Ri, representing a trust node set in the removed nodes by using Ti, and setting the edge weights of the remaining removed nodes and the node i to be 0; the position information and the speed information of the normal nodes are obtained according to a kinetic equation, a consistency control protocol is set according to the position information and the speed information of the normal nodes, the normal nodes are processed by adopting the consistency control protocol, and the consistency of node grouping in the heterogeneous multi-agent system is realized. The invention expands the system structure into a heterogeneous multi-agent system, adds a trust node mechanism and groups, and enhances the robustness of the multi-agent system.
In the above patent, the malicious attack considered belongs to a type of node attack, and although the malicious node may introduce some irrelevant data into the system, the system update always has data available, and the data introduced by the malicious node does not always have a bad effect, and even facilitates the convergence of the system at some time. The DoS attack model considered herein is a method of maliciously occupying a communication network, resulting in a lack of necessary mutual information between nodes. However, the control protocol of the multi-agent system is designed based on the mutual information between the nodes, so that the DoS attack causes greater damage to the multi-agent system, and the control protocol designed based on the DoS attack model has higher security.
The core idea of the control protocol design of the above patent is to screen the received data by sorting, eliminate the edge data at both ends, and retain the central data to ensure the system to achieve safety consistency. Whereas the attack model in this document results in no mutual information being available for the nodes, the control protocol in the above patent is not applicable to multi-agent systems that are subject to DoS attacks.
Third, in the above patent, the adopted communication topology is a fixed topology, but in practical application, the communication topology is very easy to be changed by interference or malicious attack. Therefore, the control protocol is designed by fully considering various conditions of system topology switching, and the method has stronger applicability.
Disclosure of Invention
The present invention is directed to solving the above problems of the prior art. A method for controlling the security grouping consistency of a heterogeneous unmanned system under DoS attack is provided. Unmanned system cluster control is a typical application of consistent cooperative control of multi-agent systems, and is specifically described in this patent disclosure using multi-agent systems. The technical scheme of the invention is as follows:
a security grouping consistency control method of a heterogeneous unmanned system under DoS attack comprises the following steps:
s1, converting a heterogeneous system dynamic model with a second-order agent and a first-order agent by using matrix knowledge to obtain a dynamic equation of an equivalent homogeneous system;
s2, introducing a multi-channel independent DoS attack model;
s3, introducing an estimator capable of being updated iteratively; the estimator is started when the DoS attack occurs and used for estimating the state of the neighbor agent during the DoS attack;
s4, distinguishing the information transmitted by the neighbor nodes by the agents and the estimators owned by the agents, and respectively processing the information of the agents in the same group and the information of the agents in different groups according to a security consistency protocol;
s5, setting a control protocol for updating the state of the intelligent agent, wherein the control protocol considers the condition of different state dimensions in the heterogeneous system, and each intelligent agent continuously updates the state information thereof according to the corresponding control strategy, thereby finally realizing the safe grouping consistency of the multi-intelligent-agent system.
Further, the dynamic model of the heterogeneous system using matrix knowledge to convert the second-order agent and the first-order agent is as follows:
wherein x is i (t) indicates the location information of agent i at time t,
represents a pair x i (t) derivation, v i (t) represents velocity information for agent i at time t,
is expressed as a pair v i (t) derivation, u i (t) represents the control input of agent i at time t; r is a radical of hydrogen 1 Representing a first-order set of agents, r 2 Representing a set of second-order agents;
the converted intelligent agent dynamic equation comprises:
wherein the system matrix
Input matrix
u i (t) represents the control input of agent i at time t; transforming vector W i (t) can be expressed as:
further, the step S2 also has the following constraints on DoS attacks:
wherein, Λ ij (t 1 ,t 2 ) Is indicated over a time period t 1 ,t 2 ) In the method, a channel (i, j) belongs to a set of time periods suffered by DoS attack epsilon, epsilon represents an initial edge set of a system, and (i, j) represents an edge for transmitting information between an agent i and an agent j; len (Λ) ij (t 1 ,t 2 ) Is expressed over a time period t 1 ,t 2 ) Within, the sum of the time of DoS attack suffered by the channel (i, j) epsilon;
indicating the magnitude of the attack intensity, gamma ij > 0 is the fundamental time each channel is subject to DoS attacks;
for different attack modes, define ζ (t) { (i, j) ∈ epsilon \ epsilon (t) | t ∈ len (Λ) ij (0, ∞)) }, as the set of channels that are under attack at time t, where ε \ ε (t) denotes belonging to the set ε but not to the set ε (t).
Further, the kinetic equation of the S3 estimator is as follows:
wherein the content of the first and second substances,
representing the position estimate of agent i to the neighbor agent at time t,
representing the velocity estimate of agent i to the neighbor agent at time t,
represents the control input of the estimator at time t;
the control protocol of the estimator is as follows:
wherein, c 1 And c 2 The coupling strengths, N, with respect to position and velocity, respectively Si Representing a set of agents in the same group as agent i, N Di Representing a different set of agents than agent i.
Further, the S4, the agents and the estimators owned by the agents need to distinguish information transmitted by neighboring nodes, and respectively process information of agents in the same group and information of agents in different groups according to a security consistency protocol, which specifically includes:
establishing a cooperation-competition interaction mechanism, wherein the cooperation-competition interaction mechanism is as follows: the agents in the same group have cooperative relationship, the agents in different groups have competitive relationship, and the adjacent nodes of agent i can only be in N Si And N Di In, so N i ＝N Si ∪N Di (ii) a Considering the grouping situation, the first M nodes are in one group, the last N-M nodes are in one group, and the grouping mechanism and the cooperation-competition interaction relationship are simultaneously considered in the control protocol.
Further, the step S5 specifically includes:
for heterogeneous multi-agent systems, it is said that a cooperation-competition based multi-agent system can asymptotically achieve sub-group agreement if the following conditions are satisfied:
wherein the content of the first and second substances,
meaning agent i is in the same group as agent j,
indicating that agent i is in a different group than agent j.
Further, assuming that the multi-agent system is composed of N agents, the topological relation can be a time-varying undirected graph
Is shown in which
A set of nodes is represented that is,
representing an edge set at time t, in the undirected graph, an edge (i, j) epsilon (t) for transferring information between agents i and j is equivalent to an edge (j, i) epsilon (t) for transferring information between agents j to i, namely (i, j) equals (j, i); the set of neighboring nodes of node i can be represented as
Is an adjacency matrix representing the connection relation between nodes at the time t, wherein 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; provision of a ii (t) ═ 0, i.e., no self-loops exist in the system topology; undirected graph at time t
Is defined as a Laplace matrix of
Wherein
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
Wherein
Representing the initial set of edges.
Further, the estimator-based safety control protocol is designed as follows:
wherein, c 1 And c 2 The coupling strengths, N, with respect to position and velocity, respectively Si Representing a set of agents in the same group as agent i, N Di Represents a set of agents of a different group than agent i, and ζ (t) represents a set of edges subject to DoS attacks.
The invention has the following advantages and beneficial effects:
1. the system model of the invention is a heterogeneous multi-agent system with different dynamics models as in claim 2, where both first and second order agents are present in the system, and the agents of different dynamics models in the system model can cooperate with each other to perform complex tasks in cooperation, compared to a homogeneous system where only first or second order agents are present in the same kind of work. Therefore, the heterogeneous system can describe the actual engineering more accurately.
2. The invention introduces a DoS attack model as described in claim 3 into the system and is a multichannel independent DoS attack in which multiple communication links are attacked independently. In the same type of work, the periodic DoS attack and the aperiodic DoS attack are essentially multi-channel synchronous attacks and are special conditions of the multi-channel independent DoS attack. Furthermore, the control protocol of the present invention designed for the multi-channel independent DoS attack in claim 3 is also applicable to heterogeneous systems suffering from multi-channel synchronous DoS attacks, and vice versa. Therefore, the control protocol of the invention has more universality and wide applicability of the system.
3. The invention introduces an estimator designed in claim 4 on the design of the controller, the estimator being enabled when a DoS attack occurs for estimating the state of a neighbor agent during the DoS attack. Therefore, the controller provided by the invention can effectively avoid the excessive state deviation of the intelligent agent during the DoS attack, thereby effectively weakening the adverse effect of the DoS attack on the system and accelerating the convergence of the system.
4. The invention introduces the grouping mechanism and the cooperation-competition interaction mechanism described in the claims 5 and 6 into the control protocol of the heterogeneous multi-agent system, the protocol divides the agents in the system into two groups, and compared with the single cooperation or competition interaction relationship, the cooperation-competition interaction more conforms to the interaction relationship of each unit in the real complex system, is beneficial to executing the complex tasks of the heterogeneous system, and finally can realize the convergence of the agents in the same group to the same state value described in the claim 6, and the convergence state values of the agents in different groups are opposite. In addition, the grouping mechanism is more beneficial to the decomposition of large tasks in a complex system, and the execution efficiency of a heterogeneous system is improved.
Drawings
FIG. 1 is a flow chart of system control for providing a preferred embodiment of the present invention;
FIG. 2 is a system topology diagram of an embodiment of the present invention;
FIG. 3 is a diagram illustrating the evolution of the location of an agent in accordance with an embodiment of the present invention;
fig. 4 is a diagram illustrating the evolution of the speed of the agent in accordance with an embodiment of the present invention.
Fig. 5 is a DoS attack signal diagram according to an embodiment of the present invention.
Detailed Description
Unmanned system cluster control is a typical application of consistent cooperative control of multi-agent systems, and is specifically described in this patent disclosure using multi-agent systems. The technical solutions in the embodiments of the present invention will be described in detail and clearly with reference to the accompanying drawings. The described embodiments are only some of the embodiments of the present invention.
The technical scheme for solving the technical problems is as follows:
as shown in fig. 1, a method for controlling security grouping of heterogeneous unmanned systems under DoS attack includes, but is not limited to, the following steps:
and S1, converting a heterogeneous system dynamic model with a second-order agent and a first-order agent by using matrix knowledge to obtain a dynamic equation of the equivalent homogeneous system.
The kinetic model of the heterogeneous system is as follows:
wherein x is i (t) position information of agent i at time t, v i (t) speed information of agent i at time t, u i (t) represents the control input of agent i at time t. r is 1 Representing a first-order set of agents, r 2 Representing a set of second-order agents.
The converted intelligent agent dynamic equation comprises:
wherein the system matrix
Input matrix
u i (t) represents the control input of agent i at time t. Transforming vector W i (t) depending on the agent, can be expressed as:
wherein x is i (t) position information of agent i at time t, v i (t) represents the velocity information of agent i at time t. r is 1 Representing a first-order set of agents, r 2 Representing a set of second-order agents.
S2, project engineering is considered to be generally deployed in an open environment, more complex and variable multi-channel independent DoS attacks are introduced, and system robustness is enhanced.
The DoS attacks generated in the DoS attack model are limited and may not continue indefinitely, requiring termination of attack activity and dormancy for a period of time when resources are exhausted in order to provide energy for the next attack. Therefore, there are the following constraints on DoS attacks:
wherein, Λ ij (t 1 ,t 2 ) Is indicated over a time period t 1 ,t 2 ) Within, the set of periods of time that channel (i, j) ∈ ε is subject to DoS attack, len (Λ) ij (t 1 ,t 2 ) Is expressed over a time period t 1 ,t 2 ) Within, the sum of the time that channel (i, j) ∈ ε is subject to a DoS attack.
Indicating the magnitude of the attack intensity, gamma ij > 0 is the fundamental time each channel is subject to DoS attacks.
In the same kind of work, two situations that all channels are attacked or all channels are normally communicated are discussed generally, various attack modes are considered in a multi-channel independent DoS attack model, the multi-channel independent DoS attack is more flexible, and difficulty is increased in system safety control. For different attack modes, define ζ (t) { (i, j) ∈ epsilon \ epsilon (t) | t ∈ len (Λ) ij (0, ∞)) }, as the set of channels that are under attack at time t, where ε \ ε (t) denotes belonging to the set ε but not to the set ε (t).
And S3, introducing an estimator capable of being updated iteratively, eliminating adverse effects caused by multi-channel independent DoS attack, and accelerating system convergence.
The dynamic equation of the estimator is as follows:
wherein the content of the first and second substances,
representing the position estimate of agent i to the neighbor agent at time t,
representing the velocity estimate of agent i to the neighbor agent at time t,
representing the control input of the estimator at time t.
The control protocol of the estimator is as follows:
wherein, c 1 And c 2 Coupling strengths, N, with respect to position and velocity, respectively Si Representing a set of agents in the same group as agent i, N Di Representing a different set of agents than agent i.
S4, the agents and their own estimators need to distinguish the information transmitted by the neighboring nodes, and process the information of the agents in the same group and the information of the agents in different groups according to the security consistency protocol.
The cooperative-competitive interaction mechanism refers to: there is a cooperative relationship between agents in the same group, agents in different groups are in competition, and the adjacent nodes of agent i can only be in N Si And N Di In, so N i ＝N Si ∪N Di . In addition, in order to reduce the analysis difficulty, the grouping condition is considered for the time. The first M nodes form a group, and the last N-M nodes form a group. The control protocol has more generality compared with the same kind of work because the grouping mechanism and the cooperation-competition interaction relation are simultaneously considered in the control protocol.
S5, the control protocol for updating the state of the intelligent agent additionally considers the condition of different state dimensions in the heterogeneous system, and each intelligent agent continuously updates the state information of the intelligent agent according to the corresponding control strategy, thereby finally realizing the safe grouping consistency of the multi-intelligent-agent system.
For heterogeneous multi-agent systems, it is said that a cooperation-competition based multi-agent system can asymptotically achieve grouping agreement if the following conditions are satisfied:
wherein the content of the first and second substances,
meaning agent i is in the same group as agent j,
indicating that agent i is in a different group than agent j.
Assuming that the multi-agent system is composed of N agents, the topological relation can be a time-varying undirected graph
Is shown in which
A set of nodes is represented that represents a set of nodes,
representing the set of edges at time t. In an undirected graph, the edge (i, j) ∈ epsilon (t) where agents i and j pass information is equivalent to the edge (j, i) ∈ epsilon (t) where agents j to i pass information, i.e., (i, j) ═ j, i. The set of neighboring nodes of node i can be represented as
Is an adjacency matrix representing the connection relation between nodes at the time tWherein a is 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) is 0. Provision of a ii (t) ═ 0, i.e., no self-loops exist in the system topology. Undirected graph at time t
Is defined as a Laplace matrix of
Wherein
And when i ≠ j, l ij (t)＝-a ij (t) of (d). 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
Wherein
Representing the initial set of edges.
And in order to verify the effect of the proposed safety consistency control protocol, MATLAB is adopted for simulation verification. In the description of the present specification, the one node represents one agent.
Considering a multi-agent system with 6 agents, the communication topology is shown in fig. 2. Wherein node v 1 ，v 3 ，v 4 And node v 2 ，v 5 ，v 6 Belonging to two groups respectively. Without loss of generality, the initial state of each agent is chosen as follows: x (0) [ -1, -2, -4,6,8,10] T ，v(0)＝[0.7,0.3,-0.66,-0.5] T . As can be seen from fig. 2, the communication topology has 8 edges in total, and thus, the attack pattern has 2 edges in total 8 256, which are not listed here. Setting the attack strength of the DoS attack of each channel as
i,j＝1,2,3,4,5,6,i≠j。
From the simulation results, it can be seen that the evolution process of the position state and the velocity state of all the agents is shown as shown in fig. 3 and fig. 4, respectively. The velocities of the second- order agent nodes 3, 4, 5, 6 all converge to 0 at 20.84 units of time and the positions of all agents converge to ± 2.4 at 22.64 units of time. Fig. 5 shows a DoS signal step diagram, and it can be seen that the DoS attacks suffered by the channels are different.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The above examples are to be construed as merely illustrative and not limitative of the remainder of the disclosure. After reading the description of the invention, the skilled person can make various changes or modifications to the invention, and these equivalent changes and modifications also fall into the scope of the invention defined by the claims.
Claims (8)
1. A security grouping consistency control method of heterogeneous unmanned systems under DoS attack is provided, unmanned system cluster control is a typical application of consistency cooperative control of a multi-agent system, and the multi-agent system is used for specific description, and is characterized by comprising the following steps:
s1, converting a heterogeneous system dynamic model with a second-order agent and a first-order agent by using matrix knowledge to obtain a dynamic equation of an equivalent homogeneous system;
s2, introducing a multi-channel independent DoS attack model;
s3, introducing an estimator capable of being updated iteratively, wherein the estimator is started when the DoS attack occurs and is used for estimating the state of the neighbor agent during the DoS attack;
s4, distinguishing the information transmitted by the neighbor nodes by the agents and the estimators owned by the agents, and respectively processing the information of the agents in the same group and the information of the agents in different groups according to a security consistency protocol;
s5, setting a control protocol for updating the state of the agents, wherein the control protocol considers the condition of different state dimensions in the heterogeneous system, and each agent continuously updates the state information thereof according to the corresponding control strategy, thereby finally realizing the safe grouping consistency of the multi-agent system.
2. The method according to claim 1, wherein the kinetic model of the heterogeneous system using matrix knowledge to transform second-order agents and first-order agents is as follows:
wherein x is i (t) indicates location information of agent i at time t,
represents a pair x i (t) derivation, v i (t) represents velocity information for agent i at time t,
represents a pair v i (t) derivation, u i (t) represents the control input of agent i at time t; r is 1 Representing a first-order set of agents, r 2 Representing a set of second-order agents;
the converted intelligent agent dynamic equation comprises:
wherein the system matrix
Input matrix
u i (t) represents the control input of agent i at time t; transforming vector W i (t) can be expressed as:
3. the method according to claim 2, wherein the step S2 further has the following constraints on the DoS attack:
wherein Λ is ij (t 1 ,t 2 ) Is shown over a time period t 1 ,t 2 ) Internal, channel
The set of time periods that are subject to DoS attacks,
representing the initial set of edges of the system, (i, j) representing the edges for transferring information from agent i to agent j; len (Λ) ij (t 1 ,t 2 ) Is expressed over a time period t 1 ,t 2 ) Internal, channel
The sum of the time of DoS attacks suffered;
indicating the magnitude of the attack intensity, gamma ij > 0 is the fundamental time each channel is subject to DoS attacks;
for different attack patterns, define
As a set of channels subject to attack at time t, where
Representation of belonging to a set
But not in the aggregate
4. The method for controlling the consistency of the security grouping of the heterogeneous unmanned system under the DoS attack as claimed in claim 3, wherein the kinetic equation of the S3 estimator is as follows:
wherein, the first and the second end of the pipe are connected with each other,
representing the position estimate of agent i to the neighbor agent at time t,
representing the velocity estimate of agent i to the neighbor agent at time t,
represents the control input of the estimator at time t;
the control protocol of the estimator is as follows:
wherein, c 1 And c 2 The coupling strengths, N, with respect to position and velocity, respectively Si Representing a set of agents in the same group as agent i, N Di Representing a different set of agents than agent i.
5. The method according to claim 4, wherein the S4, the agent and the estimator thereof need to distinguish information transmitted by neighboring nodes, and the information of agents in the same group and the information of agents in different groups are respectively processed according to a security consistency protocol, which specifically includes:
establishing a cooperation-competition interaction mechanism, wherein the cooperation-competition interaction mechanism refers to the following steps: the agents in the same group have cooperative relationship, the agents in different groups have competitive relationship, and the adjacent nodes of agent i can only be in N Si And N Di In, so N i ＝N Si ∪N Di (ii) a Considering the grouping situation, the first M nodes are in one group, the last N-M nodes are in one group, and the grouping mechanism and the cooperation-competition interaction relationship are simultaneously considered in the control protocol.
6. The method for controlling the consistency of the security grouping of the heterogeneous unmanned system under the DoS attack as claimed in claim 5, wherein the step S5 specifically includes:
for heterogeneous multi-agent systems, it is said that a cooperation-competition based multi-agent system can asymptotically achieve sub-group agreement if the following conditions are satisfied:
wherein, the first and the second end of the pipe are connected with each other,
meaning agent i is in the same group as agent j,
indicating that agent i is in a different group than agent j.
7. The method as claimed in claim 6, wherein the multi-agent system is composed of N agents, and the topological relation can be implemented by a time-varying undirected graph
Is shown in which
A set of nodes is represented that represents a set of nodes,
edge set representing time t, edges for passing information between agents i and j in an undirected graph
Edge for passing information with agents j to i
Equivalence, i.e., (i, j) ═ j, i; the set of neighboring nodes of node i can be represented as
Is an adjacency matrix representing the connection relation between nodes at the time t, wherein a ij (t) > 0 is the weight of the edge (i, j), if
Then a ij (t) ═ 1; otherwise, a ij (t) ═ 0; provision of a ii (t) ═ 0, i.e., no self-loops exist in the system topology; undirected graph at time t
Is defined as a Laplace matrix of
Wherein
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
Wherein
Representing the initial set of edges.
8. The method according to claim 7, wherein the security control protocol based on the estimator is designed as follows:
wherein, c 1 And c 2 The coupling strengths, N, with respect to position and velocity, respectively Si Representing a set of agents in the same group as agent i, N Di Represents a set of agents of a different group than agent i, and ζ (t) represents a set of edges subject to DoS attacks.
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| CN116560240A (en) * | 2023-07-10 | 2023-08-08 | 广东工业大学 | Computer readable storage medium and second order multi-agent consistency control system |
| CN116880434A (en) * | 2023-06-20 | 2023-10-13 | 辽宁工业大学 | Unmanned aerial vehicle-unmanned aerial vehicle cluster cooperative control method based on cloud and fog calculation under network attack |
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| CN116880434A (en) * | 2023-06-20 | 2023-10-13 | 辽宁工业大学 | Unmanned aerial vehicle-unmanned aerial vehicle cluster cooperative control method based on cloud and fog calculation under network attack |
| CN116880434B (en) * | 2023-06-20 | 2024-01-23 | 辽宁工业大学 | Unmanned aerial vehicle-unmanned aerial vehicle cluster cooperative control method based on cloud and fog calculation under network attack |
| CN116560240A (en) * | 2023-07-10 | 2023-08-08 | 广东工业大学 | Computer readable storage medium and second order multi-agent consistency control system |
| CN116560240B (en) * | 2023-07-10 | 2023-10-31 | 广东工业大学 | Computer readable storage medium and second order multi-agent consistency control system |
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