Multi-agent system bipartite consensus attack-free event-triggered control method

Abstract

The present application relates to the technical field of intelligent cooperative control, in particular to a kind of multi-agent system two-part consistency attack-free event triggered control method, first construct the mathematical model and output model of linear multi-agent system under signed directed graph, construct the distributed observer of attack-free, design complete distributed dynamic event triggered controller based on linear time-varying feedback, then for signed directed graph, construct the closed-loop dynamic system of error variable, establish the two-part consistency judgment criterion of multi-agent system by constructing Lyapunov functional;The present application does not need to exchange the observer sampling information between adjacent agents, can avoid potential network attack, does not need global information of communication topology, linear time-varying feedback structure is easy to realize, can realize system two-part consistency, greatly reduce control and communication cost, and will not produce Zeno behavior, wide application range.

Description

Technical Field

[0001] This invention relates to the field of intelligent collaborative control technology, specifically a binary consistency control method for multi-agent systems without attack events. Background Technology

[0002] Over the past two decades, the consensus problem of multi-agent systems (MAS) has received widespread attention due to their extensive applications in power grids, the energy internet, and intelligent transportation systems. In conventional MAS cooperative control research, all communication edges between agents represent cooperative relationships. However, in many practical systems such as social networks and economic systems, agents engage in competition in addition to cooperation. For MAS involving both cooperation and competition, the binary consensus problem has been extensively studied, resulting in numerous important research findings. Compared to continuous-time control protocols, event-triggered control methods only require updating the controller at the trigger moment, significantly reducing control costs. Based on this characteristic, researchers have adopted event-triggered control methods to solve the binary consensus problem in MAS and reported a series of meaningful research results in this direction. To extend the trigger time interval, related research has also proposed a dynamic event-triggered control protocol by introducing internal dynamic variables to handle the binary consensus problem in MAS.

[0003] However, most existing observer-based distributed output feedback control protocols require the exchange of observer sampling information between neighboring agents, which exposes multi-agent systems to potential network attack risks. To avoid this problem, some scholars have proposed attack-free distributed control protocols that do not require the exchange of observer sampling information between neighboring agents. However, most existing controllers are designed based on continuous time, requiring the acquisition of global information of the communication topology or requiring the controlled system to meet the constraint of strong detectability. This limits their applicability and makes it difficult to adapt to the actual application requirements of large-scale distributed multi-agent systems in complex network environments. Therefore, in view of the above situation, it is urgent to develop a binary consistency attack-free event-triggered control method for multi-agent systems to overcome the shortcomings in current practical applications. Summary of the Invention

[0004] The purpose of this invention is to provide a binary consistency attack-free event triggering control method for multi-agent systems to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A binary consensus-based attack-free event-triggered control method for multi-agent systems is proposed, applied to a linear multi-agent cooperative control system comprising a leader and multiple followers. The interaction relationships between the agents in the system are represented by a symbolic directed graph topology. The method includes the following steps: S1. Construct the state mathematical model and output model of the linear multi-agent system, and use the local output information of each agent as the input basis for control design. S2. For the multi-agent system constructed in step S1, construct a distributed observer without attack injection channels; The distributed observer only uses the local output information and local control input signal of the corresponding agent to realize state observation, without the need to transmit the relevant sampling information of the observer between adjacent agents; S3. Based on the observation status of the distributed observer described in step S2, design a fully distributed dynamic event triggering controller; The controller only uses the local observation state information of the corresponding agent and the output information of neighboring agents, without needing to obtain global information of the communication topology, and only updates the control input at the preset event trigger time; S4. Construct a closed-loop dynamic system with binary consistency for a multi-agent system. Establish a binary consistency judgment criterion for the system using the Lyapunov stability analysis method, so that the multi-agent system can achieve binary consistency while ensuring that the system does not produce Zeno behavior.

[0006] As a further aspect of the present invention: in step S2, the mathematical model of the distributed observer is: ; In the formula, , These are the outputs of the agent, The relative output of the agent, For the state of the observer, and The coefficient matrix, For the observer gain, make Let Hurwitz matrix be the edge set of the symbolic directed graph. ,if , and If it is a cooperative relationship, then ,if , and If they are in a competitive relationship, then ,otherwise ; The observer gain matrix makes the state matrix of the observation error system a Hurwitz matrix, ensuring that the observation error asymptotically converges to zero.

[0007] As a further aspect of the present invention: In step S3, the dynamic event triggering controller adopts a linear time-varying feedback control law, which is as follows: ; In the formula, , , , and It is a positive number. , , ( The trigger time will be determined later. and The time-varying feedback gain matrix satisfies the parametric Lyapunov equation: ; In the formula, and It is a coefficient matrix.

[0008] As a further aspect of the present invention: the symbolic directed graph is a structurally balanced graph, and the symbolic directed graph contains a directed spanning tree with the leader as the root node.

[0009] As a further aspect of the present invention: in step S1, the coefficient matrix of the state mathematical model of the linear multi-agent system satisfies that the system is completely controllable and completely observable.

[0010] As a further aspect of the present invention: the control input of the leader agent is always zero.

[0011] As a further aspect of the present invention: in step S4, before constructing the error closed-loop dynamic system, the cooperative and competitive interaction relationships of the symbolic directed graph are standardized by a normalized transformation matrix, providing a topological basis for the stability analysis of the closed-loop system.

[0012] As a further aspect of the present invention: in step S4, by limiting the trigger threshold parameter of the dynamic event triggering mechanism, a positive lower bound for time exists between any two adjacent triggering times of the system, thereby preventing the system from generating Zeno behavior; The triggering conditions for the dynamic event triggering controller are as follows: ; In the formula, For trigger function, It is an internal dynamic variable. , , All are positive numbers.

[0013] As a further aspect of the present invention: In step S3, the dynamic event triggering controller adopts a dynamic event triggering mechanism, which updates the control input only at the preset event triggering time, so as to reduce the update frequency of the control input and the communication frequency between the agent.

[0014] Compared with the prior art, the beneficial effects of the present invention are: This invention addresses the real-world scenario in complex network environments where agent state information cannot be measured due to equipment or economic factors, and only agent output information is available. It designs an attack-free distributed observer that eliminates the need for neighboring agents to exchange any observer sampling information, thereby fundamentally eliminating the potential network attack risk caused by observer information interaction and significantly improving the operational security of multi-agent systems. This invention designs an attack-free, fully distributed dynamic event-triggered controller based on linear time-varying feedback. The controller is a fully distributed architecture, which does not require obtaining global information of the communication topology, nor does it require imposing strongly detectable constraints on the controlled system, thus greatly expanding the applicability of the method. At the same time, the controller adopts a linear time-varying feedback structure, which is simple in form, easy to implement in engineering, and adaptable to the application requirements of large-scale distributed multi-agent systems. The dynamic event-triggered control mechanism adopted in this invention only needs to update the controller parameters at the triggering time. Compared with the traditional continuous-time control protocol, it can significantly reduce the frequency of control updates and the communication cost between agents. At the same time, through rigorous theoretical derivation, it is proven that the control method of this invention can ensure the binary consistency of multi-agent systems under symbolic directed graphs and will not produce Zeno behavior. It avoids the controller hardware wear and system instability risk caused by unlimited triggers within a finite time, and has both control performance and engineering practicality. Attached Figure Description

[0015] Figure 1 This is a flowchart of the multi-agent system binary consistency attack-free event triggering control method in an embodiment of the present invention.

[0016] Figure 2 This is a communication topology diagram of the multi-agent system used for simulation verification in this embodiment of the invention; In this diagram, agent 0 represents the leader agent, and agents 1-8 represent the followers agents. Solid lines represent cooperative relationships between agents, while dashed lines represent competitive relationships between agents.

[0017] Figure 3 This is a graph showing the first simulation results of the binary consistency error and observation error of the multi-agent system in this embodiment of the invention. Where (a)-(d) represent the trajectory changes of each state component of the agent.

[0018] Figure 4This is a second simulation result curve of the control parameters of the multi-agent system in an embodiment of the present invention.

[0019] Figure 5 This is a third simulation result curve of the time-varying feedback gain and event triggering interval of the multi-agent system in an embodiment of the present invention; Where (a) and (b) represent the trajectory changes of each control input component of the agent, respectively. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

[0022] Please see Figures 1-5 This invention provides a binary consistency attack-free event-triggered control method for multi-agent systems, applicable to linear multi-agent cooperative control systems involving cooperative and competitive interactions. Binary consistency refers to the cooperative control objective in a multi-agent system where agents within the same set tend to have consistent states, while agents in different sets tend to have opposite states. This method avoids observer information interaction between adjacent agents when only agent output information is available, fundamentally reducing the risk of network attacks. Furthermore, it eliminates the need for global information on the communication topology, achieving binary consistency in multi-agent systems through fully distributed event-triggered control. This significantly reduces control update and communication costs and avoids Zeno behavior (Zeno behavior refers to the phenomenon of an unlimited number of triggers within a finite time, which can cause controller hardware malfunction and is a problem that must be avoided in event-triggered control design). It can be widely applied to multi-agent cooperative control scenarios such as power networks, energy internet, intelligent transportation systems, social networks, and economic systems.

[0023] The multi-agent system binary consensus attack-free event triggering control method of this embodiment includes the following steps: Step 1: Construct the mathematical model and output model of the linear multi-agent system under a symbolic directed graph. This step involves constructing a mathematical model and output model for a linear multi-agent system based on a symbolic directed graph topology containing leaders and followers. Specifically: (1); in, , and They represent the first The state, output, and control input of each agent; the leader is tagged as... And its control input Followers are marked as follows ; It is a positive integer representing the number of agents. , and Let be the coefficient matrix, and It is controllable and observable, a matrix. The real part of the eigenvalues ​​is zero.

[0024] The linear multi-agent system model constructed in this step fully covers symbolic directed graph scenarios involving cooperation and competition, as well as leader-follower topologies, providing a precise mathematical foundation for the controlled objects in subsequent binary consensus control. At the same time, the model only requires the output information of the agents to realize subsequent control design, perfectly adapting to the working conditions in actual engineering where the state information of agents cannot be directly measured due to factors such as equipment and cost, thus expanding the applicability of the method.

[0025] Step 2: Construct a mathematical model for an attack-free distributed observer. For the multi-agent system constructed in step 1, to avoid the potential network attack risk caused by the exchange of observer sampling information between neighboring agents, a mathematical model of an attack-free distributed observer is constructed, specifically as follows: (2); in, , These are the outputs of the agent, The relative output of the agent, For the state of the observer, and The coefficient matrix, For the observer gain, make Let Hurwitz matrix be the edge set of the symbolic directed graph. ,if , and If it is a cooperative relationship, then ,if , and If they are in a competitive relationship, then ,otherwise .

[0026] The distributed observer constructed in this step relies solely on the output information and control input of the local agent to achieve state observation. It eliminates the need to exchange any observer sampling information between neighboring agents, thus fundamentally eliminating the network attack surface caused by observer information interaction and achieving an attack-free observer design. Furthermore, the observer only needs to be configured with a gain matrix to... Using the Hurwitz matrix guarantees asymptotic convergence of observation errors. The design process is simple, the engineering feasibility is strong, and it does not rely on global information of the communication topology, making it suitable for distributed collaborative control applications.

[0027] Step 3: Design an attack-free, fully distributed dynamic event-triggered controller based on linear time-varying feedback. Based on the attack-free distributed observer from step 2, an attack-free and fully distributed dynamic event-triggered controller based on linear time-varying feedback is designed. The specific control law is as follows: (3); in, , , and The following is a parametric Lyapunov equation. The solution; , , and It is a positive number. Triggering time ( )Depend on Sure; ; For trigger function, It is an internal dynamic variable. , , All are positive numbers.

[0028] The dynamic event-triggered controller designed in this step adopts a linear time-varying feedback structure, with a simple control law form, clear parameter tuning process, and low engineering implementation difficulty. Furthermore, the controller features a fully distributed architecture, requiring only the observation state information of the local agent and the output information of neighboring agents, without needing global information about the communication topology or the exchange of observer sampling information between neighboring agents. This further mitigates the risk of network attacks and adapts to the application requirements of large-scale distributed multi-agent systems. In addition, updating the control input based on the dynamic event triggering mechanism updates the controller parameters only at the trigger moment. Compared to traditional continuous-time control protocols, this significantly reduces the frequency of control updates and the communication cost between agents. Moreover, it can adapt to different control accuracies and communication resource constraints by adjusting the trigger parameters, offering high application flexibility.

[0029] Step 4: Definition of structural properties and canonical transformation of symbolic directed graphs picture This is a structural balance diagram, meaning there are two subsets. and ,satisfy and When intelligent agents and Belonging to the same set , If they are in a cooperative relationship, then they are in a cooperative relationship; when and Belonging to different sets , If they are in a competitive relationship, then they are competitors; let's call them... For the image The Laplace matrix, where , If the leader belongs to And the diagram Given a directed spanning tree rooted at the leader, the Laplace matrix is... It has the following form: ; in, , Define the canonical transformation matrix. If here ,but ;like ,but Obviously, and All are non-singular matrices.

[0030] This step addresses the structural balance characteristics of symbolic directed graphs by standardizing the cooperation-competition relationship through a normalized transformation matrix. This provides a topological theoretical foundation for the subsequent construction and stability analysis of the closed-loop error system, ensuring the rigor of the theoretical derivation.

[0031] Step 5: Construct a closed-loop dynamic system for the error variable, build a Lyapunov functional, and establish a bipartite consistency criterion. By utilizing a non-attack-free observer based on linear time-varying feedback and a fully distributed dynamic event-triggered controller, a multi-agent system can achieve binary consistency without exhibiting Zeno behavior. The specific derivation process is as follows: definition and From (1), we can obtain: (4); in, .

[0032] make and According to (2), we can obtain: (5); Furthermore, from (4) and (5), it can be deduced that: (6); For systems (5) and (6), the following Lyapunov functionals are constructed: (7); in, It is a constant. satisfy , It satisfies the following Lyapunov matrix equations: ; From trigger condition (3), we can obtain Therefore, we have: (8); Further from (8), we can obtain: (9); This indicates that for all All have Established.

[0033] Let and represent the minimum and maximum eigenvalues ​​of the corresponding real symmetric matrix, respectively. For ease of proof, let . Based on the properties of the parametric Lyapunov equation, we can obtain from equation (6): (10); in, , It is a constant.

[0034] Using Young's inequalities and We can obtain: (11); Based on the properties of the parametric Lyapunov equation, we can derive: (12); according to From equation (12), we can obtain: (13); in, It is a positive number.

[0035] Substituting equations (11) and (13) into equation (10), we get: (14); From (6) and (7), we can deduce that: (15); Obviously: (16); in, It is a positive number.

[0036] based on And (12), we can obtain: (17); in, and All are normal numbers.

[0037] From equations (15)-(17), we can obtain: (18); Based on the triggering condition and (6), we can obtain: (19); According to (12), we have: (20); in, , .

[0038] Combining (19) and (20), we can obtain: (twenty one); in, , .

[0039] Therefore, from (14), (18) and (21), we can obtain: (twenty two); in, , , as well as ; Select a sufficiently small , and Make Established. (Select) To meet Therefore, due to Decreasing over time and It is obvious that Makes any ,have , , , and Established; Combined , and It can be deduced that: (twenty three); definition: (twenty four); Therefore, from (23), we can obtain: (25); According to equation (7), we can obtain: (26); in, It is a constant.

[0040] Based on equations (25) and (26), we obtain: (27); This means and Established. That is: (28); This means that the multi-agent system (1) under a symbolic directed graph achieves binary consensus. At the same time, it can be proven through rigorous derivation that there is a positive lower bound between any two adjacent triggering times, and the system will not exhibit Zeno behavior.

[0041] This step fully preserves all the stability derivation formulas and processes in the disclosure document. By constructing a Lyapunov functional adapted to the closed-loop error system, and combining linear system stability theory and event triggering conditions, it rigorously proves that the attack-free distributed observer and fully distributed dynamic event-triggered controller designed in this implementation can make the closed-loop error system asymptotically stable, that is, the multi-agent system under a signed directed graph can achieve binary consensus. At the same time, through rigorous theoretical derivation, it is proved that the system will not exhibit Zeno behavior, ensuring the feasibility of the control scheme in practical engineering applications, avoiding the controller hardware wear and system instability risk caused by an infinite number of triggers within a finite time, and improving the theoretical completeness of the control method.

[0042] Step 6: Simulation Verification To further verify the effectiveness and engineering applicability of the control method proposed in this embodiment, a dual-mass spring system was selected as the controlled object for simulation verification, as detailed below: Consider a linear multi-agent system consisting of nine bimask springs, where the network topology is as follows: Figure 2 As shown. For a dual-mass spring system, There are two mass blocks; , is the spring constant; and represents the displacement and input of the two masses. From... Figure 2 In the diagram, it can be clearly seen that the network topology is structurally balanced, where solid (dashed) lines represent cooperative (competitive) relationships, and the weight of each solid (dashed) line is set to 1 (-1). That is, and .

[0043] definition , , and It is the first Displacement and input of a dual-mass spring system , , .

[0044] The two-mass spring system can then be modeled using the system model from step 1, where: , , ; in, kg, kg, N / m, N / m.

[0045] Choose from the following Make It is a Hurwitz matrix: ; Let the parameters in controller equation (3) be , The parameters for the corresponding event triggering conditions in the controller are: , , , By utilizing a non-attack-free observer based on linear time-varying feedback and a fully distributed dynamic event-triggered controller, multi-agent systems can achieve binary consensus. Figure 3 (a)-(d) represent the trajectory changes of each state component of the agent, respectively. Figure 4 The trigger interval for each agent is given. Figure 5 (a)-(b) represent the trajectory changes of each control input component of the agent, respectively. The simulation results intuitively verify the effectiveness of the control method proposed in this embodiment.

[0046] It should be noted that, in this invention, although the specification describes the embodiments, not every embodiment contains only one independent technical solution. This way of describing the specification is only for clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A binary consensus attack-free event-triggered control method for a multi-agent system, applied to a linear multi-agent cooperative control system comprising a leader and multiple followers, wherein the interaction relationships between agents in the system are represented by a symbolic directed graph topology, characterized in that... Includes the following steps: S1. Construct the state mathematical model and output model of the linear multi-agent system, and use the local output information of each agent as the input basis for control design. S2. For the multi-agent system constructed in step S1, construct a distributed observer without attack injection channels; The distributed observer only uses the local output information and local control input signal of the corresponding agent to realize state observation, without the need to transmit the relevant sampling information of the observer between adjacent agents; S3. Based on the observation status of the distributed observer described in step S2, design a fully distributed dynamic event triggering controller; The controller only uses the local observation state information of the corresponding agent and the output information of neighboring agents, without needing to obtain global information of the communication topology, and only updates the control input at the preset event trigger time; S4. Construct a dynamic error closed-loop system for binary consistency in a multi-agent system. Establish a binary consistency judgment criterion for the system using the Lyapunov stability analysis method, so that the multi-agent system can achieve binary consistency while ensuring that the system does not produce Zeno behavior.

2. The multi-agent system binary consistency attack-free event triggering control method according to claim 1, characterized in that, In step S2, the mathematical model of the distributed observer is: ； In the formula, , These are the outputs of the agent, The relative output of the agent, For the state of the observer, It is a positive integer representing the number of agents. and The coefficient matrix, For the observer gain, make Let Hurwitz matrix be the edge set of the symbolic directed graph. ,if , and If it is a cooperative relationship, then ,if , and If they are in a competitive relationship, then ,otherwise ; The observer gain matrix makes the state matrix of the observation error system a Hurwitz matrix, ensuring that the observation error asymptotically converges to zero.

3. The multi-agent system binary consistency attack-free event triggering control method according to claim 1, characterized in that, In step S3, the dynamic event triggering controller adopts a linear time-varying feedback control law, which is as follows: ； In the formula, , , , and It is a positive number. , , ( The trigger time is determined later. and The time-varying feedback gain matrix satisfies the parametric Lyapunov equation: ； In the formula, and It is a coefficient matrix.

4. The multi-agent system binary consistency attack-free event triggering control method according to claim 1, characterized in that, The symbolic directed graph is a structurally balanced graph, and the symbolic directed graph contains a directed spanning tree with the leader as the root node.

5. The multi-agent system binary consistency attack-free event triggering control method according to claim 1, characterized in that, In step S1, the coefficient matrix of the state mathematical model of the linear multi-agent system satisfies that the system is completely controllable and completely observable.

6. The multi-agent system binary consistency attack-free event triggering control method according to claim 1, characterized in that, The control input to the leader agent is always zero.

7. The multi-agent system binary consistency attack-free event triggering control method according to claim 1, characterized in that, In step S4, before constructing the error closed-loop dynamic system, the cooperative and competitive interaction relationships of the symbolic directed graph are standardized by a normalized transformation matrix, providing a topological basis for the stability analysis of the closed-loop system.

8. The multi-agent system binary consistency attack-free event triggering control method according to claim 1, characterized in that, In step S4, by limiting the trigger threshold parameter of the dynamic event triggering mechanism, a positive lower bound on time exists between any two adjacent triggering times of the system, thereby preventing the system from exhibiting Zeno behavior. The triggering conditions for the dynamic event triggering controller are as follows: In the formula, For trigger function, It is an internal dynamic variable. , , All are positive numbers.

9. The multi-agent system binary consistency attack-free event triggering control method according to claim 1, characterized in that, In step S3, the dynamic event triggering controller adopts a dynamic event triggering mechanism, which updates the control input only at the preset event triggering time, so as to reduce the frequency of control input updates and the frequency of communication between the agent.

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