Multi-agent space-time dynamic system intrusion tolerance and fault tolerance cooperative security consistency control method

Abstract

The invention discloses a multi-agent spatio-temporal dynamic system intrusion tolerance and fault tolerance cooperative security consistency control method. The method comprises the following steps: constructing mathematical models of a leader and a follower of a multi-agent spatio-temporal dynamic system based on a partial differential equation; constructing a mathematical model of actuator faults and spoofing attacks; defining a consistency condition to obtain an error system; constructing a proper Lyapunov functional, and obtaining a system stability criterion by using a Lyapunov stability theory; and the error of the multi-agent space-time dynamic system tends to zero by using the state feedback controller, so that the system realizes safety consistency control. The invention comprehensively considers that a multi-agent space-time dynamic system is easy to have actuator faults in a complex environment and is easy to suffer from network attacks in network communication, introduces an intrusion tolerance and fault tolerance cooperative security consistency control method, improves the robustness of the system, and improves the reliability of the system. And the multi-agent space-time dynamic system can achieve a safety consistency control target.

Description

Technical Field

[0001] The present invention relates to the field of intelligent control, and in particular to an intrusion-tolerant and fault-tolerant collaborative security consistency control method for a multi-agent spatiotemporal dynamic system. Background Art

[0002] A multi-agent system is composed of multiple agents that cooperate or compete with each other. It is a distributed network system with certain intelligence and integrates control optimization and other technologies. It can complete complex tasks through information interaction. In recent years, multi-agent systems have been widely used in aerospace, national defense, industry and other fields. Typical multi-agent control systems include aircraft formation clusters, satellite formation clusters, robot collaborative control clusters, air-ground cluster collaborative operations, etc. Therefore, many researchers are paying attention to the collaborative control problem of multi-agent systems. The collaborative control of multi-agent systems can complete many different types of tasks. Typical tasks include consistency, formation control, cluster control, swarming control and network optimization. Among them, the consistency problem is the most basic and most critical problem in the coordinated control of multi-agent systems.

[0003] Multi-agent systems are widely used in the industrial and military fields. The stability and safety requirements of their control are very strict. Any carelessness will cause immeasurable economic losses. For example, on May 1, 2018, at the Xi'an Red May City Wall International Cultural Festival, a major error occurred in the aircraft formation, and the left part of the aerial target pattern slid down on a large scale, resulting in the failure of the performance. Therefore, studying the safety consistency control of the intrusion tolerance and fault tolerance coordination of multi-agent systems is crucial to improving system safety! According to the current research results on the safety control of multi-agent systems, most of the existing research is described by ordinary differential equations (ODE). The multi-agent system represented by ODE modeling is limited to a single time function, ignoring the influence of the spatial distribution of the subject. Therefore, this type of model cannot cover the inherent spatiotemporal characteristics of the system. Therefore, using ordinary differential equations (PDE) to model multi-agent systems can simultaneously describe the changes of the system in time and space, and is suitable for modeling dynamic behaviors in multi-agent systems; so far, some researchers have preliminarily studied the cooperative control problem of multi-agent systems based on partial differential equation modeling, and have achieved some meaningful research results, but the intrusion-tolerant and fault-tolerant cooperative safety consistency control problem of multi-agent spatiotemporal dynamic systems under deception attacks and actuator failures has not yet been considered. Summary of the invention

[0004] The present invention provides an intrusion-tolerant and fault-tolerant collaborative safety consistency control method for a multi-agent spatiotemporal dynamic system, aiming to solve the problem of intrusion-tolerant and fault-tolerant collaborative safety consistency control of a multi-agent system modeled based on partial differential equations under deception attacks and actuator failures, which has not been considered so far.

[0005] A method for intrusion-tolerant and fault-tolerant collaborative safety consistency control of a multi-agent spatiotemporal dynamic system, the method comprising: Step 1: Construct a multi-agent spatiotemporal dynamic system model based on partial differential equation modeling; Step 2: Establish a mathematical model for the actuator failure and deception attack of some agents; Step 3: Introduce the leader-follower consistency condition to obtain the error system; Step 4: Design a security consistency controller that is tolerant to intrusion and fault under deception attacks and execution failures; Step 5: Construct the corresponding Lyapunov function and obtain the conditions for the system to achieve consistency control.

[0006] As a further technical solution of the present invention, step 1: construct a multi-agent spatiotemporal dynamic system model based on partial differential equation modeling, the multi-agent spatiotemporal dynamic system includes Agents, each agent is labeled , the virtual agent leader is labeled 0, and the leader agent model in the multi-agent spatiotemporal dynamic system is: ; in, Represents the state variables of the leader agent, spatial variables , time variable , the initial state of the leader agent is , is a known constant real matrix; The mathematical model of a single agent in a multi-agent spatiotemporal dynamic system is: ; in, Indicates The state variables of an agent, , The initial value of the follower agent is expressed as , Indicates a control input with a fault.

[0007] As a further technical solution of the present invention, the mathematical model of actuator failure of some agents is expressed as: ; in, Indicates The actuator of an agent changes over time The influence factor of the actuator is changed, assuming the influence factor is bounded and satisfies the following inequality , Indicates The control input of an agent.

[0008] As a further technical solution of the present invention, the deception attack refers to a form of network attack aimed at weakening the reliability of information transmission by tampering with the data transmitted on the wireless communication network between intelligent agents. Specifically, assuming that the attacker can intercept the data transmitted from the intelligent agent, To Agent Prepare the data signal for transmission over the network and use a nonlinear function The data to be transmitted are transformed into the following expression: ; in, is a nonlinear function that satisfies the following inequality: , It is a nonlinear function Determine the constant matrix.

[0009] As a further technical solution of the present invention, in step 3, for any given initial state, if the following equation relationship holds, the leader-follower multi-agent spatiotemporal dynamic system is said to achieve the desired consistency control: ; definition , then the error system is: Formula 1: ; ; , .

[0010] As a further technical solution of the present invention, in step 4, the following control protocol is designed by comprehensively considering the influence of deception attack and actuator failure: ; in, c is the control gain, The communication weight matrix between agents, if the agent With Agent can communicate with each other, then ,otherwise , For intelligent agents The coupling weight between the leader and When the intelligent agent Can receive information from the leader; when When the intelligent agent Unable to receive leader's message.

[0011] As a further technical solution of the present invention, in step 5, the multi-agent system with spatiotemporal characteristics under deception attack realizes intrusion tolerance and fault tolerance collaborative security consistency control. If there is a matrix The following conditions are established: Formula 2: ; in, ; ; ; ; For the error system, the following Lyapunov function is constructed: ; Taking the derivative of the above formula, we can get : ; Combining the inequality technique with Formula 2, we get tends to zero, and further obtains tends to zero; therefore, the multi-agent partial differential equation system with actuator failure under deception attack achieves intrusion-tolerant and fault-tolerant collaborative security consistency control under the control protocol.

[0012] Beneficial effects achieved by the present invention: The present invention proposes an intrusion-tolerant and fault-tolerant collaborative safety consistency control for a multi-agent spatiotemporal dynamic system under deception attacks and actuator failures; taking into account the spatiotemporal dynamics, infinite-dimensional characteristics, and complex topological structure of the multi-agent system. The present invention uses partial differential equations to model the multi-agent system, and models the system more accurately; for each agent, only the information of the agents adjacent to it is needed to achieve consistency control. Compared with traditional consistency control protocols, this protocol comprehensively considers the intrusion-tolerant and fault-tolerant collaborative safety control of the system in the face of network attacks and actuator failures, and effectively improves the stability and robustness of the system; the intrusion-tolerant and fault-tolerant collaborative safety consistency control of a multi-agent spatiotemporal dynamic system under deception attacks and actuator failures is applicable to any actual 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

[0013] Figure 1 This is a flow chart of the intrusion-tolerant and fault-tolerant collaborative security consistency control method for multi-agent spatiotemporal dynamic systems.

[0014] Figure 2 Communication topology diagram of a multi-agent spatiotemporal dynamic system.

[0015] Figure 3This is a first simulation result analysis diagram of an embodiment of the present invention.

[0016] Figure 4 This is a second simulation result analysis diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0017] The technical solution of the present invention is described in detail below in conjunction with the specific drawings.

[0018] like Figure 1 As shown, an embodiment of the present invention provides a method for intrusion tolerance and fault tolerance collaborative security consistency control of a multi-agent spatiotemporal dynamic system, the method comprising: Step 1: Construct a multi-agent spatiotemporal dynamic system model based on partial differential equation modeling; Step 2: Establish a mathematical model for the actuator failure and deception attack of some agents; Step 3: Introduce the leader-follower consistency condition to obtain the error system; Step 4: Design a security consistency controller that is tolerant to intrusion and fault under deception attacks and execution failures; Step 5: Construct the corresponding Lyapunov function to obtain the conditions for the system to achieve consistency control; Realize intrusion-tolerant and fault-tolerant collaborative security consistency control of multi-agent spatiotemporal dynamic systems under deception attacks and actuator failures.

[0019] Step 1 of this embodiment: construct a multi-agent spatiotemporal dynamic system model based on partial differential equation modeling, and the multi-agent spatiotemporal dynamic system includes Agents, each agent is labeled , the virtual agent leader is labeled 0, and the leader agent model in the multi-agent spatiotemporal dynamic system is: ; in, Represents the state variables of the leader agent, spatial variables , time variable , the initial state of the leader agent is , is a known constant real matrix; The mathematical model of a single agent in a multi-agent spatiotemporal dynamic system is: ; in, Indicates The state variables of an agent, , The initial value of the follower agent is expressed as , Indicates a control input with a fault.

[0020] Step 2 of this embodiment: For the multi-agent spatiotemporal dynamic system under study, considering that some agents may have actuator failures and may be subject to network attacks during network communication, a mathematical model is established to describe attacks and failures.

[0021] The mathematical model of actuator failure in some agents is expressed as: ; in, Indicates The actuator of an agent changes over time The influence factor of the actuator is changed, assuming the influence factor is bounded and satisfies the following inequality , Indicates The control input of an agent.

[0022] The deception attack in this embodiment refers to a form of network attack that aims to weaken the reliability of information transmission by tampering with the data transmitted on the wireless communication network between intelligent agents. Specifically, assuming that the attacker can intercept the data transmitted from the intelligent agent, To Agent Prepare the data signal for transmission over the network and use a nonlinear function The data to be transmitted are transformed into the following expression: ; in, is a nonlinear function that satisfies the following inequality: , It is a nonlinear function Determine the constant matrix.

[0023] In step 3 of this embodiment, for any given initial state, if the following equation relationship holds, the leader-follower multi-agent spatiotemporal dynamic system is said to achieve the desired consistency control: ; definition , then the error system is: Formula 1: ; ; , .

[0024] In step 4 of this embodiment, the following control protocol is designed by comprehensively considering the impact of spoofing attacks and actuator failures: ; in, c is the control gain, The communication weight matrix between agents, if the agent With Agent can communicate with each other, then ,otherwise , For intelligent agents The coupling weight between the leader and When the intelligent agent Can receive information from the leader; when When the intelligent agent Unable to receive leader's message.

[0025] In step 5 of this embodiment, the multi-agent system with spatiotemporal characteristics under deception attack realizes intrusion tolerance and fault tolerance collaborative security consistency control. If there is a matrix The following conditions are established: Formula 2: ; in, ; ; ; ; For the error system, the following Lyapunov function is constructed: ; Taking the derivative of the above formula, we can get : ; Combining the inequality technique with Formula 2, we get tends to zero, and further obtains tends to zero; therefore, the multi-agent partial differential equation system with actuator failure under deception attack achieves intrusion-tolerant and fault-tolerant collaborative security consistency control under the control protocol.

[0026] Select examples for simulation verification; make , Obviously, it is easy to verify The following inequality is satisfied: ; Consider a leader-follower multi-agent spatiotemporal dynamic system consisting of 5 nodes, with a topological structure such as Figure 2 shown.

[0027] Select the following matrices and parameters: , , , , , .

[0028] Using the LMI toolbox in MATLAB, we can obtain This makes Formula 2 valid. Therefore, the multi-agent spatiotemporal dynamic system can achieve consistent control.

[0029] Select the initial state of the agent as: , , , , .

[0030] Figure 3 and Figure 4 Describes the error signal in open-loop and closed-loop situations respectively. Figure 3 It can be seen that the error of the agent that does not use the fault-tolerant consistency protocol cannot converge with the change of time and space, and fails to achieve consistency control. Figure 4 It can be seen that the error of the agent using the fault-tolerant consistency protocol eventually tends to zero as time and space change, achieving consistency control.

[0031] It should be understood that, although each step in the flow chart of each embodiment of the present invention is shown in sequence according to the indication of the arrow, these steps are not necessarily performed in sequence according to the order indicated by the arrow. Unless there is a clear explanation in this article, the execution of these steps does not have a strict order restriction, 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.

[0032] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the program can be stored in a non-volatile computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application 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. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0033] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described 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.

[0034] The above-mentioned embodiments only express several implementation methods of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

[0035] 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 protection scope of the present invention.

Claims

1. A method for coordinated safety consistency control of intrusion-tolerant and fault-tolerant multi-agent spatiotemporal dynamic systems, characterized in that: The method comprises: Step 1: Construct a multi-agent spatiotemporal dynamic system model based on partial differential equation modeling; Step 2: Establish a mathematical model for the actuator failure and deception attack of some agents; Step 3: Introduce the leader-follower consistency condition to obtain the error system; Step 4: Design a security consistency controller that is tolerant to intrusion and fault under deception attacks and execution failures; Step 5: Construct the corresponding Lyapunov function and obtain the conditions for the system to achieve consistency control.

2. The intrusion-tolerant and fault-tolerant collaborative safety consistency control method for a multi-agent spatiotemporal dynamic system according to claim 1 is characterized in that: Step 1: Construct a multi-agent spatiotemporal dynamic system model based on partial differential equation modeling. The multi-agent spatiotemporal dynamic system includes Agents, each agent is labeled , the virtual agent leader is labeled 0, and the leader agent model in the multi-agent spatiotemporal dynamic system is: ； in, Represents the state variables of the leader agent, spatial variables , time variable , the initial state of the leader agent is , is a known constant real matrix; The mathematical model of a single agent in a multi-agent spatiotemporal dynamic system is: ； in, Indicates The state variables of an agent, , The initial value of the follower agent is expressed as , Indicates a control input with a fault.

3. The intrusion-tolerant and fault-tolerant collaborative safety consistency control method for a multi-agent spatiotemporal dynamic system according to claim 1 is characterized in that: The mathematical model of actuator failure in some agents is expressed as: ； in, Indicates The actuator of an agent changes over time Changing actuator impact factors, assuming impact factors is bounded and satisfies the following inequality , Indicates The control input of an agent.

4. The intrusion-tolerant and fault-tolerant collaborative safety consistency control method for a multi-agent spatiotemporal dynamic system according to claim 1 is characterized in that: The spoofing attack is a form of network attack that aims to weaken the reliability of information transmission by tampering with the data transmitted on the wireless communication network between intelligent agents. To Agent Prepare the data signal for transmission over the network and use a nonlinear function The data to be transmitted are transformed into the following expression: ； in, is a nonlinear function that satisfies the following inequality: , It is a nonlinear function Determine the constant matrix.

5. The intrusion-tolerant and fault-tolerant collaborative safety consistency control method for a multi-agent spatiotemporal dynamic system according to claim 1 is characterized in that: In step 3, for any given initial state, if the following equation holds, the leader-follower multi-agent spatiotemporal dynamic system is said to achieve the desired consistency control: ； definition , then the error system is: Formula 1: ; ； , 。 6. The intrusion-tolerant and fault-tolerant collaborative safety consistency control method for a multi-agent spatiotemporal dynamic system according to claim 1 is characterized in that: In step 4, considering the impact of spoofing attacks and actuator failures, the following control protocol is designed: ； in, c is the control gain, The communication weight matrix between agents, if the agent With Agent Communication between ,otherwise , For intelligent agents The coupling weight between the leader and When the intelligent agent Receive the leader's message; when When the intelligent agent Unable to receive leader's message.

7. The intrusion-tolerant and fault-tolerant collaborative safety consistency control method for a multi-agent spatiotemporal dynamic system according to claim 5 is characterized in that: In step 5, the multi-agent system with spatiotemporal characteristics under deception attack realizes intrusion tolerance and fault tolerance collaborative security consistency control. If there is a matrix The following conditions are established: Formula 2: ; in, ; ； ； ； For the error system, the following Lyapunov function is constructed: ； The derivative is : ； Combining the inequality technique with Formula 2, we get tends to zero, and further obtains tends to zero; therefore, the multi-agent partial differential equation system with actuator failure under deception attack achieves intrusion-tolerant and fault-tolerant collaborative security consistency control under the control protocol.

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