Multi-agent spatio-temporal dynamic system security boundary consistency control method

Abstract

The invention discloses a security boundary consistency control method for a multi-agent spatio-temporal dynamic system. The method specifically comprises the following technical steps: firstly, constructing a leader-follower spatio-temporal dynamic mathematical model of the multi-agent system based on a partial differential equation; then establishing an abnormal working condition mathematical model containing an actuator fault and a network spoofing attack; deducing to obtain an error dynamic system equation by defining a system consistency control target; constructing an energy function by using a Lyapunov stability theory, and deducing to obtain a system stability criterion; finally, a security boundary consistency control method is designed, and multi-agent space-time dynamic consistency control is achieved. The method effectively solves the problem of high cost caused by arrangement of actuators in a whole spatial domain in a traditional scheme and the problem that a multi-agent system is easily interfered by network attacks in a communication process, and has remarkable application value in engineering practice.

Description

Technical Field

[0001] The present invention relates to the field of intelligent control, and in particular to a method for controlling the safety boundary consistency of a multi-agent spatiotemporal dynamic system. Background Art

[0002] A multi-agent system is a distributed network system composed of multiple collaborating or competing agents. These agents possess a certain degree of intelligence and integrate control and optimization technologies. Through information exchange between agents, these systems can accomplish complex tasks in fields such as aerospace, defense, and industry. In recent years, multi-agent systems have been widely used in various scenarios. Consequently, the problem of coordinated control of multi-agent systems has attracted extensive research attention. Cooperative control of multi-agent systems can accomplish a variety of tasks, including consensus, formation control, cluster control, swarming control, and network optimization. Consensus, as the most fundamental and critical issue in the coordinated control of multi-agent systems, is crucial for ensuring system stability and reliability.

[0003] Multi-agent systems have widespread applications in industry and the military, where control stability and safety are crucial. Any failure can result in significant economic losses. For example, in automotive manufacturing lines, multi-agent systems are widely used for collaborative assembly by robotic arms. Failures in communication or collaboration between robotic arms can cause the entire production line to stall, leading to significant economic losses. Therefore, research on safe and consistent control of multi-agent systems is crucial for ensuring system stability and safety.

[0004] Current research in the field of multi-agent system safety control is demonstrating a significant paradigm shift in modeling. Traditional research primarily employs ordinary differential equation (ODE) modeling. These models describe system evolution through single-dimensional functions of the time variable. While they effectively characterize the temporal dynamic coupling between agents, they are unable to characterize the system's spatial distribution and spatiotemporal coupling effects. This modeling approach essentially simplifies the spatially extended multi-agent system into a point-mass model, filtering out the system's inherent spatiotemporal coordination characteristics 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 breakthrough progress in recent years. By introducing spatial dimensional variables, PDE models can simultaneously characterize the continuous evolution of intelligent agents in both time and space. They are particularly suitable for describing typical multi-agent systems with spatial distribution characteristics, such as drone swarms and distributed sensor networks. Currently, scholars have constructed a variety of spatiotemporal coupling models, such as reaction-diffusion PDEs and hyperbolic PDEs. Based on these models, they have conducted research on key issues such as coordinated control and formation optimization, and have achieved milestone results in spatiotemporal consistency control and distributed state estimation.

[0006] It is noteworthy that existing research on the safety consistency of multi-agent spatiotemporal dynamic systems has mostly adopted intra-domain control strategies, which deploy distributed controllers or actuators within the system's spatial domain. In contrast, this paper proposes a boundary consistency control method that achieves coordinated control of the global system by designing the control inputs of the agents at the spatial boundaries. This control approach only requires applying control at the limited boundaries of the system's spatial domain, significantly reducing actuator deployment density and hardware costs. Furthermore, in terms of engineering implementation, boundary controllers are easier to physically deploy and have stronger anti-interference capabilities.

[0007] In recent years, some researchers have preliminarily studied the consistency control problem of multi-agent spatiotemporal dynamic systems and achieved some meaningful results. However, the problem of safety boundary consistency control of multi-agent spatiotemporal dynamic systems under deception attacks and actuator failures has not been considered so far. Summary of the Invention

[0008] The present invention provides a multi-agent spatiotemporal dynamic system security boundary consistency control method resistant to deception attacks and actuator failures, aiming to solve problems that have not been considered so far in the consistency control of multi-agent spatiotemporal dynamic systems.

[0009] A method for controlling the security boundary consistency of a multi-agent spatiotemporal dynamic system against 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 of some agents at the system boundary and a numerical model of deception attacks in data transmission;

[0012] Step 3: Define the leader-follower consistency error and 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 safety boundary consistency control.

[0015] As a further technical solution of the present invention, step 1: construct a multi-agent spatiotemporal dynamic system model based on parabolic partial differential equations, the multi-agent spatiotemporal dynamic system includes Agents, each agent is labeled , the leader label agent is , the leader agent model in the multi-agent spatiotemporal dynamic system is:

[0016] ;

[0017] in, Indicates that the leader agent is time The state, spatial variables , time variable , the initial state of the leader agent is , is a positive definite matrix, is a known constant real matrix;

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

[0019] ;

[0020] in, Indicates the An intelligent agent in time The state of being, , The initial value of the follower agent is expressed as , Control input indicating an actuator fault has occurred.

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

[0022] ;

[0023] in, Indicates the The actuator influence factor of each agent, which changes with time Change, assuming impact factor is bounded and satisfies the following inequality ,in, and are the lower and upper bounds of the impact factor respectively. Indicates the The control input of an agent.

[0024] As a further technical solution of the present invention, the spoofing attack is a type of network attack that reduces the reliability of information transmission by tampering with data transmitted on a wireless communication network between agents. The attacker intercepts the data signal intended for transmission from agent j to agent i over the network and transforms the intercepted data using a nonlinear function, thereby tampering with the communication data. Its mathematical expression is:

[0025] ;

[0026] in, is a nonlinear function that satisfies the following inequality: , It is a nonlinear function Determine the constant matrix.

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

[0028]

[0029] For any initial state, if the error signal satisfies the following equation, the leader-follower multi-agent spatiotemporal dynamic system is said to achieve the desired consistency control:

[0030] .

[0031] As a further technical solution of the present invention, in step 4, a boundary control protocol is designed by comprehensively analyzing the impact of deception attacks and actuator failures as follows:

[0032] ;

[0033] in, is the control gain, is the communication weight matrix between agents. If the agent With the agent If there is communication between ,otherwise , For intelligent agents The coupling weight coefficient between the leader and When the agent Data can be transferred between the leader and the When the agent Data cannot be transferred between leaders. . is the Laplace matrix of the system, , is the in-degree matrix of the system, .

[0034] As a further technical solution of the present invention, in step 5, the multi-agent spatiotemporal dynamic system realizes safety boundary consistency control under the conditions of deception attack and actuator failure. If there is a matrix The following conditions are met:

[0035] Formula 2: ;

[0036] in, ;

[0037] ;

[0038] ;

[0039] ;

[0040] ;

[0041] ;

[0042] For the error system, the following Lyapunov function is constructed:

[0043]

[0044] Taking the derivative of the above formula, we can get :

[0045] ;

[0046] Combining the inequality technique with Formula 2, we can derive tends to zero, and thus the system state error is further deduced tends to zero; therefore, the multi-agent spatiotemporal dynamic system with actuator failures under deception attacks achieves secure consistency control under the bounded consistency control protocol.

[0047] Beneficial effects achieved by the present invention:

[0048] The present invention proposes a method for consistency control of the security boundary of a multi-agent PDE system against combined deception attacks and actuator failures; in view of the inherent spatiotemporal coupling dynamic characteristics, infinite-dimensional state space characteristics and complex topological structure constraints of the multi-agent system, an accurate mathematical description of the spatiotemporal evolution law of the system is achieved by introducing spatial dimension variables. Based on the distributed interaction mechanism, each agent only needs the local state information of the adjacent nodes to achieve consistency control. The proposed security boundary consistency control protocol deeply integrates network security defense mechanisms and fault tolerance strategies on the basis of traditional consistency algorithms, effectively solving system control problems under combined threats such as data tampering induced by network attacks and sudden failures of actuators. Compared with traditional consistency control protocols, this protocol effectively improves the stability and robustness of the system, greatly reduces the deployment density of actuators and hardware costs, and at the engineering implementation level, is easier to physically deploy and has stronger anti-interference capabilities.

[0049] The security boundary consistency control of multi-agent spatiotemporal dynamic systems against deception attacks and actuator failures is applicable to any practical system modeled by the mathematical model of a single agent considered by the present invention, and has a wide range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 Flowchart of the safety boundary consistency control method for multi-agent spatiotemporal dynamic systems against deception attacks and actuator failures.

[0051] Figure 2 Communication topology diagram of a multi-agent spatiotemporal dynamic system.

[0052] Figure 3 This is the first simulation result analysis diagram of the embodiment of the present invention, where sub-diagrams (1)-(8) respectively represent the error signal norm of each intelligent agent in the open-loop state.

[0053] Figure 4 This is a second simulation result analysis diagram of an embodiment of the present invention, wherein sub-diagrams (1)-(8) respectively represent the error signal norm of each intelligent agent in the closed-loop state. DETAILED DESCRIPTION

[0054] The technical solution of the present invention is described in detail below with reference to the accompanying drawings.

[0055] like Figure 1 As shown, an embodiment of the present invention provides a method for controlling the security boundary consistency of a multi-agent spatiotemporal dynamic system against deception attacks and actuator failures, the method comprising:

[0056] Step 1: Construct a multi-agent spatiotemporal dynamic system model based on parabolic partial differential equations;

[0057] Step 2: Establish a spatiotemporal representation of actuator failures of some agents at the system boundary and a numerical model of deception attacks in data transmission;

[0058] Step 3: Define the leader-follower consistency error and obtain the consistency state error system;

[0059] Step 4: Design a security boundary consistency controller under deception attacks and execution failures;

[0060] Step 5: Construct the corresponding Lyapunov function to obtain the conditions for the system to achieve safety boundary consistency control;

[0061] The security boundary consistency control of multi-agent spatiotemporal dynamic systems against deception attacks and actuator failures is achieved.

[0062] 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 Agents, each agent is labeled , the leader label agent is , the leader agent model in the multi-agent spatiotemporal dynamic system is:

[0063] ;

[0064] in, Indicates that the leader agent is time The state, spatial variables , time variable , the initial state of the leader agent is , is a positive definite matrix, is a known constant real matrix;

[0065] The mathematical model of a single follower agent in a multi-agent spatiotemporal dynamic system is:

[0066] ;

[0067] in, Indicates the An intelligent agent in time The state of being, , The initial value of the follower agent is expressed as , Control input indicating an actuator fault has occurred.

[0068] Step 2 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.

[0069] The mathematical description of actuator failure in some agents is:

[0070] ;

[0071] in, Indicates the The actuator influence factor of each agent, which changes with time Change, assuming impact factor is bounded and satisfies the following inequality ,in, and are the lower and upper bounds of the impact factor respectively. Indicates the The control input of an agent.

[0072] The spoofing attack described in this embodiment is a type of network attack that tampered with data transmitted over a wireless communication network between agents, reducing the reliability of information transmission. The attacker intercepts the data signal intended for transmission from agent j to agent i over the network and transforms the intercepted data using a nonlinear function, thereby tampering with the communication data. The mathematical expression is:

[0073] ;

[0074] in, is a nonlinear function that satisfies the following inequality: , It is a nonlinear function Determine the constant matrix.

[0075] In step 3 of this embodiment, the leader-follower consistency error is defined as: , then the error system can be obtained as:

[0076]

[0077] For any initial state, if the following equation is satisfied, the leader-follower multi-agent spatiotemporal dynamic system is said to achieve the desired consistency control:

[0078] .

[0079] In step 4 of this embodiment, the impact of spoofing attacks and actuator failures is comprehensively analyzed to design a security boundary consistency controller under spoofing attacks and execution failures:

[0080] ;

[0081] Where k is the control gain, is the communication weight matrix between agents. If the agent With the agent If there is communication between ,otherwise , For intelligent agents The coupling weight coefficient between the leader and When the agent Data can be transferred between the leader and the When the agent Data cannot be transferred between leaders. . is the Laplace matrix of the system, , is the in-degree matrix of the system, .

[0082] In step 5 of this embodiment, the multi-agent spatiotemporal dynamic system realizes safety boundary consistency control under the conditions of deception attack and actuator failure. If there is a matrix The following conditions are met:

[0083] Formula 2: ;

[0084] in, ;

[0085] ;

[0086] ;

[0087] ;

[0088] ;

[0089] ;

[0090] For the error system, the following Lyapunov function is constructed:

[0091]

[0092] Taking the derivative of the above formula, we can get :

[0093] ;

[0094] Combining the inequality technique with Formula 2, we can get It tends to zero, and further, the direct state error between the leader and the follower tends to zero; therefore, the multi-agent spatiotemporal dynamic system with actuator failure under deception attack achieves safe consistency control under the boundary consistency control protocol.

[0095] Select examples for simulation verification;

[0096] make , ,

[0097] Obviously, it is easy to verify The following inequality is satisfied:

[0098] ;

[0099] Consider a leader-follower multi-agent PDE system consisting of 5 nodes with the topology Figure 2 shown.

[0100] Select the following matrices and parameters:

[0101] , ,

[0102] , ,

[0103] , .

[0104] Using the LMI toolbox in MATLAB, we can get This makes Formula 2 valid. Therefore, the multi-agent PDE system can achieve consistent control.

[0105] Select the initial state of the agent as:

[0106] , , ,

[0107] , .

[0108] Figure 3 and Figure 4 The error signals of each agent in the multi-agent system under open-loop and closed-loop control modes are shown respectively. The evolution law of the spatiotemporal state error norm of . The simulation data shows that the open-loop system without the safety boundary consistency control protocol ( Figure 3 ), the error norm of the agent shows a divergent characteristic over time, and its error norm shows a divergent trend as time grows. In sharp contrast, the closed-loop system ( Figure 4 ) shows significant error suppression ability. The state error norms of all intelligent agents show an exponential decay trend under the control and eventually converge with the growth of time.

[0109] It should be understood that, although the various steps in the flow chart of each embodiment of the present invention are shown in sequence according to the indication of the arrows, these steps are not necessarily performed in sequence according to the order indicated by the arrows. Unless otherwise specified herein, the execution of these steps is not strictly limited in order, and these steps can be performed in other orders. Moreover, at least a portion of the steps in each embodiment may include a plurality of sub-steps or a plurality of stages, and these sub-steps or stages are not necessarily performed at the same time, but can be performed at different times, and the execution order of these sub-steps or stages is not necessarily performed in sequence, but can be performed in turn or alternately with at least a portion of other steps or sub-steps or stages of other steps.

[0110] Those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing the relevant hardware through a computer program. The program can be stored in a non-volatile computer-readable storage medium. When executed, the program can include the processes of the above-described method embodiments. Any reference to memory, storage, database, or other media used in the various embodiments provided herein may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may 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), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct RAMbus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM).

[0111] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned 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.

[0112] The above-described embodiments merely illustrate several implementations of the present invention, and while their descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

[0113] 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 in the scope of protection of the present invention.

Claims

1. A method for controlling the safety boundary consistency of a multi-agent spatiotemporal dynamic system, characterized by: The method comprises: Step 1: Construct a multi-agent spatiotemporal dynamic system model based on parabolic partial differential equations. The multi-agent spatiotemporal dynamic system includes Agents, each agent is labeled , the leader label agent is , the leader agent model in the multi-agent spatiotemporal dynamic system is: ； in, Indicates that the leader agent is time The state, spatial variables , time variable , the initial state of the leader agent is , is a positive definite matrix, is a known constant real matrix; The mathematical model of a single follower agent in a multi-agent spatiotemporal dynamic system is: ； in, Indicates the An intelligent agent in time The state of being, . The initial value of the follower agent is expressed as , A control input indicating an actuator fault has occurred; Step 2: Establish a spatiotemporal representation of actuator failures of some agents at the system boundary and a numerical model of deception attacks in data transmission; Step 3: Define the leader-follower consistency error and 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 safety boundary consistency control.

2. A method for controlling the safety boundary consistency of a multi-agent spatiotemporal dynamic system according to claim 1, characterized in that: During operation, some agents may experience actuator failures, which can be mathematically described as: ； in, Indicates the The actuator influence factor of each agent, which changes with time Change, assuming impact factor is bounded and satisfies the following inequality ,in, and are the lower and upper bounds of the impact factor respectively. Indicates the The control input of an agent.

3. The method for controlling the safety boundary consistency of a multi-agent spatiotemporal dynamic system according to claim 1, characterized in that: The agents in a multi-agent spatiotemporal dynamic system need to interact frequently through the network, which is usually open and vulnerable to network attacks. The present invention considers a deception attack, which is a form of network attack that reduces the reliability of information transmission by tampering with the data transmitted on the wireless communication network between agents. The attacker intercepts the data from the agent and To the agent Prepare the data signal transmitted via the network and use a nonlinear function to transform the intercepted data, thereby tampering with the communication data. Its mathematical expression is: ； in, is a nonlinear function that satisfies the following inequality: , It is a nonlinear function Determine the constant matrix.

4. A method for controlling the safety boundary consistency of a multi-agent spatiotemporal dynamic system according to claim 1, characterized in that: Defining leader-follower consensus error , then the error system can be obtained as: For any initial state, if the error signal satisfies the following equation, the leader-follower multi-agent spatiotemporal dynamic system is said to achieve the desired consistency control: 。 5. The method for controlling the safety boundary consistency of a multi-agent spatiotemporal dynamic system according to claim 1, characterized in that: After comprehensively analyzing the impact of deception attacks and actuator failures, a boundary control protocol was designed as follows: ； Where k is the control gain, is the communication weight matrix between agents. If the agent With the agent If there is communication between ,otherwise , For intelligent agents The coupling weight coefficient between the leader and When the agent Data can be transferred between the leader and the When the agent Data cannot be transferred between leaders. . is the Laplace matrix of the system, , is the in-degree matrix of the system, .

6. A method for controlling the safety boundary consistency of a multi-agent spatiotemporal dynamic system according to claim 1, characterized in that A safe boundary consistency control method for multi-agent spatiotemporal dynamic systems under deception attacks and actuator failures is implemented if there exists a positive definite matrix The following conditions are met: Formula 2: ; in, ; ； ； ； ; ; For the error system, the following Lyapunov function is constructed: ； Taking the derivative we get : ； Combining the inequality technique with Formula 2, we can derive tends to zero, and thus the system state error is further deduced tends to zero; therefore, the multi-agent spatiotemporal dynamic system with actuator failures under deception attacks achieves secure consistency control under the boundary control protocol.

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