Quantized event-triggered multi-agent system safety consensus control method and device

Abstract

The application provides a multi-agent system safety consistency control method and device based on quantization event triggering, relates to the technical field of data processing, and integrates the quantization level into the data transmission time triggering mechanism by combining the characteristics of the quantizer based on the quantization event triggering mechanism, guarantees triggering only once on the same quantization level, avoids repeated transmission of the same information, eliminates unnecessary triggering, improves the channel resource utilization rate, and achieves the effect of saving communication resources in the multi-agent system.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a method and apparatus for secure consistency control of multi-agent systems based on quantized event triggering. Background Technology

[0002] Multi-agent systems (MAS) are systems composed of multiple individual agents with certain perception, computation, and execution capabilities. Each agent possesses a degree of autonomy, independence, and learning ability. Compared to single agents, MAS can accomplish complex tasks that single agents cannot, and exhibits higher stability, reliability, flexibility, scalability, and fault tolerance. They have wide applications in fields such as unmanned aerial vehicles (UAVs), smart grids, and transportation systems. Consistent coordination is one of the most important research problems in MAS, aiming to design appropriate control strategies based on the interaction information between agents to achieve follower-leader behavior. However, network-based communication between agents faces challenges such as limited communication resources and vulnerability to malicious attacks.

[0003] Existing technologies employ periodic sampling at fixed time intervals, with communication between agents occurring synchronously at fixed periods. In reality, the state at most sampling moments does not change significantly, or even remains zero, leading to a large number of invalid or low-value data packets continuously occupying the channel. Periodic sampling causes the state to be sampled and transmitted at fixed time intervals even when it is slowly changing or tending to stabilize, resulting in a large number of identical or similar pieces of information being transmitted repeatedly, excessively occupying the channel and wasting communication resources. Channel bandwidth and communication resources are limited; unnecessary communication wastes a lot of resources on invalid data transmission, and may even occupy communication resources for valid data, preventing the transmission of important data and affecting the stability, consistency, and other performance aspects of the system. Summary of the Invention

[0004] This invention provides a method and apparatus for secure consistency control of multi-agent systems based on quantized event triggering, which solves the defects of communication resource waste in existing multi-agent systems and achieves the effect of saving communication resources in multi-agent systems.

[0005] This invention provides a method for secure consistency control of a multi-agent system based on quantized event triggering, comprising:

[0006] The output state data of the target agent is input into the quantizer of the target agent to obtain the quantized output data of the target agent. When the data input to the quantizer is at the same quantization level, the output data of the quantizer remains unchanged.

[0007] Receive the quantized output data of the neighboring intelligent agent, determine a first time based on the quantized output data of the target intelligent agent and the neighboring intelligent agent, and send the quantized output data of the target intelligent agent at the first time to the observers of the target intelligent agent and the neighboring intelligent agents;

[0008] The observation state data of the target intelligent agent is input into the quantizer to obtain the quantized observation data of the target intelligent agent. The quantized observation data of the neighboring intelligent agents is received. The second time is determined based on the quantized observation data of the target intelligent agent and the neighboring intelligent agents. The quantized observation data of the target intelligent agent at the second time is sent to the controller of the target intelligent agent and the neighboring intelligent agents.

[0009] Obtain the control input data of the target intelligent agent output by the controller;

[0010] Specifically, at the third moment after receiving the output state data of the target intelligent agent, the observer of the target intelligent agent resets the observation state data of the target intelligent agent based on the output state data and control input data of the target intelligent agent. At other times besides the third moment, the observer outputs the observation state data of the target intelligent agent based on the quantized output data and the quantized observation data of the target intelligent agent.

[0011] According to the present invention, a method for secure consistency control of a multi-agent system based on quantized event triggering is provided, wherein the formula for determining the first moment is:

[0012] ;

[0013] Where inf represents the infimum. , , , , Trigger parameters , and Given a positive constant, This represents the sector boundary of the quantizer. This represents the output state data of the target agent i at time t. It is the set of neighboring intelligent agents of intelligent agent i. C represents the numerical value indicating the relationship between agents i and j, and C is the system output matrix of the multi-agent system. , Let i be the actual state data of agent i at time t. and Let represent the observed state data of agents i and j at time t, respectively. Indicates that agent i is in The quantized output data at time [time], This represents the first moment for agent i. Indicates that agent i is in The next first moment after that, Indicates that agent i is in The quantified observation data at that time, It is an intelligent agent At the second moment, Indicates that agent j is in The quantized output data at time [time], Let J represent the first moment of agent j. Indicates that agent j is in The quantified observation data at that time, This represents the second moment of agent j.

[0014] According to the present invention, a method for secure consistency control of a multi-agent system based on quantized event triggering is provided, wherein the formula for determining the second moment is:

[0015] ;

[0016] in, , , , It is an intelligent agent At the second moment, Indicates that agent i is in The next second moment after that, It is an intelligent agent At the second moment, the trigger parameter , and Given a positive constant, Indicates that agent i is in The quantified observation data at time [time], Indicates that agent j is in The quantitative observation data at that time.

[0017] According to the present invention, a method for security consistency control of a multi-agent system based on quantized event triggering is provided, wherein the formula for the observer to reset the observation state data of the target agent at the third time step is as follows:

[0018] = , ;

[0019] in, For the third moment of the target intelligent agent i, Let represent the elastic prediction state of agent i at time t. satisfy:

[0020] , ;

[0021] express The derivative at time t, R is the state reset gain. Let A be the control input data of agent i at time t, and let A and B be the system state matrix and system control matrix of the multi-agent system, respectively. A constant matrix to characterize the nonlinear part, This represents the nonlinear dynamics of the elastically predicted state in a multi-agent system. It satisfies the Lipschitz continuity condition.

[0022] According to the present invention, a method for secure consistency control of a multi-agent system based on quantized event triggering is provided. The method further provides a formula for the observer to output the observation state data of the target agent at times other than the third time point, based on the quantized output data and the quantized observation data of the target agent:

[0023] when hour,

[0024] ;

[0025] in, express The derivative at time t, Represents the coupling coefficient. Indicates the observer gain. This represents the nonlinear dynamics of the real state data in a multi-agent system. It satisfies the Lipschitz continuity condition.

[0026] According to the present invention, a method for secure consistency control of a multi-agent system based on quantized event triggering is provided, wherein the formula for the control input data output by the controller is:

[0027] ;

[0028] in, It is the coupling coefficient. It controls the gain.

[0029] The present invention also provides a multi-agent system security consistency control device based on quantized event triggering, comprising:

[0030] The quantization module is used to input the output state data of the target agent into the quantizer of the target agent to obtain the quantized output data of the target agent. When the data input to the quantizer is at the same quantization level, the output data of the quantizer remains unchanged.

[0031] The first channel transmission module is used to receive the quantized output data of the neighboring intelligent agent, determine a first moment based on the quantized output data of the target intelligent agent and the neighboring intelligent agent, and send the quantized output data of the target intelligent agent at the first moment to the observers of the target intelligent agent and the neighboring intelligent agents;

[0032] The second channel transmission module is used to input the observation state data of the target intelligent agent into the quantizer to obtain the quantized observation data of the target intelligent agent, receive the quantized observation data of the neighboring intelligent agents, determine the second time based on the quantized observation data of the target intelligent agent and the neighboring intelligent agents, and send the quantized observation data of the target intelligent agent at the second time to the controller of the target intelligent agent and the neighboring intelligent agents.

[0033] The control module is used to acquire the control input data of the target intelligent agent output by the controller;

[0034] Specifically, at the third moment after receiving the output state data of the target intelligent agent, the observer of the target intelligent agent resets the observation state data of the target intelligent agent based on the output state data and control input data of the target intelligent agent. At other times besides the third moment, the observer outputs the observation state data of the target intelligent agent based on the quantized output data and the quantized observation data of the target intelligent agent.

[0035] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the multi-agent system security consistency control method based on quantized event triggering as described above.

[0036] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the multi-agent system security consistency control method based on quantization event triggering as described above.

[0037] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the multi-agent system security consistency control method based on quantized event triggering as described above.

[0038] The present invention provides a method and apparatus for security and consistency control of multi-agent systems based on quantization event triggering. By using a quantization-based event triggering mechanism and combining the characteristics of the quantizer, the quantization level is integrated into the data transmission time triggering mechanism, ensuring that the same quantization level is triggered only once. This avoids repeated transmission of the same information, eliminates unnecessary triggering, improves channel resource utilization, and achieves the effect of saving communication resources in multi-agent systems. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0040] Figure 1 This is a flowchart illustrating the security and consistency control method for multi-agent systems based on quantized event triggering provided by the present invention.

[0041] Figure 2 This is a schematic diagram of channel data transmission in the multi-agent system security consistency control method based on quantization event triggering provided by the present invention.

[0042] Figure 3 This is a schematic diagram of the quantizer-based event triggering mechanism in a verification example of the multi-agent system security consistency control method based on quantization event triggering provided by the present invention.

[0043] Figure 4 This is a schematic diagram illustrating the impact of a DoS attack on the communication topology in a verification example of the multi-agent system security consistency control method based on quantized event triggering provided by this invention.

[0044] Figure 5a , Figure 5b , Figure 5c and Figure 5d This is a trajectory diagram of the system state under no-DoS attack conditions in a verification example of the multi-agent system security consistency control method based on quantized event triggering provided by the present invention.

[0045] Figure 6a and Figure 6b This is a diagram showing the event triggering times of the system state in the absence of a DoS attack in a verification example of the multi-agent system security consistency control method based on quantized event triggering provided by this invention.

[0046] Figure 7a , Figure 7b , Figure 7c and Figure 7dThis is a trajectory diagram of the system state under a DoS attack on the PO channel in a verification example of the multi-agent system security consistency control method based on quantized event triggering provided by the present invention.

[0047] Figure 8a and Figure 8b This is a diagram showing the event triggering times of the system state under a DoS attack on the PO channel in a verification example of the multi-agent system security consistency control method based on quantized event triggering provided by this invention.

[0048] Figure 9a , Figure 9b , Figure 9c and Figure 9d This is a trajectory diagram of the system state when the PO channel and OC channel are simultaneously subjected to a DoS attack in a verification example of the multi-agent system security consistency control method based on quantized event triggering provided by the present invention.

[0049] Figure 10a and Figure 10b This is a diagram showing the event triggering times of the system state when both the PO channel and OC channel are simultaneously subjected to a DoS attack, in a verification example of the multi-agent system security consistency control method based on quantized event triggering provided by this invention.

[0050] Figure 11 This is a schematic diagram of the structure of the multi-agent system security consistency control device based on quantized event triggering provided by the present invention.

[0051] Figure 12 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0053] It should be understood that, when used in this specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0054] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0055] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0056] As used in this specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrases "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0057] The following description, in conjunction with the accompanying drawings, describes the security and consistency control method for multi-agent systems based on quantized event triggering provided by this invention. For example... Figure 1 As shown, the method for secure consistency control of a multi-agent system based on quantized event triggering includes the following steps:

[0058] S110. Input the output state data of the target intelligent agent into the quantizer of the target intelligent agent to obtain the quantized output data of the target intelligent agent. When the data input to the quantizer is at the same quantization level, the output data of the quantizer remains unchanged.

[0059] S120: Receive the quantized output data of the neighboring intelligent agent, determine the first moment based on the quantized output data of the target intelligent agent and the neighboring intelligent agents, and send the quantized output data of the target intelligent agent at the first moment to the observers of the target intelligent agent and the neighboring intelligent agents.

[0060] S130. Input the observation state data of the target intelligent agent into the quantizer to obtain the quantized observation data of the target intelligent agent, receive the quantized observation data of the neighboring intelligent agents, determine the second time based on the quantized observation data of the target intelligent agent and the neighboring intelligent agents, and send the quantized observation data of the target intelligent agent at the second time to the controller of the target intelligent agent and the neighboring intelligent agents.

[0061] S140. Obtain the control input data of the target intelligent agent output by the controller;

[0062] Specifically, at the third moment after receiving the target agent's output state data, the observer of the target agent resets the target agent's observation state data based on the target agent's output state data and control input data. At other times besides the third moment, the observer outputs the target agent's observation state data based on the target agent's quantized output data and quantized observation data.

[0063] The security and consistency control method for multi-agent systems based on quantization event triggering provided in this application integrates the quantization level into the data transmission time triggering mechanism by using a quantization-based event triggering mechanism and combining the characteristics of the quantizer. This ensures that the same quantization level is triggered only once, avoiding repeated transmission of the same information, eliminating unnecessary triggering, improving channel resource utilization, and achieving the effect of saving communication resources in multi-agent systems.

[0064] The method provided in this application is executed by a target agent in a multi-agent system. The target agent is any agent in the multi-agent system. In other words, each agent in the multi-agent system can serve as the target agent. The steps executed by the target agent as described in the method provided in this application can also be executed by other agents in the same multi-agent system as the target agent.

[0065] In a multi-agent system, the agents can communicate with each other. To describe the topological relationships between the agents, a multi-agent system topology diagram can be proposed. The following section first explains the multi-agent system topology diagram.

[0066] The interactions between agents can be represented as a directed graph. , A set of intelligent agent nodes. Let be a set of directed edges. Let be an adjacency matrix, representing the numerical relationships between edges. , ,otherwise . In order to enable intelligent agents A set of neighboring intelligent agents that transmit information. Consider a set including a leader and... A multi-agent system with 1,000 followers, where the leader is numbered 0 and the followers are numbered 10. Its directed graph is The corresponding Laplace matrix is

[0067] ;

[0068] in For the connection between followers and leaders. For follower topology graph Laplace matrix A leader is considered to have a direct path to all his followers if and only if there exists a directed path between the leader and all his followers. All eigenvalues ​​of have positive real parts. Definition .

[0069] Suppose in a directed graph If there exists a directed spanning tree where the root node is the leader, meaning each follower has at least one path connected to the leader, then there exists a positive vector. Make ,in .

[0070] Consider a nonlinear multi-agent system consisting of one leader and N followers. The leader's dynamic equation is: The dynamic equation for the follower is:

[0071] ;

[0072] in Indicates the leader's status. , , , These represent the follower's actual state data, output data, and control input data, respectively. , , Given a system matrix with appropriate dimensions. and This represents the nonlinear dynamics of the system, satisfying the Lipschitz condition. ,in , where is the given Lipschitz condition parameter. It is a constant matrix that characterizes the nonlinear part of the system.

[0073] The method provided in this application uses a quantizer to implement a quantization-based event triggering mechanism. For an agent in a multi-agent system, the data at a certain moment will only be sent to the neighboring agent when the quantizer output data at a certain moment meets certain conditions.

[0074] Specifically, constructing a quantizer For a given input have:

[0075]

[0076] Among them, quantification level , Quantization density It is a given constant. It is the boundary of the sector domain. Let quantization density be quantization error. Then we have: .

[0077] like Figure 3 As shown, when the input is quantized Belongs to quantization interval At that time, the quantizer has a unique quantization output. This means that data values ​​transmitted via event triggers remain unchanged within this range, constituting unnecessary event triggering and wasting communication resources. Therefore, in conjunction with quantization precision parameters... Design a quantization-based event triggering mechanism to ensure that the event trigger occurs only once within the quantization interval, guaranteeing that the same data is transmitted only once.

[0078] In the method provided in this application, such as Figure 2 As shown, data transmission between agents utilizes two channels: the controlled object-observer (PO) channel and the observer-controller (OC) channel. The PO channel transmits information from an agent to the observers of its neighboring agents, while the OC channel transmits information from the observers of an agent to the controllers of its neighboring agents. The PO channel is used to transmit quantized output data between agents, and the OC channel is used to transmit quantized observation data between agents.

[0079] The method provided in this application independently designs the triggering conditions for data transmission events based on the network characteristics of PO and OC channels, realizing asynchronous transmission and on-demand communication between the two channels. This allows the two channels to independently determine the timing of communication based on their respective local state changes, further reducing the overall communication frequency and resource consumption.

[0080] Understandably, the neighboring agents of the target agent also use the same event triggering conditions as the target agent. The quantized output data received by the target agent from the neighboring agents is the result of the neighboring agents sending their quantized output data to the target agent's observer at the first moment after identifying the neighboring agent. Similarly, the quantized observation data received by the target agent from the neighboring agents is the result of the neighboring agents sending their quantized observation data to the target agent's controller at the second moment after identifying the neighboring agent.

[0081] Specifically, the formula for determining the first moment is:

[0082] ;

[0083] Here, inf represents the infimum. PO channel event triggering error , , , Trigger parameters , and Given a positive constant, This represents the sector boundary of the quantizer. This represents the output state data of the target agent i at time t. It is the set of neighboring intelligent agents of intelligent agent i. C represents the numerical value indicating the relationship between agents i and j, and C is the system output matrix of the multi-agent system. , Let i be the actual state data of agent i at time t. and Let represent the observed state data of agents i and j at time t, respectively. Indicates that agent i is in Quantized output data at any given moment This represents the first moment of agent i. Indicates that agent i is in The next first moment after that, Indicates that agent i is in Quantitative observation data at any given time It is an intelligent agent The second moment, Indicates that agent j is in Quantized output data at any given moment This represents the first moment of agent j. Indicates that agent j is in Quantitative observation data at any given time This represents the second moment of agent j.

[0084] The formula for determining the second moment is:

[0085] ;

[0086] in, , OC channel event triggering error , It is an intelligent agent The second moment, Indicates that agent i is in The next second moment after that, Is the intelligent agent i in The next second moment, It is an intelligent agent The second moment, trigger parameters , and Given a positive constant, Indicates that agent i is in Quantitative observation data at any given time Indicates that agent j is in Quantitative observation data at any given time.

[0087] The formula for the observer to output the observation state data is:

[0088] ;

[0089] in, , indicating the first The observed state of a follower Represents the coupling coefficient. Indicates the observer gain. Defines the virtual observer for the leader. . . To reset the time, indicating continuous. The instant after a continuous data transmission is successfully completed. It is a system Observable index, This represents the time interval between two consecutive data transmissions. Indicates the first The elastic prediction state of a follower has the following dynamics:

[0090] ;

[0091] in, , It is the state reset gain.

[0092] Based on the observer's observation data, the controller outputs control input data, as shown in the formula:

[0093] ;

[0094] in, It is the coupling coefficient. It controls the gain.

[0095] After obtaining the control input data, the target intelligent agent is controlled based on the control input data.

[0096] Define consistency error Observation error Reset error :

[0097] .

[0098] Considering the asynchronous network setup of the observer and controller, the PO and OC channels used for communication between agents are susceptible to DoS attacks. Observers are common targets of DoS attacks, so we first consider the PO channel being attacked by DoS. The situation where both the observer and controller are attacked by DoS is more complex than the situation where only the controller is attacked. To avoid redundant analysis, we consider (1) the PO channel being attacked by DoS and (2) the PO and OC channels being attacked by DoS simultaneously. The following describes the consistency of the multi-agent system under the method provided in this application in the case of attack (1) or (2).

[0099] Assume that DoS attacks cannot occur at an infinitely high frequency, and that the effects of a DoS attack cannot last indefinitely. That is, there exists a constant. , So that in the time interval Number of DoS attacks Duration during a DoS attack And the maximum blocking rate satisfies:

[0100] , , , ;

[0101] in This represents the average dwell time between the on / off moments of a consecutive DoS attack. This indicates the proportion of time the attack takes place within a given time window.

[0102] set up Indicates the first The time interval of a DoS attack. Indicates the first A time interval free from DoS attacks. Due to DoS attacks are not continuous; use Indicates the range of DoS attacks corresponding to the The continuous intervals formed by using This indicates the range corresponding to no DoS attack. A continuous interval.

[0103] For a multi-agent system, when it is subjected to a DoS attack, if the observation error... If the system is bounded, then it can achieve practical security estimation; if the consistency error is... If the system is bounded, then it can achieve practical consistency.

[0104] In a multi-agent system operating based on the method provided in this application, under the quantization-based asynchronous event triggering mechanism and elastic prediction mechanism, the practical safety consistency of the nonlinear multi-agent system can be guaranteed when certain conditions are met.

[0105] (1) In the absence of a DoS attack, there are normal numbers , , If the following LMIs are true, then the system can achieve practical safety consistency.

[0106] ;

[0107] ;

[0108] ;

[0109] in , , , It is a positive number. , It is a positive definite matrix.

[0110] Consider the following Lyapunov function:

[0111] ;

[0112] in , The topology diagram of the multi-agent system, obtained in the previous section, is... It is a positive definite symmetric matrix.

[0113] When the event triggering mechanism in the method provided in this application is satisfied... and It will be reset to 0. (Assuming...) Then we have:

[0114] ;

[0115] in , , , , , . , , , .

[0116] definition , In the no-DoS attack zone In, Lyapunov functions for:

[0117] ;

[0118] in , , ; , For matrix spectral radius, , ; ; , For matrix spectral radius, . , , , , , For matrix The smallest eigenvalue, , , .

[0119] definition

[0120]

[0121] in,

[0122] ,

[0123] ,

[0124] .

[0125] The derivative of the Lyapunov function can then be rewritten as:

[0126] ;

[0127] when At that time, for all have .

[0128] It can be obtained in the range without DoS attack. Consistency error and observation error It is bounded.

[0129] (2) In the case of a DoS attack on the PO channel, if the DoS attack model satisfies the assumptions above and has positive definite constants. , If the following LMIs are true, then the system can achieve practical safety consistency.

[0130] ;

[0131] ;

[0132] in It is the Laplace matrix of the directed graph of the system when the PO channel is subjected to a DoS attack. For matrix The smallest eigenvalue.

[0133] In the DoS attack zone In this context, a DoS attack alters the observer's communication topology, and the corresponding Laplace matrix... Become , Become The observation error increases. The derivative of the Lyapunov function becomes

[0134] ;

[0135] for ,have .

[0136] at this time, If the negative definite representation disappears, the system cannot achieve practical safety consistency. Therefore, a resilient prediction mechanism is considered.

[0137] Consider the following Lyapunov function:

[0138] ,in It is a positive definite symmetric matrix.

[0139] for , and According to the Lipschitz conditional assumptions, we have ,but

[0140] .

[0141] Define the reset gain as When the following Riccati equation holds, ,

[0142] ;

[0143] In conclusion, Therefore, when hour, ,Right now For intervals At other times on the platform, regardless of whether a DoS attack exists, combined with the PO channel event triggering error, when When the time is right, the derivative of the observation error can be obtained. It is bounded. According to the integral factor method, In the DoS attack zone It is internally bounded. In summary, when the PO channel is subjected to a DoS attack, the observer state is affected. Through the resilient prediction mechanism, the observer state can be reset, enabling the system to achieve practical security consistency.

[0144] (3) When both the PO channel and the OC channel are subjected to a DoS attack, if the DoS attack model satisfies the assumptions above and has positive definite constants. , If the following LMIs are true, then the system can achieve practical safety consistency.

[0145] ;

[0146] ;

[0147] in It is the Laplace matrix corresponding to the directed graph of the system when the OC channel is subjected to a DoS attack. For matrix The smallest eigenvalue.

[0148] In the DoS attack zone In this context, a DoS attack alters the observer's communication topology, and the corresponding Laplace matrix... Become , Become Observational error and consistency error increase. The assumptions in this paper hold:

[0149] .

[0150] In the interval In the context of a DoS attack targeting only the PO channel, the Lyapunov functions for both the absence and presence of a DoS attack are as follows:

[0151] No DoS attack: ;

[0152] There is a DoS attack: ;

[0153] When inequalities At the time of its establishment, It is negative definite over the entire interval, combined with We can obtain:

[0154] .

[0155] When a DoS attack simultaneously targets both the PO and OC channels, the Lyapunov functions for both scenarios with and without a DoS attack are as follows:

[0156] No DoS attack: ;

[0157] There is a DoS attack: ;

[0158] Similar to the analysis above, we have:

[0159] .

[0160] In summary, under the condition that a DoS attack exists, a sufficient condition for the system to achieve practical security consistency is that the DoS attack interval satisfies the following formula.

[0161] .

[0162] Since the multi-agent system in the method provided in this application is a continuous-time system, it is necessary to ensure that the Zeno phenomenon (i.e., an infinite number of event triggers within a finite time interval) does not occur under the quantization-based dual-channel asynchronous event-triggered control method designed above. Because the event-triggered mechanism is ineffective during the DoS attack period, the Zeno phenomenon will not occur when the channel is under a DoS attack; subsequent analysis will be conducted on a channel where normal communication is possible. The following demonstrates the sufficient conditions for avoiding the Zeno phenomenon in the nonlinear multi-agent system using the method provided in this application.

[0163] To ensure the system does not exhibit the Zeno phenomenon, i.e., for intelligent agents... The PO and OC channels have constants. , , making , Based on the preceding analysis and the properties of Lyapunov functions... achievable It is bounded. Since the leader state is bounded by default, combining the expressions for consistency error and observation error, we can obtain... and It is bounded.

[0164] (1) PO channel

[0165] Combining the quantization error expression and the Lipschitz condition, the PO channel triggering error is analyzed. Differentiation yields: .

[0166] because and It is bounded. It is also bounded, let the boundary be... For any ,have:

[0167] .

[0168] At the trigger time have It is always true, and there is a condition before the triggering time. Therefore, the following inequalities hold:

[0169] .

[0170] (2) OC channel

[0171] OC channel triggering error Differentiation yields:

[0172] .

[0173] Similar to (1), It is bounded; let the boundary be... For any ,have .

[0174] That is, the Zeno phenomenon will not occur in either the PO channel or the OC channel.

[0175] The effectiveness of the method provided in this application is demonstrated through experiments based on a practical application example. The experimental example of the method provided in this application consists of a system composed of six rotary joint robotic arms driven by single-link DC motors. This system can be viewed as a multi-agent system consisting of one leader and five followers. Under no-attack conditions, the communication topology of the system is as follows: Figure 4 In (1), when the PO channel is subjected to a DoS attack, the topology is as follows: Figure 4 (2) When both the PO channel and the OC channel are simultaneously subjected to a DoS attack, the topology is as follows: Figure 4 (3) The dynamic equation of the robotic arm system can be expressed as:

[0176] ;

[0177] in , and They represent the first The inertia, angular displacement, and angular velocity of a robotic arm motor; , and They represent the first The inertia, angular displacement, and angular velocity of each link in the robotic arm.

[0178] definition , , , The robotic arm system can be modeled as the multi-agent system described above, in which...

[0179] ;

[0180] and , , .system It is considerable, considerable index. Let the observer coupling coefficient be... Controller coupling coefficient Define parameters .

[0181] Figure 5a , Figure 5b , Figure 5c , Figure 5d and Figure 6a , Figure 6b These represent the trajectory of the system state and the event trigger time in the absence of a DoS attack, respectively; Figure 7a , Figure 7b , Figure 7c , Figure 7d and Figure 8a , Figure 8b These represent the trajectory of the system state and the event trigger time under a DoS attack on the PO channel, respectively; Figure 9a , Figure 9b , Figure 9c , Figure 9d and Figure 10a , Figure 10b These represent the trajectory of the system state and the event trigger time when both the PO channel and OC channel are simultaneously subjected to a DoS attack, respectively. Figure 6a , Figure 8a and Figure 10a The PO channel event trigger time. Figure 6b , Figure 8b and Figure 10b This is the trigger time for the OC channel event.

[0182] Depend on Figure 5a , Figure 5b , Figure 5c , Figure 5d , Figure 7a , Figure 7b , Figure 7c , Figure 7d and Figure 9a , Figure 9b , Figure 9c , Figure 9d It can be seen that, under the design mechanism of this invention, the system can achieve practical safety consistency in all three cases. Figure 6a , Figure 6b , Figure 8a , Figure 8b and Figure 10a , Figure 10b It can be seen that the quantization-based event-triggered control method designed in this invention significantly reduces the communication frequency between intelligent agents, saves communication resources, and demonstrates the effectiveness and superiority of the designed control method.

[0183] The following describes the security and consistency control device for a multi-agent system based on quantized event triggering provided by this invention. The security and consistency control device for a multi-agent system based on quantized event triggering described below can be referred to in correspondence with the security and consistency control method for a multi-agent system based on quantized event triggering described above. For example... Figure 11 As shown, the multi-agent system security consistency control device based on quantized event triggering provided by the present invention includes:

[0184] Quantization module 1110 is used to input the output state data of the target intelligent agent into the quantizer of the target intelligent agent to obtain the quantized output data of the target intelligent agent. When the data input to the quantizer is at the same quantization level, the output data of the quantizer remains unchanged.

[0185] The first channel transmission module 1120 is used to receive the quantized output data of the neighboring intelligent agent, determine the first moment based on the quantized output data of the target intelligent agent and the neighboring intelligent agents, and send the quantized output data of the target intelligent agent at the first moment to the observers of the target intelligent agent and the neighboring intelligent agents.

[0186] The second channel transmission module 1130 is used to input the observation state data of the target intelligent agent into the quantizer to obtain the quantized observation data of the target intelligent agent, receive the quantized observation data of the neighboring intelligent agents, determine the second time based on the quantized observation data of the target intelligent agent and the neighboring intelligent agents, and send the quantized observation data of the target intelligent agent at the second time to the controllers of the target intelligent agent and the neighboring intelligent agents.

[0187] Control module 1140 is used to acquire control input data of the target intelligent agent output by the controller;

[0188] Specifically, at the third moment after receiving the target agent's output state data, the observer of the target agent resets the target agent's observation state data based on the target agent's output state data and control input data. At other times besides the third moment, the observer outputs the target agent's observation state data based on the target agent's quantized output data and quantized observation data.

[0189] Figure 12 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 12 As shown, the electronic device may include: a processor 1210, a communication interface 1220, a memory 1230, and a communication bus 1240. The processor 1210, communication interface 1220, and memory 1230 communicate with each other via the communication bus 1240. The processor 1210 can call logical instructions in the memory 1230 to execute a multi-agent system security consistency control method based on quantization event triggering. This multi-agent system security consistency control method based on quantization event triggering includes: inputting the output state data of the target agent into the quantizer of the target agent to obtain the quantized output data of the target agent; when the data input to the quantizer is at the same quantization level, the output data of the quantizer remains unchanged; receiving the quantized output data of neighboring agents; determining a first moment based on the quantized output data of the target agent and neighboring agents; sending the quantized output data of the target agent at the first moment to the observers of the target agent and neighboring agents; sending the output state data of the target agent at the first moment to the observer of the target agent; inputting the observation state data of the target agent into the quantizer to obtain... The system receives quantized observation data from the target intelligent agent and quantized observation data from neighboring intelligent agents. Based on the quantized observation data of the target intelligent agent and neighboring intelligent agents, it determines the second time step and sends the quantized observation data of the target intelligent agent at the second time step to the controllers of the target intelligent agent and neighboring intelligent agents. It also obtains the control input data of the target intelligent agent output by the controller. Specifically, at the third time step after receiving the output state data of the target intelligent agent, the observer of the target intelligent agent resets the observation state data of the target intelligent agent based on the output state data and control input data of the target intelligent agent. At other times besides the third time step, it outputs the observation state data of the target intelligent agent based on the quantized output data and quantized observation data of the target intelligent agent.

[0190] Furthermore, the logical instructions in the aforementioned memory 1230 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0191] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the multi-agent system security consistency control method based on quantization event triggering provided by the above methods. This multi-agent system security consistency control method based on quantization event triggering includes: inputting the output state data of a target agent into the quantizer of the target agent to obtain the quantized output data of the target agent; when the data input to the quantizer is at the same quantization level, the output data of the quantizer remains unchanged; receiving the quantized output data of neighboring agents; determining a first moment based on the quantized output data of the target agent and neighboring agents; sending the quantized output data of the target agent at the first moment to the observers of the target agent and neighboring agents; sending the output state data of the target agent at the first moment to the observer of the target agent; inputting the observation state data of the target agent into the quantizer to obtain... The system receives quantized observation data from the target intelligent agent and quantized observation data from neighboring intelligent agents. Based on the quantized observation data of the target intelligent agent and neighboring intelligent agents, it determines the second time step and sends the quantized observation data of the target intelligent agent at the second time step to the controllers of the target intelligent agent and neighboring intelligent agents. It also obtains the control input data of the target intelligent agent output by the controller. Specifically, at the third time step after receiving the output state data of the target intelligent agent, the observer of the target intelligent agent resets the observation state data of the target intelligent agent based on the output state data and control input data of the target intelligent agent. At other times besides the third time step, it outputs the observation state data of the target intelligent agent based on the quantized output data and quantized observation data of the target intelligent agent.

[0192] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the multi-agent system security consistency control method based on quantization event triggering provided by the above methods. This multi-agent system security consistency control method based on quantization event triggering includes: inputting the output state data of a target agent into the quantizer of the target agent to obtain quantized output data of the target agent; when the data input to the quantizer is at the same quantization level, the output data of the quantizer remains unchanged; receiving the quantized output data of neighboring agents; determining a first moment based on the quantized output data of the target agent and neighboring agents; sending the quantized output data of the target agent at the first moment to the observers of the target agent and neighboring agents; sending the output state data of the target agent at the first moment to the observer of the target agent; inputting the observation state data of the target agent into the quantizer to obtain... The system receives quantized observation data from the target intelligent agent and quantized observation data from neighboring intelligent agents. Based on the quantized observation data of the target intelligent agent and neighboring intelligent agents, it determines the second time step and sends the quantized observation data of the target intelligent agent at the second time step to the controllers of the target intelligent agent and neighboring intelligent agents. It also obtains the control input data of the target intelligent agent output by the controller. Specifically, at the third time step after receiving the output state data of the target intelligent agent, the observer of the target intelligent agent resets the observation state data of the target intelligent agent based on the output state data and control input data of the target intelligent agent. At other times besides the third time step, it outputs the observation state data of the target intelligent agent based on the quantized output data and quantized observation data of the target intelligent agent.

[0193] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0194] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0195] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for safety consensus control of multi-agent systems based on quantized event-triggering, characterized in that, The method comprises the following steps: inputting output state data of a target agent into a quantizer of the target agent to obtain quantized output data of the target agent, wherein the output data of the quantizer is unchanged when the data input into the quantizer is at the same quantization level; receiving the quantized output data of a neighbor agent, determining a first time based on the quantized output data of the target agent and the neighbor agent, and sending the quantized output data of the target agent at the first time to an observer of the target agent and the neighbor agent; inputting observed state data of the target agent into the quantizer to obtain quantized observed data of the target agent, receiving the quantized observed data of the neighbor agent, determining a second time based on the quantized observed data of the target agent and the neighbor agent, and sending the quantized observed data of the target agent at the second time to a controller of the target agent and the neighbor agent; obtaining control input data of the target agent output by the controller; wherein the observer of the target agent resets the observed state data of the target agent based on the output state data and the control input data of the target agent at a third time when the output state data of the target agent is received, and outputs the observed state data of the target agent based on the quantized output data and the quantized observed data of the target agent at other times than the third time.

2. The method of claim 1, wherein The determination formula of the first time is: ； where inf denotes the infimum, , , , , , triggering parameter , and are given positive numbers, denotes the sector boundary of the quantizer, denotes the output state data of the target agent i at time t, is the neighbor agent set of agent i, is a numerical value representing the relationship between agents i and j, and C is the system output matrix of the multi-agent system, , is the real state data of agent i at time t, and respectively denote the observation state data of agents i and j at time t, denotes the quantized output data of agent i at time, denotes the first time of agent i, denotes the next first time of agent i after , denotes the quantized observation data of agent i at time, denotes the second time of agent i, denotes the quantized output data of agent j at time, denotes the first time of agent j, denotes the quantized observation data of agent j at time, denotes the second time of agent j.

3. The method of claim 2, wherein The determination formula of the second time is: ； wherein , , , is the second time instant of the agent , denotes the next second time instant of the agent i after , is the second time instant of the agent , the triggering parameter , and are given positive constants, denotes the quantized observation data of the agent i at time instant, denotes the quantized observation data of the agent j at time instant.

4. The method of claim 3, wherein The formula for resetting the observed state data of the target agent by the observer at the third time is: = ， ； wherein, is the third time instant for the target agent i, denotes the elastic predicted state of agent i at time t, satisfies: ， ； denotes the derivative at time t, R is the state reset gain, is the control input data of agent i at time t, A and B are the system state matrix and the system control matrix of the multi-agent system, respectively, is a constant matrix representing the nonlinear part, denotes the nonlinear dynamics of the elastic predicted state in the multi-agent system, satisfies the Lipschitz continuous condition.

5. The method of claim 4, wherein The formula for outputting the observed state data of the target agent by the observer at other times than the third time based on the quantized output data and the quantized observed data of the target agent is: When time, ； wherein, represents derivative at time t, represents a coupling coefficient, represents an observer gain, represents a nonlinear dynamics of real state data in a multi-agent system, satisfies the Lipschitz continuity condition.

6. The method of claim 5, wherein The formula for the control input data output by the controller is: ； wherein is a coupling coefficient, is a control gain.

7. A device for safety-consistent control of a multi-agent system based on quantized event-triggering, characterized in that, The method comprises the following steps: a quantization module for inputting output state data of a target agent into a quantizer of the target agent to obtain quantized output data of the target agent, wherein the output data of the quantizer is unchanged when the data input into the quantizer is at the same quantization level; a first channel transmission module for receiving the quantized output data of a neighbor agent, determining a first time based on the quantized output data of the target agent and the neighbor agent, and sending the quantized output data of the target agent at the first time to an observer of the target agent and the neighbor agent; a second channel transmission module, configured to input the observation state data of the target agent into the quantizer to obtain quantized observation data of the target agent, receive the quantized observation data of the neighbor agent, determine a second time based on the quantized observation data of the target agent and the neighbor agent, and send the quantized observation data of the target agent at the second time to the controllers of the target agent and the neighbor agent; a control module, configured to obtain the control input data of the target agent output by the controller; wherein the observer of the target agent resets the observation state data of the target agent based on the output state data and control input data of the target agent at a third time when the output state data of the target agent is received, and outputs the observation state data of the target agent based on the quantized output data and the quantized observation data of the target agent at other times than the third time.

8. An electronic device comprising a memory, a processor, and a computer program stored on the memory and running on the processor, characterized in that, The processor executes the computer program to implement the method for safe and consistent control of a multi-agent system based on quantized event triggering according to any one of claims 1 to 6. 9.A non-transitory computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to implement the method for safe and consistent control of a multi-agent system based on quantized event triggering according to any one of claims 1 to 6.

10. A computer program product comprising a computer program, characterized in that, The computer program is executed by the processor to implement the method for safe and consistent control of a multi-agent system based on quantized event triggering according to any one of claims 1 to 6.

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