A multi-agent spatio-temporal dynamic system security boundary consistency control method

Abstract

The application discloses a kind of multi-agent spatiotemporal dynamic system security boundary consistency control method, specifically including the following technical steps: first, based on partial differential equation, the leader-follower spatiotemporal dynamic mathematical model of multi-agent system is constructed;Then, the abnormal condition mathematical model including actuator failure and network deception attack is established;By defining the system consistency control target, the error dynamic system equation is derived;Using Lyapunov stability theory, an energy function is constructed, and a system stability criterion is derived;Finally, a security boundary consistency control method is designed, realizing the consistency control of multi-agent spatiotemporal dynamics.The method effectively solves the high cost problem caused by the traditional scheme of full space domain layout actuator, and the problem that multi-agent system is easily disturbed by network attack in communication process, and has significant application value in engineering practice.

Description

Technical Field

[0001] This invention relates to the field of intelligent control, and in particular to a method for consistent control of the safety boundary of a multi-agent spatiotemporal dynamic system. Background Technology

[0002] A multi-agent system is a distributed network system composed of multiple cooperating or competing agents. These agents possess a certain degree of intelligence and integrate control and optimization technologies. Through information interaction between agents, the system can accomplish complex tasks in fields such as aerospace, defense, and industry. In recent years, multi-agent systems have been widely applied in various scenarios. Therefore, the cooperative control problem of multi-agent systems has attracted widespread attention from researchers. Cooperative control of multi-agent systems can accomplish various types of tasks, including consensus, formation control, swarm control, congestion control, and network optimization. Among these, the consensus problem, as the most fundamental and critical issue in the coordinated control of multi-agent systems, is of great significance for ensuring the stability and reliability of the system.

[0003] Multi-agent systems have wide applications in industrial and military fields, and the stability and security of their control are crucial; any failure can lead to huge economic losses. For example, in automobile manufacturing production lines, multi-agent systems are widely used for the collaborative assembly of robotic arms. If communication or cooperation between robotic arms fails, it can cause the entire production line to stop, resulting in significant economic losses. Therefore, researching safe and consistent control of multi-agent systems is of great importance to ensuring the stability and security of the system!

[0004] Current research in the field of multi-agent system safety control exhibits a significant trend towards a shift in modeling paradigms. Traditional research primarily employs ordinary differential equation (ODE) modeling methods. These models describe system evolution through single-dimensional functions of time variables. While they effectively characterize the temporal dynamic coupling between agents, they fail to represent the spatial distribution characteristics and spatiotemporal coupling effects of the system. This modeling approach essentially simplifies multi-agent systems with spatially extended characteristics into point mass models, causing the inherent spatiotemporal collaborative features of the system to be filtered out during the modeling process. This severely restricts the accurate modeling and analysis of swarm intelligence behavior in complex scenarios.

[0005] To address this theoretical limitation, modeling methods based on partial differential equations (PDEs) have made groundbreaking progress in recent years. By introducing spatial dimension variables, PDE models can simultaneously characterize the continuous evolution of agents in both time and space, making them particularly suitable for describing typical multi-agent systems with spatial distribution characteristics, such as UAV swarms and distributed sensor networks. Currently, researchers have constructed various spatiotemporal coupled models, including reaction-diffusion PDEs and hyperbolic PDEs, and based on these, have conducted research on key issues such as cooperative control and formation optimization, achieving landmark results in spatiotemporal consistency control and distributed state estimation.

[0006] It is noteworthy that existing research on the security and consistency of multi-agent spatiotemporal dynamic systems largely employs intra-domain control strategies, i.e., setting up distributed controllers or actuators within the system's spatial domain. In contrast, this invention proposes a boundary consistency control method, which achieves global system collaborative control by designing the control inputs of agents at the spatial boundaries. This control approach only requires applying control actions at the finite boundaries of the system's spatial domain, significantly reducing actuator deployment density and hardware costs. Furthermore, at the engineering implementation level, the boundary controller is easier to physically deploy and possesses stronger anti-interference capabilities.

[0007] In recent years, some researchers have conducted preliminary studies on the consistency control problem of multi-agent spatiotemporal dynamic systems and obtained some meaningful research results. However, the security boundary consistency control problem of multi-agent spatiotemporal dynamic systems under deception attacks and actuator failures has not yet been considered. Summary of the Invention

[0008] This invention provides a method for security boundary consistency control of multi-agent spatiotemporal dynamic systems in response to deception attacks and actuator failures, aiming to solve a problem that has not been considered to date in the consistency control of multi-agent spatiotemporal dynamic systems.

[0009] A method for security boundary consistency control of a multi-agent spatiotemporal dynamic system facing deception attacks and actuator failures, the method comprising:

[0010] Step 1: Construct a multi-agent spatiotemporal dynamic system model based on parabolic partial differential equations;

[0011] Step 2: Establish a spatiotemporal representation of actuator failures occurring at the system boundary for some intelligent agents and a numerical model of deception attacks during data transmission;

[0012] Step 3: Define the leader-follower consistency error to obtain the consistency state error system;

[0013] Step 4: Design a security boundary consistency controller under deception attacks and execution failures;

[0014] Step 5: Construct the corresponding Lyapunov function to obtain the conditions for the system to achieve security boundary consistency control.

[0015] As a further technical solution of the present invention, step one: constructing a multi-agent spatiotemporal dynamic system model based on parabolic partial differential equations, wherein the multi-agent spatiotemporal dynamic system includes There are 1 follower agent, each agent is labeled as follows: The leader is labeled as an intelligent agent. The leader agent model in the multi-agent spatiotemporal dynamic system is as follows:

[0016] ;

[0017] in, This indicates that the leader agent is at time t. The state at that location, space variables Time variable The initial state of the leader agent is , It is a positive definite matrix. It is a known constant real matrix;

[0018] The mathematical model of a single follower agent in a multi-agent spatiotemporal dynamic system is as follows:

[0019] ;

[0020] in, Indicates the first At time t, an intelligent agent The state of being, , The initial values ​​of each follower agent are represented as follows: , The control input indicates that an actuator malfunction has occurred.

[0021] As a further technical solution of the present invention, the mathematical description of actuator failure in some intelligent agents is as follows:

[0022] ;

[0023] in, Indicates the first The actuator influence factor of an agent, which varies with time. Changes, assuming influencing factors It is bounded and satisfies the following inequalities ,in, and These are the lower and upper bounds of the impact factor, respectively. Furthermore... Indicates the first The control input for each intelligent agent.

[0024] As a further technical solution of the present invention, the deception attack is a form of network attack that reduces the reliability of information transmission by tampering with data transmitted on a wireless communication network between intelligent agents. The attacker intercepts data signals from agent j to agent i that are about to be transmitted via the network, and transforms the intercepted data using a nonlinear function, thereby tampering with the communication data. Its mathematical expression is:

[0025] ;

[0026] in, It is a nonlinear function that satisfies the following inequalities: , It is composed of nonlinear functions A defined constant matrix.

[0027] As a further technical solution of the present invention, a leader-follower consistency error is defined. Then the error system can be obtained as follows:

[0028]

[0029]

[0030]

[0031] For any initial state, if the error signal satisfies the following equation, then the leader-follower multi-agent spatiotemporal dynamic system is said to have achieved the desired consensus control:

[0032] .

[0033] As a further technical solution of the present invention, in step four, based on a comprehensive analysis of the impact of deception attacks and actuator failures, a boundary control protocol is designed as follows:

[0034] ;

[0035] Where k is the control gain. It is the communication weight matrix between agents. If the agents With intelligent agents If there is communication, then ,otherwise , For intelligent agents The coupling weight coefficient between the leader and the leader, when At that time, intelligent agent Data can be transmitted between the leader and the leader; when At that time, intelligent agent Leaders cannot transmit data. . Let Laplace's matrix be the system's matrix. , It is the in-degree matrix of the system. .

[0036] As a further technical solution of the present invention, in step five, the multi-agent spatiotemporal dynamic system implements security boundary consistency control in the case of deception attacks and actuator failures, if a matrix exists... Make the following conditions true:

[0037] Formula 2: ;

[0038] in, ;

[0039] ;

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] For error systems, the following Lyapunov function is constructed:

[0045]

[0046] Differentiating the above equation, we get :

[0047] ;

[0048] Combining inequality techniques and Formula 2, we derive... The error approaches zero, thus further deriving the system state error. The value tends to zero; therefore, a multi-agent spatiotemporal dynamic system with actuator failure under a deception attack achieves secure consistency control under a boundary consistency control protocol.

[0049] The beneficial effects achieved by this invention are as follows:

[0050] This invention proposes a security boundary consistency control method for multi-agent PDE systems facing combined threats of deception attacks and actuator failures. Addressing the inherent spatiotemporal coupling dynamics, infinite-dimensional state space characteristics, and complex topological constraints of multi-agent systems, a precise mathematical description of the system's spatiotemporal evolution is achieved by introducing spatial dimension variables. Based on a distributed interaction mechanism, each agent only needs local state information from adjacent nodes to achieve consistency control. The proposed security boundary consistency control protocol, building upon traditional consistency algorithms, deeply integrates network security defense mechanisms and fault tolerance strategies, effectively solving system control problems under combined threats such as data tampering induced by network attacks and sudden actuator failures. Compared to traditional consistency control protocols, this protocol effectively improves system stability and robustness, significantly reduces actuator deployment density and hardware costs, and is easier to physically deploy and possesses stronger anti-interference capabilities at the engineering implementation level.

[0051] The security boundary consistency control for multi-agent spatiotemporal dynamic systems resistant to deception attacks and actuator failures is applicable to any real-world system modeled by the mathematical model of the single agent considered in this invention, and has a wide range of applications. Attached Figure Description

[0052] Figure 1 The flowchart shows a method for security boundary consistency control in a multi-agent spatiotemporal dynamic system facing deception attacks and actuator failures.

[0053] Figure 2 This is a communication topology diagram for a multi-agent spatiotemporal dynamic system.

[0054] Figure 3 The first simulation result analysis diagram of the present invention is shown, where sub-graphs (1)-(8) represent the error signal norm of each agent in the open-loop state.

[0055] Figure 4 The second simulation result analysis diagram of the present invention is shown, where sub-graphs (1)-(8) represent the error signal norm of each agent in the closed loop state. Detailed Implementation

[0056] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0057] like Figure 1 As shown, this embodiment of the invention provides a method for security boundary consistency control of a multi-agent spatiotemporal dynamic system oriented towards deception attacks and actuator failures, the method comprising:

[0058] Step 1: Construct a multi-agent spatiotemporal dynamic system model based on parabolic partial differential equations;

[0059] Step 2: Establish a spatiotemporal representation of actuator failures occurring at the system boundary for some intelligent agents and a numerical model of deception attacks during data transmission;

[0060] Step 3: Define the leader-follower consistency error to obtain the consistency state error system;

[0061] Step 4: Design a security boundary consistency controller under deception attacks and execution failures;

[0062] Step 5: Construct the corresponding Lyapunov function to obtain the conditions for the system to achieve security boundary consistency control;

[0063] It realizes the security boundary consistency control of a multi-agent spatiotemporal dynamic system facing deception attacks and actuator failures.

[0064] Step 1 of this embodiment: Construct a multi-agent spatiotemporal dynamic system model based on parabolic partial differential equations. The multi-agent spatiotemporal dynamic system includes N follower agents, each labeled as follows: The leader is labeled as an intelligent agent. The leader agent model in the multi-agent spatiotemporal dynamic system is as follows:

[0065] ;

[0066] in, This indicates that the leader agent is at time t. The state at that location, space variables Time variable The initial state of the leader agent is , It is a positive definite matrix. It is a known constant real matrix;

[0067] The mathematical model of a single follower agent in a multi-agent spatiotemporal dynamic system is as follows:

[0068] ;

[0069] in, Indicates the first At time t, an intelligent agent The state of being, , The initial values ​​of each follower agent are represented as follows: , The control input indicates that an actuator malfunction has occurred.

[0070] Step two of this embodiment: For the multi-agent spatiotemporal dynamic system under study, considering that some agents may face actuator failures and network attacks during network communication, a mathematical model is established to describe the attacks and failures.

[0071] The mathematical description of actuator failure in some intelligent agents is as follows:

[0072] ;

[0073] in, Indicates the first The actuator influence factor of an agent, which varies with time. Changes, assuming influencing factors It is bounded and satisfies the following inequalities ,in, and These are the lower and upper bounds of the impact factor, respectively. Furthermore... Indicates the first The control input for each intelligent agent.

[0074] The deception attack described in this embodiment is a form of network attack that reduces the reliability of information transmission by tampering with data transmitted over a wireless communication network between agents. The attacker intercepts data signals from agent j to agent i that are about to be transmitted via the network, and then uses a nonlinear function to transform the intercepted data, thereby tampering with the communication data. Its mathematical expression is:

[0075] ;

[0076] in, It is a nonlinear function that satisfies the following inequalities: F is a nonlinear function A defined constant matrix.

[0077] In step three of this embodiment, the leader-follower consistency error is defined. Then the error system can be obtained as follows:

[0078]

[0079]

[0080]

[0081] For any initial state, if the following equation is satisfied, then the leader-follower multi-agent spatiotemporal dynamic system is said to have achieved the desired consistent control:

[0082] .

[0083] In step four of this embodiment, the impact of deception attacks and actuator failures is comprehensively analyzed, and a security boundary consistency controller is designed under both deception attacks and execution failures:

[0084] ;

[0085] Where k is the control gain. It is the communication weight matrix between agents. If the agents With intelligent agents If there is communication, then ,otherwise , For intelligent agents The coupling weight coefficient between the leader and the leader, when At that time, intelligent agent Data can be transmitted between the leader and the leader; when At that time, intelligent agent Leaders cannot transmit data. . Let Laplace's matrix be the system's matrix. , It is the in-degree matrix of the system. .

[0086] In step five of this embodiment, the multi-agent spatiotemporal dynamic system implements security boundary consistency control in the event of deception attacks and actuator failures. If a matrix exists... Make the following conditions true:

[0087] Formula 2: ;

[0088] in, ;

[0089] ;

[0090] ;

[0091] ;

[0092] ;

[0093] ;

[0094] For error systems, the following Lyapunov function is constructed:

[0095]

[0096] Differentiating the above equation, we get :

[0097] ;

[0098] Combining inequality techniques and Formula 2, we can obtain The state error between the leader and followers approaches zero, and the state error between the leader and followers approaches zero. Therefore, the multi-agent spatiotemporal dynamic system with actuator failure under deception attack achieves safe consistency control under the boundary consistency control protocol.

[0099] Select examples for simulation verification;

[0100] make , , Obviously, it is easy to verify. The following inequalities must be satisfied:

[0101] ;

[0102] Consider a leader-follower multi-agent (PDE) system consisting of 5 nodes, with the following topology: Figure 2 As shown.

[0103] Choose the following matrix and parameters:

[0104] , ,

[0105] , ,

[0106] , .

[0107] Using the LMI toolbox in MATLAB, k can be obtained. This makes Equation 2 valid. Therefore, the multi-agent PDE system can achieve consistent control.

[0108] The initial state of the agent is selected as follows:

[0109] , , ,

[0110] , .

[0111] Figure 3 and Figure 4 The error signals of each agent in the multi-agent system under both open-loop and closed-loop control modes are shown respectively. The evolution law of the spatiotemporal state error norm. Simulation data shows that the open-loop system without a security boundary consistency control protocol ( Figure 3 In this context, the error norm of the agent exhibits divergent characteristics over time, showing a trend of divergence as the error norm increases. In stark contrast, the closed-loop system employing the boundary security consistency control protocol designed in this invention... Figure 4 It exhibits significant error suppression capabilities, with the state error norm of all agents showing an exponential decay trend under control, eventually converging over time.

[0112] It should be understood that although the steps in the flowcharts of the various embodiments of the present invention are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the various embodiments may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps.

[0113] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0114] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0115] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

[0116] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for consistency control of safety boundaries in a multi-agent spatiotemporal dynamic system, characterized in that, The method includes; Step 1: Construct a multi-agent spatiotemporal dynamic system model based on parabolic partial differential equations. The multi-agent spatiotemporal dynamic system includes... Intelligent agents, each labeled as The leader agent is labeled l, and the leader agent model in the multi-agent spatiotemporal dynamic system is as follows: ； in, This indicates that the leader agent is at time t. The state at that location, space variables Time variable The initial state of the leader agent is A is a positive definite matrix, and A is a known constant real matrix. The mathematical model of a single follower agent in a multi-agent spatiotemporal dynamic system is as follows: ； in, This indicates that the i-th agent at time t... The state of being, The initial values ​​of the N follower agents are represented as follows: Control inputs indicating an actuator malfunction; Step 2: Establish a spatiotemporal representation of actuator failures occurring at the system boundary for some intelligent agents and a mathematical model of deception attacks during data transmission; Step 3: Define the leader-follower consistency error to obtain the consistency state error system; Step 4: Design a security boundary consistency controller under deception attacks and execution failures; Step 5: Construct the corresponding Lyapunov function to obtain the conditions for the system to achieve security boundary consistency control; During operation, some agents may experience actuator failures, which can be mathematically described as follows: ； in, Let represent the actuator influence factor of the i-th agent, which changes with time t. Assume the influence factor... It is bounded and satisfies the following inequalities ,in, and These are the lower and upper bounds of the impact factor, respectively. This represents the control input of the i-th agent; Based on a comprehensive analysis of the impact of deception attacks and actuator failures, a boundary control protocol is designed as follows: ； Where k is the control gain. This is the communication weight matrix between agents. If there is communication between agent j and agent i, then... ,otherwise Let be the coupling weight coefficient between agent i and the leader, when At this time, data can be transmitted between agent i and the leader; when At this time, data transmission is not possible between agent i and the leader. , Let Laplace's matrix be the system's matrix. , It is the in-degree matrix of the system. .

2. The method for security boundary consistency control of a multi-agent spatiotemporal dynamic system according to claim 1, characterized in that, In multi-agent spatiotemporal dynamic systems, agents frequently interact via networks, making them vulnerable to network attacks. A deception attack is considered, a form of network attack that reduces the reliability of information transmission by tampering with data transmitted over the wireless communication network between agents. The attacker intercepts data signals from agent to agent preparing to transmit via the network and transforms the intercepted data using a nonlinear function, thereby altering the communication data. Its mathematical expression is: ； in, It is a nonlinear function that satisfies the following inequalities: F is a nonlinear function A defined constant matrix.

3. The method for security boundary consistency control of a multi-agent spatiotemporal dynamic system according to claim 1, characterized in that, Define the leader-follower consistency error Then the error system can be obtained as follows: ； ； For any initial state, if the error signal satisfies the following equation, then the leader-follower multi-agent spatiotemporal dynamic system is said to have achieved the desired consensus control: 。

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