Multi-agent security optimization tracking control method based on cross-layer coupling event triggering

Abstract

The application discloses a kind of multi-agent security optimization tracking control methods based on cross-layer coupling event triggering, establish the communication topology model of multi-agent system and the system model influenced by unknown external interference and compound false data injection attack;Respectively build the communication layer event triggering condition for neighborhood information interaction and the actuator update-oriented execution layer event triggering condition;According to the execution layer triggering condition, update control input on demand, according to the communication layer triggering condition, neighborhood information interaction is carried out on demand, and distributed tracking control of follower to leader is realized;A composite control strategy is constructed by combining backstepping method and reinforcement learning, which includes a feedforward compensator based on disturbance observer and a feedback optimization controller based on attack compensation;The application can suppress uncertainty under the condition of compound false data injection attack and external interference, reduce communication occupation and actuator update overhead, and ensure the stability of closed-loop system and the performance of leader-follower consistency tracking.

Description

Technical Field

[0001] This invention relates to the cooperative control of multi-agent systems, specifically to a multi-agent safety optimization tracking control method based on cross-layer coupling event triggering. Background Technology

[0002] Multi-agent systems (MAS) consist of multiple independent agents with autonomous perception, intelligent decision-making, and execution capabilities, forming a collaborative system through a communication network. They enable information sharing, task decomposition, collaborative planning, and distributed control, exhibiting significant scalability and system resilience, and represent an important evolutionary direction for intelligent control and new equipment systems. Compared to single-agent systems, MAS can achieve collaborative compensation and functional reconfiguration in situations such as sudden changes in task scenarios or partial equipment failures, demonstrating higher environmental adaptability and task reliability. With the deep integration of technologies such as artificial intelligence, network communication, and embedded computing, the enhancement of MAS collaborative and intelligent capabilities has become a crucial technical support for the intelligent upgrading of equipment systems and the autonomous control of complex engineering systems.

[0003] Multi-agent systems have been widely applied in fields such as intelligent manufacturing multi-machine collaborative scheduling, unmanned swarm formation and collaborative reconnaissance, smart grids and energy management, vehicle-road cooperative transportation systems, and emergency disaster search and rescue. However, because they rely on open communication networks for information exchange, system operation is susceptible to bandwidth bottlenecks, latency fluctuations, data packet loss, and external environmental disturbances. Meanwhile, cybersecurity threats are becoming increasingly severe, with attack methods becoming more intelligent and covert. Multiple attack forms can simultaneously affect the system; for example, injecting false data to manipulate collaborative information, denial-of-service attacks to disrupt communication links, and electromagnetic interference to damage sensor circuits can lead to amplified collaborative decision-making biases, formation disruption, and even system-wide paralysis.

[0004] On the other hand, in traditional fixed-period communication architectures, each agent needs to continuously sample and broadcast its state at high frequency. Even slight state changes result in repeated data transmission, leading to significant communication redundancy. As the number of agents increases, this intensive communication causes bandwidth congestion and accumulated latency, exacerbating computational and energy consumption, thus significantly weakening cooperative control performance and scalability. While existing event-triggered control strategies can save resources by communicating on demand based on state errors, most only employ a single trigger condition, making it difficult to simultaneously address multiple sources of performance degradation. In complex adversarial environments where attacks and interference coexist, a single trigger mechanism is prone to untimely or excessive triggering, making it difficult to balance system security, robustness, and communication efficiency. Summary of the Invention

[0005] Purpose of the invention: To address the above-mentioned shortcomings, this invention provides a stable, reliable, and efficient event-triggered multi-agent safety optimization tracking control method based on cross-layer coupled event triggering.

[0006] Technical Solution: To solve the above problems, the present invention provides a multi-agent safety optimization tracking control method based on cross-layer coupling event triggering, comprising the following steps:

[0007] (1) Establish a communication topology model for a multi-agent system, wherein the multi-agent system includes a leader and several followers; the communication topology model includes information transmission between the leader and followers and information interaction between followers; and construct a mathematical model of the multi-agent system considering unknown external interference.

[0008] (2) Based on the communication topology model of a multi-agent system, construct the communication layer event triggering conditions for communication between agents; and construct the execution layer event triggering conditions for updating the agent's own actuator;

[0009] (3) Construct an interference observer to estimate and compensate for unknown external interference and attacks, and construct a feedforward controller based on the interference observer, and construct a feedback controller for the agent using the backstepping control method;

[0010] (4) Determine whether the agent updates the actuator based on the execution layer event triggering condition, and track the follower that updates the actuator through the feedback controller. Determine whether the agents trigger communication based on the communication layer event triggering condition, and track the follower that triggers communication through the feedforward controller or feedback controller.

[0011] Furthermore, the event triggering condition of the communication layer is as follows:

[0012] ;

[0013] in, Indicates the triggering time of the communication layer event. Indicates the first One follower The event triggering variable at a given moment. Indicates the first One follower The output signal at time, Indicates the first One follower The output signal at time, , , Represents design constants. This indicates the leader's output signal;

[0014] The execution layer event triggering condition is as follows:

[0015] ;

[0016] ;

[0017] ;

[0018] in, Indicates the triggering time of the execution layer event. Indicates the first One follower Input signal at time, yes Feedback control law at any moment yes Feedback control law at any moment This refers to the consistency error of a multi-agent system in the absence of attacks. , , , , Represents design constants. , , Indicates an intermediate variable.

[0019] Furthermore, the mathematical model of the constructed multi-agent system is as follows:

[0020] ;

[0021] in, Indicates the first The positional status of each follower Indicates the first The speed state of a follower This indicates the positional uncertainty in the system. This represents the speed uncertainty in the system. Indicates system gain. It is composite interference. Indicates the first The output signal of a follower Indicates the first The control input signal of a follower.

[0022] Furthermore, the feedforward controller is:

[0023] ;

[0024] in, Follower of the feedforward controller output The control input signal, This represents the observed estimate of unknown external disturbances.

[0025] Furthermore, the interference observer is:

[0026] ;

[0027] ;

[0028] in, Indicates the first The first follower and the first The connection between followers This indicates the total number of followers. , Represents auxiliary variables. The degree matrix represents the first The degree of association of a follower Indicates the first The connection between a follower and a leader This represents an estimate of the ideal weight vector. Represents a basis function vector. This represents the error in the second step of the backstepping control method.

[0029] Furthermore, the feedback controller is:

[0030] ;

[0031] ;

[0032] Among them, the backstep control method is used to estimate the uncertain filter variables. Triggering variables obtained based on communication layer event triggering conditions , Indicates the presence of trigger variables Feedback control law, , It is a design constant. Indicates the presence of trigger variables The error, This represents the weight vector of the recognition neural network. The basis functions of the recognition neural network are represented. This represents the weight vector of the evaluation neural network. This indicates that the evaluation neural network contains trigger variables. basis functions, Indicates the presence of trigger variables Error variables, This represents the estimated value of the optimal virtual control signal.

[0033] Furthermore, considering the optimal virtual control law for the event-triggered mechanism, it is:

[0034] ;

[0035] in, It is a design constant. For consistency errors based on event-triggered mechanisms, and This represents the weight vector of the recognition neural network. This represents the weight vector of the evaluation neural network. , and It contains trigger variables The basis functions.

[0036] Furthermore, by employing an identification neural network and a judgment neural network to estimate the ideal evaluation weights of the optimal cost function, the adaptive law of the identification neural network is obtained as follows:

[0037] ;

[0038] ;

[0039] in, , , and Design constant;

[0040] The evaluation law for the weight update of a neural network is as follows:

[0041] ;

[0042] in, For learning rate, Indicates intermediate variables. It is the number of nodes in the neural network. Indicates the first Next storage time Indicate intermediate variables In the The variable value at the next storage time. express In the The variable value for the storage time.

[0043] The present invention employs a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above method.

[0044] The present invention employs a computer-readable storage medium on which a computer program is stored, and when the computer program is executed by a processor, it implements the steps of the above method.

[0045] Beneficial effects: Compared with the prior art, the significant advantages of this invention are: it sets up two types of event triggering mechanisms. The communication layer is used to adjust the intermittent communication between agents to reduce the communication bandwidth occupation; the execution layer is used to adjust the update frequency of the actuators inside a single agent to reduce the amount of computation and improve the utilization rate of data transmission resources. It can ensure the global stability of the system and the leader-follower consistency control performance while significantly reducing communication and data transmission overhead.

[0046] To address the potential for complex spoofing attacks and complex interference to the system, an attack compensation mechanism is designed to suppress the adverse effects of the attacks. A distributed interference observer is also constructed to estimate and compensate for external interference, thereby improving the security and reliability of the system under malicious attacks. Furthermore, it has been rigorously proven that the system does not exhibit Zeno behavior. Attached Figure Description

[0047] Figure 1 This is a flowchart illustrating the tracking control method of the present invention. Detailed Implementation

[0048] like Figure 1 As shown in the figure, this embodiment presents a multi-agent safety optimization tracking and control method based on cross-layer coupling event triggering, which includes the following steps:

[0049] (1) Establish a communication topology model for a multi-agent system, wherein the multi-agent system includes a leader and several followers; the communication topology model includes information transmission between the leader and followers and information interaction between followers; and construct a mathematical model of the multi-agent system considering unknown external interference.

[0050] (2) Based on the communication topology model of a multi-agent system, construct the communication layer event triggering conditions for communication between agents; and construct the execution layer event triggering conditions for updating the agent's own actuator;

[0051] (3) Construct an interference observer to estimate and compensate for unknown external interference and attacks, and construct a feedforward controller based on the interference observer, and construct a feedback controller for the agent using the backstepping control method;

[0052] (4) Determine whether the agent updates the actuator based on the execution layer event triggering condition, and track the follower that updates the actuator through the feedback controller. Determine whether the agents trigger communication based on the communication layer event triggering condition, and track the follower that triggers communication through the feedforward controller or feedback controller.

[0053] This embodiment's control method addresses complex network security threats and external disturbances. Based on a dual-event triggering mechanism, it employs distributed adaptive anti-attack and anti-interference collaborative control to solve the problem of decreased stability and consistency performance in multi-agent systems due to limited communication resources under the combined effects of spoofed data injection attacks and lumped interference. It ensures global system stability and leader-follower consistency control performance while significantly reducing communication and data transmission overhead. Specifically, this embodiment employs the following technical solutions: First, graph theory tools are introduced to establish the information interaction topology between agents, providing a theoretical basis for distributed control strategy design. Second, a leader-follower dynamics model is constructed to clarify collaborative behavior constraints and state tracking objectives. Then, to address system performance degradation caused by complex spoofed data injection attacks and lumped external interference, an anti-attack compensation mechanism and a distributed interference observer are designed to achieve dynamic compensation and robust suppression. Finally, a dual-event triggering mechanism is proposed, constructing complementary triggering conditions based on control error and attack estimation information to update communication and control commands on demand, thereby effectively reducing network load and computational redundancy. Finally, by combining backstepping control and adaptive control methods, a cooperative safety control law that can be implemented in a distributed manner is formed to ensure that the system can maintain stable tracking and cooperative consistency capabilities even in complex adversarial environments. The design process of the control method is described in detail below.

[0054] Step 1, introduce a directed graph To represent the information exchange between various intelligent agents, where Represents the set of agent nodes. Denotes the set of edges. Let represent the adjacency matrix, and with respect to the weights. If the intelligent agent Able to direct intelligent agents Send signal, ,otherwise Subsequently, the degree matrix is ​​defined as follows: The Laplace matrix is ,in , representing the degree matrix of the first The degree of association of a follower.

[0055] Define augmented graph ,in ,and , This represents the leader node. Similarly, if the leader node... Able to direct intelligent agents Sending a signal, then ,otherwise .

[0056] Augmented graph For a connected graph, it contains nodes A spanning tree structure with root, where nodes The information can be transmitted along the directed path to all other nodes in the graph, while ensuring that each following node sends the information to at least one of its neighbors.

[0057] Step 2: Establish a multi-agent system model considering complex interference. This model consists of... It consists of one follower and one leader, whose first... The dynamic equations for each follower are expressed as follows:

[0058] (1);

[0059] in, , Indicates the first The positional status of each follower Indicates the first The speed state of a follower Indicates system gain. and Indicates the uncertainties in the system. Indicates terms with uncertain positions. Represents the velocity uncertainty term. It is composite interference. and They represent the first The leader's output signal is the input and output signal of each follower. .

[0060] Assumption 2: Leader outputs signals and its first derivative and second derivative All are bounded, meaning there exists a positive constant. , so that: .

[0061] Assumption 3: Leader Node The information transmission channel is unaffected by composite fake data injection attacks, and the attack signal satisfies the global Lipschitz condition.

[0062] Assumption 4: Unknown lumped interference signal and its first derivative Both are bounded.

[0063] Lemma 1: For any continuous and unknown nonlinear function Radial basis function neural networks can effectively approximate it, and its expression is as follows:

[0064] ;

[0065] in, This represents the approximation error, and , It is a constant, a basis function The expression is , It is an ideal weight vector.

[0066] The optimal solution for the weight vector is:

[0067] ;

[0068] in, Represents the number of nodes in the neural network. This is the weight vector. Next, let the basis functions take the following Gaussian function form:

[0069] ;

[0070] in, and Indicates design parameters.

[0071] Step 3: To reduce the communication load of the multi-agent system during the cooperative control process and to reduce the frequent actions of the agent actuators, thereby improving resource utilization efficiency and system feasibility, the following two types of event triggering mechanisms were designed:

[0072] Communication layer: For multi-agent systems, the communication layer is the first... Taking an intelligent agent as the research object, it is assumed that it has neighboring intelligent agents during its operation. For intelligent agents Receive from neighboring intelligent agents The information is designed such that the event triggering conditions for the communication layer are:

[0073] (2)

[0074] In the formula, Indicates the triggering time of the communication layer event. Indicates the first One follower The event triggering variable at a given moment. Indicates the first One follower The output signal at time, Indicates the first One follower The output signal at time, , and This represents the design constant.

[0075] Execution Layer: For each individual agent in a multi-agent system, frequent use of the actuator can easily lead to its aging. Therefore, for the first... For each intelligent agent, to reduce the frequency of actuator actions and extend their lifespan, the execution layer event triggering conditions are designed as follows:

[0076] (3);

[0077] In the formula,

[0078]

[0079]

[0080] in, Indicates the triggering time of the execution layer event. Indicates the first One follower Input signal at time, yes Feedback control law at any moment yes Feedback control law at any moment This refers to the consistency error of a multi-agent system in the absence of attacks. , , , and Represents design constants. , , This represents an intermediate variable used to simplify the expression and has no actual meaning.

[0081] Step 4: In a multi-agent system, agents need to exchange state information and control commands through a communication network to achieve coordination, task cooperation, and distributed decision-making. This process typically involves real-time interaction of key data such as position, velocity, state estimates, and control inputs. However, this reliance on the communication network also exposes the system to potential security threats. Especially in open network environments, malicious attackers can inject false data into the transmission link, tampering with, forging, or maliciously interfering with communication data, causing agents to receive distorted system states or incorrect control information. Such attacks will disrupt the consistency error convergence characteristics, causing deviations in cooperative behavior, performance degradation, and in severe cases, even leading to global system failure or instability.

[0082] Because multi-agent cooperative control is extremely sensitive to data accuracy and consistency, false data will spread rapidly along the interaction topology, causing error amplification and distortion of control decisions. Therefore, to ensure the stable operation of the system in complex adversarial environments, it is urgent to design a distributed security control mechanism with the ability to resist false data injection, thereby improving the reliability and resilience of the system.

[0083] Based on the above security risk analysis, the mechanism by which attacks affect the communication process can be further abstracted. Attackers manipulate specific communication links, and in the... The first agent directs to the first When an agent transmits state information, it injects a composite spurious signal, causing the first agent to... The interaction data received by the agent generates an invalid bias. In this case, its received information model can be described as:

[0084] (4);

[0085] in, and These are attack functions, and all are bounded. Next, the consensus error of a multi-agent system without attacks is defined as follows:

[0086] (5);

[0087] Therefore, combining equations (4) and (5), the following consistency error under the influence of a composite fake data injection attack can be derived:

[0088] (6);

[0089] in .

[0090] To facilitate subsequent stability analysis of the closed-loop system, the following lemma is given:

[0091] Lemma 2: For consistency errors Consistency error based on event-triggered mechanism ,in The following relationship holds:

[0092] ;

[0093] in , ,and These are the constants to be designed.

[0094] Proof: Based on the event triggering conditions of the communication layer, within the time interval Within this context, the following relationship holds:

[0095] ;

[0096] Furthermore, according to assumption 3, the following inequality holds:

[0097] ;

[0098] Based on the above analysis, we have

[0099]

[0100] Lemma 2 is now proven.

[0101] Step 5: To address lumped disturbances, a distributed disturbance observer is designed to accurately estimate and compensate for unknown lumped disturbances, thereby improving the overall control performance of the multi-agent system. The specific design concept is as follows.

[0102] To facilitate the design of the subsequent control system, before constructing the distributed disturbance observer, a radial basis function neural network given in Lemma 1 is first introduced to approximate the modeling uncertainties in the multi-agent system and compensate for the unknown nonlinear terms introduced by the subsequent distributed disturbance observer. Its specific approximation form is as follows:

[0103] (7);

[0104] in , Indicates the constant to be designed. It is an ideal weight vector. Represents a basis function vector. It is the approximation error.

[0105] make Based on equation (7), the distributed interference observer is designed as follows:

[0106] (8);

[0107] (9);

[0108] In the formula It is a new auxiliary variable that has been introduced. and They are and The estimated value, This is the second step error, the specific expression of which will be given later. Following this, the following relationship can be derived:

[0109] (10);

[0110] In the formula and This is the estimation error. Then, regarding the weights... Design the following adaptive law with parameters:

[0111] (11);

[0112] in and These are the constants to be designed.

[0113] Step 6: Design of a distributed adaptive security control strategy based on a dual-event triggering mechanism.

[0114] First, a backstepping control method is adopted to construct an event-triggered robust cooperative controller for a multi-agent system through two-step iteration.

[0115] Step 1: To enhance the robustness of multi-agent systems under attack conditions, the following optimal performance index function containing attack information is defined:

[0116] (12);

[0117] In the formula For the constant to be designed, This represents the optimal virtual control signal. For attack function The known upper bound of .

[0118] Taking the time derivative of both sides of equation (12) yields the following Hamilton-Jacobi-Bellman equation:

[0119] (13);

[0120] in Then, by solving... The following optimal virtual control law is obtained:

[0121] (14);

[0122] Based on the communication layer event triggering conditions and equation (14), the following optimal virtual control law based on the event triggering mechanism is obtained:

[0123] (15);

[0124] In the formula and Indicates the presence of trigger variables The partial derivatives of the optimal virtual control law and the optimal performance index function. Further, the Hamilton-Jacobi-Bellman equation based on the event-triggered mechanism can be obtained as follows:

[0125] (16);

[0126] To achieve consistent control performance, variables are introduced. Its specific definition is as follows:

[0127] (17);

[0128] in These are the constants to be designed.

[0129] According to equation (17), the following relationship can be derived:

[0130] (18);

[0131] Then, substituting equation (18) into equation (14), we can obtain:

[0132] (19);

[0133] in ,and Because the optimal virtual control signal (19) contains an unknown nonlinear function. , and We introduce a radial basis function neural network to approximate them, as shown in the following expression:

[0134] ;

[0135] In the formula , and Represents the ideal weight vector. , and Denotes basis functions. , and Let represent the approximation error, and for each approximation error, the following conditions are satisfied: , and ,in , and It is a constant.

[0136] Based on the above analysis, although a radial basis function neural network has been introduced, the ideal weights remain unknown, preventing the existing virtual controller from being directly implemented. Therefore, an identification neural network and an evaluation neural network are introduced to perform online estimation and performance evaluation of the unknown weights, thereby constructing the following practically applicable control strategy:

[0137] (20);

[0138] (twenty one);

[0139] in and This represents the weight vector of the recognition neural network. This represents the weight vector of the evaluation neural network. and They are and The estimated value. Then, combining equations (15) and (21), the optimal virtual control law considering the event triggering mechanism is designed as follows:

[0140] (twenty two);

[0141] in , and It contains trigger variables The basis functions. Then, the adaptive law of the recognition neural network is designed:

[0142] (twenty three);

[0143] (twenty four);

[0144] In the formula , , and This represents the constant to be designed.

[0145] To derive the weight update law for the evaluation neural network, combining equations (16) and (22), the Hamilton-Jacobi-Bellman equation based on the event-triggered mechanism is constructed as follows:

[0146] (25);

[0147] In the formula This represents the Bellman residual. Next, to derive the weight update rate, the objective function is defined as... Based on gradient descent, the following law for evaluating the weight update of a neural network can be derived:

[0148] (26);

[0149] In the formula , It's the learning rate. It is the number of nodes in the neural network. Indicates the first Next storage time and They represent and In the The value at the current time.

[0150] Then, construct the following Lyapunov function:

[0151] (27);

[0152] in , and Indicates the estimation error. Represents a constant.

[0153] For the selected Lyapunov function By finding the time derivative and combining it with Young's inequality and Lemma 2, we can obtain the following inequality:

[0154] (28);

[0155] In the formula:

[0156] ;

[0157] ;

[0158]

[0159] ;

[0160] in, and It is a positive number. yes The smallest eigenvalue, and , yes The upper bound, and .

[0161] Step 2: For the variables given in Step 1 It is mainly obtained from the following first-order filters:

[0162] (29);

[0163] in This represents the constant to be designed.

[0164] For error and Differentiation yields:

[0165] (30);

[0166] (31);

[0167] In the formula And assume .

[0168] Following this, after introducing the execution layer event triggering conditions, the control input signals can be organized to obtain:

[0169] (32);

[0170] In the formula , and It is a bounded time-varying parameter.

[0171] Discrete control signals are reconstructed into continuous signals through a zero-order hold.

[0172] For the second step, the optimal performance index function is defined as follows:

[0173] (33);

[0174] In the formula For the constant to be designed, This represents the optimal feedback control signal.

[0175] Taking the time derivative of both sides of equation (33) yields the following Hamilton-Jacobi-Bellman equation:

[0176] (34);

[0177] In the formula Then, by solving... The following optimal feedback control law is obtained:

[0178] (35);

[0179] Based on the above analysis, the following event-triggered optimal feedback control law can be derived:

[0180] (36);

[0181] In the formula and Indicates the presence of trigger variables The partial derivatives of the optimal feedback control law and the optimal performance index function. And for... Its trigger expression is as follows:

[0182] (37);

[0183] In the formula It is the triggering time of the communication layer event triggering condition. , and This represents the constant to be designed.

[0184] Based on equations (34) and (37), the following Hamilton-Jacobi-Bellman equation based on the event-triggered mechanism can be derived:

[0185] (38);

[0186] To achieve consistent control performance, variables are introduced. Its specific definition is as follows:

[0187] (39);

[0188] in These are the constants to be designed.

[0189] According to equation (39), the following relationship can be derived:

[0190] (40);

[0191] Then, substituting equation (40) into equation (35), we can obtain:

[0192] (41);

[0193] In the formula Because the optimal feedback control signal (41) contains an unknown nonlinear function. and We introduce a radial basis function neural network to approximate them, as shown in the following expression:

[0194]

[0195] In the formula and Represents the ideal weight vector. and Denotes basis functions. and Let represent the approximation error, and for each approximation error, the following conditions are satisfied: and ,in and It is a constant.

[0196] Based on the above analysis, although a radial basis function neural network has been introduced, the ideal weights remain unknown, preventing the existing feedback controller from being directly implemented. Therefore, an identification neural network and an evaluation neural network are introduced to perform online estimation and performance evaluation of the unknown weights, thereby constructing the following practically applicable control strategy:

[0197] (42);

[0198] (43);

[0199] in This represents the weight vector of the recognition neural network. This represents the weight vector of the evaluation neural network. yes The estimated value. Then, combining equations (37) and (43), the optimal feedback control law considering the event triggering mechanism is designed as follows:

[0200] (44);

[0201] In the formula ,and Indicates the presence of trigger variables The basis functions are then derived. Based on the design of the distributed interference observer, the following feedforward controller is given:

[0202] (45);

[0203] Next, the following neural network weight update law is designed:

[0204] (46);

[0205] (47);

[0206] in, It is the Bellman residual, and

[0207]

[0208] and Representing variables respectively and In the Store the value at that moment. Indicates the learning rate. and These are the constants to be designed.

[0209] Construct the following Lyapunov function:

[0210]

[0211] in These are the constants to be designed. and This represents the estimation error. Then, combining Young's inequality and Lemma 2, we can... After differentiation and scaling, we can obtain:

[0212] (48);

[0213] In the formula:

[0214] ;

[0215] yes The upper realm,

[0216] ;

[0217] It is a constant. yes The smallest eigenvalue, where and ,and yes The upper boundary.

[0218] Based on the above analysis and discussion, the following theorem is derived:

[0219] Theorem: Consider by A multi-agent system consisting of one follower and one leader, wherein the first... The dynamics of the agent are shown in equation (1). If assumptions 1 to 4 are satisfied, the distributed adaptive virtual control law satisfies equation (22), the event-triggered feedback control law satisfies equation (44), the feedforward control law satisfies equation (45), the parameter update law satisfies equations (23)-(24), (26), (46)-(47), and the distributed disturbance observer satisfies equations (8)-(9), if suitable parameters exist. , , , , , , , , as well as Make them satisfy the given constraints:

[0220]

[0221] The following conclusions can be drawn:

[0222] (1) All signals within the closed-loop system (1) are bounded;

[0223] (2) Multi-agent systems can achieve leader-follower tracking control;

[0224] (3) Neither of the two event triggering mechanisms exhibits the Zeno phenomenon.

[0225] Proof: Combining steps one and two, we construct the following integrated Lyapunov function:

[0226]

[0227] Combining equations (28) and (48), we can obtain:

[0228]

[0229] In the formula:

[0230] ;

[0231] ;

[0232] ;

[0233] ;

[0234] ;

[0235] ;

[0236] Then define the Lyapunov for the entire cluster. Based on the above analysis, ,in ,and Therefore, all error signals within the closed-loop system are eventually uniformly bounded, and the multi-agent system can achieve consistent control performance.

[0237] The two event triggering mechanisms were then analyzed to verify the avoidability of the Zeno phenomenon. The specific process is as follows:

[0238] when At that time, the communication layer event triggering conditions are met if the following conditions are satisfied: ,in It is a constant. At the same time, the following condition is also satisfied: Subsequently, one can obtain... ,in This is the lower bound of the execution interval for the communication layer event triggering conditions. Therefore, it can be concluded that the Zeno phenomenon does not exist in the communication layer event triggering conditions.

[0239] when At that time, the following two conditions must be met for the execution layer event triggering condition:

[0240] Scenario 1: When the communication layer event triggering conditions are not met, consider the execution layer event triggering conditions. In this situation, there are ,in It is a constant. At the same time, we can obtain... Subsequently, one can obtain... ,in This is the lower bound of the execution interval of the execution layer event triggering condition. Therefore, it can be proven that the execution layer event triggering condition will not be triggered an infinite number of times within a finite time interval.

[0241] Scenario 2: When the communication layer event triggering condition is met, the execution layer event triggering condition also needs to be triggered. Analysis of the communication layer event triggering condition shows that the execution layer event triggering condition does not exhibit Zeno behavior. Therefore, it can be concluded that in this case, the execution layer event triggering condition is not triggered indefinitely.

[0242] Combining the two scenarios above, it can be concluded that the Zeno phenomenon does not exist in the event triggering conditions of the execution layer.

[0243] Based on all the above analyses, we can conclude that all signals within the closed-loop system (1) are bounded, the multi-agent system can achieve leader-follower tracking control, and neither event triggering mechanism exhibits the Zeno phenomenon. Thus, the theorem is proven.

Claims

1. A multi-agent safety optimization tracking control method based on cross-layer coupling event triggering, characterized in that, Includes the following steps: (1) Establish a communication topology model for a multi-agent system, wherein the multi-agent system includes a leader and several followers; the communication topology model includes information transmission between the leader and followers and information interaction between followers; And construct a mathematical model of a multi-agent system that considers unknown external disturbances; (2) Based on the communication topology model of a multi-agent system, construct the communication layer event triggering conditions for communication between agents; And the conditions for triggering execution layer events that update the agent's own executor; (3) Construct an interference observer to estimate and compensate for unknown external interference and attacks, and construct a feedforward controller based on the interference observer, and construct a feedback controller for the agent using the backstepping control method; (4) Determine whether the agent updates the actuator based on the execution layer event triggering condition, and track the follower that updates the actuator through the feedback controller. Determine whether the agents trigger communication based on the communication layer event triggering condition, and track the follower that triggers communication through the feedforward controller or the feedback controller. The communication layer event triggering condition is as follows: ； in, Indicates the triggering time of the communication layer event. Indicates the first One follower The event triggering variable at a given moment. Indicates the first One follower The output signal at time, Indicates the first One follower The output signal at time, , , Represents design constants. This indicates the leader's output signal; The execution layer event triggering condition is as follows: ； ； ； in, Indicates the triggering time of the execution layer event. Indicates the first One follower Input signal at time, yes Feedback control law at any moment yes Feedback control law at any moment This refers to the consistency error of a multi-agent system in the absence of attacks. , , , , Represents design constants. , , Indicates an intermediate variable.

2. The multi-agent safety optimization tracking control method based on cross-layer coupling event triggering according to claim 1, characterized in that, The mathematical model of the constructed multi-agent system is as follows: ； in, Indicates the first The positional status of each follower Indicates the first The speed state of a follower This indicates the positional uncertainty in the system. This represents the speed uncertainty in the system. Indicates system gain. It is composite interference. Indicates the first The output signal of a follower Indicates the first The control input signal of a follower.

3. The multi-agent safety optimization tracking control method based on cross-layer coupling event triggering according to claim 2, characterized in that, The feedforward controller is: ； in, Follower of the feedforward controller output The control input signal, This represents the observed estimate of unknown external disturbances.

4. The multi-agent safety optimization tracking control method based on cross-layer coupling event triggering according to claim 3, characterized in that, The interference observer is: ； ； in, Indicates the first The first follower and the first The connection between followers This indicates the total number of followers. , Represents auxiliary variables. The degree matrix represents the first The degree of association of a follower Indicates the first The connection between a follower and a leader This represents an estimate of the ideal weight vector. Represents a basis function vector. This represents the error in the second step of the backstepping control method. This represents the design constant.

5. The multi-agent safety optimization tracking control method based on cross-layer coupling event triggering according to claim 4, characterized in that, The feedback controller is: ； ； Among them, the backstep control method is used to estimate the uncertain filter variables. Triggering variables obtained based on communication layer event triggering conditions , Indicates the presence of trigger variables Feedback control law, , It is a design constant. Indicates the presence of trigger variables The error, This represents the weight vector of the recognition neural network. The basis functions of the recognition neural network are represented. This represents the weight vector of the evaluation neural network. This indicates that the evaluation neural network contains trigger variables. basis functions, Indicates the presence of trigger variables Error variables, This represents the estimated value of the optimal virtual control signal.

6. The multi-agent safety optimization tracking control method based on cross-layer coupling event triggering according to claim 5, characterized in that, The optimal virtual control law considering the event-triggered mechanism is: ； in, It is a design constant. For consistency errors based on event-triggered mechanisms, and This represents the weight vector of the recognition neural network. This represents the weight vector of the evaluation neural network. , and It contains trigger variables The basis functions.

7. The multi-agent safety optimization tracking control method based on cross-layer coupling event triggering according to claim 6, characterized in that, By employing an identification neural network and a judgment neural network to estimate the ideal evaluation weights of the optimal cost function, the adaptive law of the identification neural network is obtained as follows: ； ； in, , , and Design constant; The evaluation law for the weight update of a neural network is as follows: ； in, For learning rate, Indicates intermediate variables. It is the number of nodes in the neural network. Indicates the first Next storage time Indicate intermediate variables In the The variable value at the next storage time. express In the The variable value for the storage time.

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 7.

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