Network Topology Optimization Method for Multi-Agent Systems Based on Stability Analysis Model

Abstract

The present invention discloses a network topology optimization method for a multi-agent system based on a stability analysis model. This method explores the conditions for maintaining system stability during material transportation by AGVs, as well as the topology optimization method that can improve system performance. First, the channel environment is analyzed, and the conditions for establishing connections between AGVs and between AGVs and the base station are defined by analyzing channel parameters. AGV groups with the same task are defined as a cluster, and information interaction between clusters is carried out through MEC. Then, the time delay is analyzed and a network topology analysis model for the stability of the multi-agent collaborative system is established by means of an artificial potential field function. Subsequently, by maximizing the second smallest eigenvalue of the Laplacian matrix under certain constraints, the connection of the overall topology is changed, thereby improving the system performance. In the analysis of the network topology structure, both the intra-cluster topology and the inter-cluster connection topology are comprehensively considered.

Description

Technical Field

[0001] The present invention belongs to the technical field of mobile communication, and particularly relates to a network topology optimization method for multi-agent system control based on a stability analysis model. Background Art

[0002] Industrial Internet is an important promoter of the intelligent transformation of the global industrial system and an important cornerstone for the deployment and implementation of intelligent manufacturing. In recent years, multi-agent systems have received extensive attention. With the continuous development of multi-agent technology, multi-agent formation has been particularly prominent in applications in military, industrial and other fields. In the industrial aspect, logistics is the driving force of an enterprise's competitiveness and plays a crucial role in economic growth. However, the current logistics industry still faces problems such as high costs and low efficiency. The development of intelligent logistics has brought opportunities to solve these problems. Traditional warehousing and logistics systems use a large amount of manpower to handle and load and unload materials, resulting in low overall work efficiency, poor consistency, and inability to ensure good cooperation. Industrial Internet integrates industrial systems, the Internet, sensing technologies, edge computing, etc., and reconstructs the industrial system, thereby improving the work efficiency of industrial parks. In the 5G industrial Internet scenario, Automated Guided Vehicles (AGVs) play an increasingly important role in logistics handling. AGV cars reduce the cumbersome work of manual handling and improve the efficiency of material transportation in the entire industrial park. When a single AGV car executes a task, due to the constraints of its own hardware conditions, it will affect the execution efficiency of the task; if the task assignment information is sent to each car, it will also waste resources. Therefore, multi-agent formation is introduced to jointly complete tasks.

[0003] The core idea of a multi-agent system is to divide and conquer, decomposing a complex dynamic system into relatively independent subsystems, and completing complex tasks through the cooperation between subsystems. A multi-agent system needs to achieve the organic linkage of different production links, and the resources that each agent can call and the designed technical indicators are not the same. Therefore, the research on multi-agent systems mainly focuses on the organization and coordination between multiple agents and the stability of the entire network.

[0004] Although formation control and obstacle avoidance control, as two major aspects of classical control, have been gradually mature in the field of control research, there is less research on the communication topology of multi-agent, especially AGV car formation, and most of them do not refine the time delay problems existing in the system while considering formation and obstacle avoidance, nor do they consider the impact of the topological structure on the system stability.

[0005] Therefore, it is necessary to comprehensively consider the influence of channel conditions and network topology on control performance, and explore the channel conditions required to ensure system stability. Summary of the Invention

[0006] In order to explore the influence of channel conditions on the network topology and further on the control performance, the present invention provides a network topology optimization method for multi-agent system control based on a stability analysis model, comprehensively considering the conditions for the system to remain stable after taking into account time delay and obstacle avoidance requirements, optimizing the topology to improve the system performance, and proposing the conditions that the channel should meet.

[0007] To achieve the above object, the present invention is realized through the following technical solutions:

[0008] The present invention is a network topology optimization method for multi-agent system control based on a stability analysis model, including the following steps:

[0009] Step S1: Combine channel fading, antenna gain and other channel environments to set the conditions for establishing connections between AGVs and between the cluster head and the base station, so as to judge the topological connection situations between AGVs and between the cluster head and the base station under different channel environments;

[0010] Step S2: Consider the time delay of the AGVs in each cluster transmitting information to the MEC through the cluster head and queuing in the MEC, the time delay of the MEC transmitting the calculated data to the cluster head controller through 5G, and the time delay of the cluster head controller transmitting the control information to each AGV actuator;

[0011] Step S3: Implement the separation and aggregation principles by setting the ideal distance between the AGV and the cluster head in each cluster and the artificial potential field function, and complete the transportation task on the premise of ensuring the stability of the system;

[0012] Step S4: Use the Lyapunov stability theorem to analyze the conditions for the above system to reach stability, and use LMI to calculate the parameters that meet the conditions;

[0013] Step S5: Optimize the system performance by maximizing the second smallest eigenvalue of the Laplacian matrix. In order to prevent the agents from approaching each other arbitrarily in the maximization target and colliding, and considering the need for external obstacle avoidance functions in real life, some constraints are imposed on the topology optimization problem;

[0014] Step S6: Analyze the feasibility of the models established in Steps S1 - S3 from two cases: within a single cluster and considering the information interaction between two clusters through simulation, as well as the influence on the system topology and performance under different channel environments. Finally, use the algorithm in Step S4 to compare the performance of the optimized topology with the previous topology to verify the feasibility of the optimization algorithm.

[0015] Further, in the above Step S1, the elements of the communication quality matrix between the AGVs within the cluster are defined as:

[0016]

[0017] Among them, d ij represents the distance between two AGV vehicles, and the average power of the noise in the wireless channel is σ 2 . The vehicle is equipped with a directive antenna with a gain of , so that the node has different gains in the directions of other nodes. There is a controllable transmit power P ij in the directions facing different vehicles. n′ represents the path loss exponent, which increases with the increase of obstacles, and its value range is 2 to 6. When it is 2, it represents the free space environment. a ij represents the connection probability between node i and the node. If it is greater than a certain value, a connection is established. represents the probability that the signal-to-noise ratio between node i and node j is greater than the threshold signal-to-noise ratio γ, and Γ ij represents the signal-to-noise ratio between node i and node j, and t represents the current time.

[0018] For the connection between the cluster head and the base station, the Shannon formula is used to calculate the channel capacity between the cluster head of the i-th cluster and the k-th base station: Among them, W k represents the bandwidth of the k-th base station, Pi represents the transmit power of the vehicle of the cluster head of the i-th cluster, represents the antenna gain of the vehicle of the cluster head of the i-th cluster, and d ik represents the distance from the vehicle of the cluster head of the i-th cluster to the k-th base station. C ik represents the channel capacity between the cluster head of the i-th cluster and the k-th base station, and n 0 represents the noise density. We select the base station with a larger corresponding transmission rate for connection by calculating the magnitude of the transmission rate from the cluster head to the base station.

[0019] Furthermore, in step S2, each agent is remotely operated through a communication network. The information of each vehicle i is sampled by the sampler in the vehicle with a period of h. The sampled data can be sent to other vehicles via Zigbee or Wi-Fi, and sent to the MEC via the cluster head using 5G. Then, after being calculated by the MEC, the information is sent to the controller of the cluster head, and finally, the control information is sent from the cluster head controller to the actuator in vehicle i. The k-th sampling time is denoted as t k , then 0 < t k+1 - t k = h k ≤h. Network delay will occur in information propagation, specifically including:

[0020] ④ When the current vehicle sends a data packet to a neighbor node through the sampler in the vehicle, it will also be sent to the MEC through the cluster head. After receiving the data packet, the neighbor node also transmits its own data to the MEC through the cluster head via its own sampler for calculation. Therefore, it needs to queue in the MEC queue and then be sent to the cluster head controller after calculation. There is a delay in queuing in the MEC during this process. j represents the agent connected to node i, and Ni represents the set of vehicles connected to vehicle i;

[0021] ⑤ The time delay exists during the process that the MEC transmits the calculated data to the cluster head controller through the 5G network

[0022] ⑥ The cluster head controller also needs to integrate information when transmitting the control information to the actuator in the vehicle, and this process also includes time delay

[0023] So the total time delay is Define the total time delay of all vehicles in the distributed multi-agent system during the control process at the k-th sampling time as τ k = max i {τ ik | i = 1,..., N}, and we assume that τ k is also bounded, τ m ≤ τ k ≤ τ M .

[0024] Furthermore, in the step S3, an artificial potential field function is set. Consider a multi-agent system composed of N vehicles, and the dynamic equation of each vehicle is as follows:

[0025]

[0026] Among them, x i (t) represents the position of vehicle i, B ∈ R N×N , and it is a constant matrix, u i (t) represents the externally input control equation.

[0027] By setting the ideal distance from the cluster head for formation control and using the artificial potential field function for obstacle avoidance control, the obtained AGV state equation is as follows:

[0028]

[0029] Among them, t k + τ k ≤ t ≤ t k+1 + τ k+1 , K represents the feedback gain matrix, K ∈ R N×N . t k is the k-th sampling time, τ k is the time delay during the control process of k sampling times, r i represents the ideal distance between vehicle i and the cluster head, r j represents the ideal distance between vehicle j and the cluster head, so as to form the desired formation. It means that the AGVs form a formation according to the preset ideal distance from the cluster head, forming a certain formation. d i It indicates whether the vehicle i is the cluster head. It is 1 only when i is N, that is, the i-th cluster head, and 0 in other cases. It represents the gravitational force exerted on the cluster head vehicle by the target point, which prompts the entire cluster to move towards the target point, thereby completing the transportation task. Then it represents the repulsive force exerted by the AGVs within the cluster to avoid collision with each other, ||X ij (t k )|| represents the distance between vehicle i and vehicle j at the k-th sampling time, a ij It represents the connection situation between vehicle i and vehicle j in the adjacency matrix, x i It represents the position information of vehicle i. Then it is the repulsive force generated when the distance between the AGV and the external obstacle is less than a certain distance for external obstacle avoidance, o h (t k ) represents the position of the obstacle h at the k-th sampling time, and ||·|| represents the Euclidean distance between two nodes. and The specific formulas of and are as follows:

[0030]

[0031]

[0032] Taking the negative gradient of the above formula, we get

[0033]

[0034] Among them, μ 1 is a constant, t k +τ k ≤t≤t k+1 +τ k+1 . r represents the maximum communication distance of the vehicle, X tar represents the position information of the target point

[0035] The function for obstacle avoidance within the cluster among AGVs is as follows:

[0036]

[0037] Among them, μ 2 is a constant, t k +τ k ≤t≤t k+1 +τ k+1 , d α is the threshold distance that needs to be avoided between vehicles. ||X ij (t k )|| represents vehicle i and vehicle j at tk Distance at a moment

[0038] The internal obstacle avoidance control input is defined as:

[0039]

[0040] where ||x ij (t k )|| represents the distance between vehicle i and vehicle j at time t k .

[0041] When performing external obstacle avoidance, that is, the obstacle avoidance control between the vehicle and the obstacle. For the convenience of calculation, all obstacles are set as mass points, and ob = {o 1 , o 2 ,..., o n} is the set of obstacle positions. It is set that the distance between the vehicle and the obstacle cannot be less than d β . If the distance between the vehicle and the obstacle is greater than or equal to d β , the repulsive force is 0; if the distance is less than d β , there is a repulsive force.

[0042]

[0043] where μ 3 is a constant, t k +τ k ≤t≤t k+1 +τ k+1 . ||x i (t k )-o h (t k )|| represents the distance between vehicle i and obstacle h at time t k , so the control equation for the external obstacle avoidance of vehicle i is:

[0044]

[0045] where N io represents the set of obstacles that will exert a force on vehicle i. ||x i (t k )-o h (t k )|| represents the distance between vehicle i and obstacle h at time t k .

[0046] Furthermore, in step S4, let

[0047]

[0048]

[0049] Δ = De - A

[0050] D = col{0, 0, ..., 0, 1}

[0051]

[0052]

[0053]

[0054] where De is the node degree matrix, A is the node communication quality matrix, and Δ is the Laplacian matrix. x(t) represents the position information matrix of each agent at time t, r represents the relative distance matrix between each agent and the cluster head, u α (t) represents the matrix of forces between agents, u β (t) represents the matrix of forces between agents and obstacles. D has only the Nth value equal to 1, indicating that the Nth agent is the cluster head. Additionally, let d(t) = t - t k , from t k + τ k ≤ t ≤ t k+1 + τ k+1 we can obtain τ k ≤ d(t) ≤ h + τ k+1 , then it can be further seen that τ m ≤ d(t) ≤ h + τ M . For convenience of analysis, denote d m = τ m , d M = h + τ M , that is, d m ≤ d(t) ≤ d M . Then the state equation of the trolley can be simplified as:

[0055]

[0056] Δ t corresponding to the Laplacian matrix at time t, set the Lyapunov functional:

[0057] V(t) = V 1 (x(t), t) + V 2 (x(t), t) + V 3 (x(t), t)

[0058] where,

[0059] V 1 (x(t), t) = x T (t)Px(t)

[0060]

[0061]

[0062] where P > 0, Q 1 > 0, Q 2 > 0, R 1 > 0, R 2 > 0, d M > 0, d m > 0, σ = d M -d m . For simplicity of notation, let H i denote a block matrix, For example:

[0063] It has been proven that the stability condition is as follows:

[0064] Let d m > 0, d M > 0. If there exist a real matrix P > 0, Q 1 > 0, Q 2 > 0, R 1 > 0, R 2 > 0, constants a, b > 0, σ = d M -d m , and a real matrix S of appropriate dimension such that the following inequality holds, then the system is stable.

[0065]

[0066] where,

[0067]

[0068] Ξ = BH 1 -KΔ t (H 2 +r)+H 5 +H 6 +H 7

[0069]

[0070] Proof:

[0071] Let

[0072]

[0073] For t ∈ [t k +τ k , t k+1 +τ k+1 ), we have

[0074]

[0075] Among them,

[0076] Define

[0077] ψ(t) = [x T (t), x T (t - d(t)), x T (t - d m ), x T (t - d M ), (u ta (t)) T , (u α (t)) T , (u β (t)) T T .

[0078] Lemma 1: If there exist a constant matrix R > 0 and R ∈ R n×n , a scalar τ > 0, and a vector function such that the following integral inequality holds:

[0079]

[0080] Lemma 2: For given positive integers n, m, a scalar η in the interval (0, 1), and a given matrix R > 0, two matrices W 1 and W 2 , define the function f(η, R) for all vectors m in R as:

[0081]

[0082] If there exists a matrix S ∈ R n×n , such that then the following holds:

[0083]

[0084] From Lemma 1 and Lemma 2, it can be obtained that:

[0085]

[0086]

[0087] So It can be seen that if then And can be transformed into Thus, it is proved.​

[0088] Furthermore, in step S5, considering that the second smallest eigenvalue of the Laplacian matrix Δ of the formation topology adjacency matrix is an important index affecting the system control stability. Δ = De - A. In order to prevent the agents from approaching each other arbitrarily in maximizing the objective and resulting in collisions, and considering the need for external obstacle avoidance function in real life, the topology optimization problem is transformed into the following problem:

[0089]

[0090]

[0091] where i = 1, 2,..., n - 1, j = 2, 3,.., n and i < j. x i represents the position information of vehicle i, x j the position information of vehicle j, d α represents the minimum allowable distance between vehicles, o h represents the position information of obstacle h, d β represents the minimum allowable distance between a vehicle and an obstacle.

[0092] Due to the non - linear correlation between the relative distances of agents and the Laplacian matrix, the above problem is a non - linear optimization problem. For the convenience of analysis, the problem is transformed using the following two lemmas.

[0093] Lemma 3: Consider the m - dimensional subspace i ∈R n formed by vectors p denoted as P = [p 1 , p 2 ,..., p m ∈ R n×m . Then the matrix M satisfies: for any non - zero vector x ∈ P, x T Mx > 0 if and only if P T MP > 0 holds.

[0094] Lemma 4: For the Laplacian matrix Δ, its second smallest eigenvalue λ 2 (Δ) ≥ 0 is equivalent to P T ΔP ≥ 0, where P = [p 1 , p 2 ,..., p n-1 , p i ∈R n , i = 1, 2,..., m are unit orthogonal vectors, satisfying:

[0095] ① p i T1 = 0, i = 1, 2, ..., n - 1 ② p i T p j = 0, i ≠ j.

[0096] From the above two theorems, x T Δx ≥ 0 can be transformed into P T ΔP ≥ 0, where P is a matrix composed of non - zero vectors of 1 ⊥ Therefore, the optimization problem can be transformed into the following problem:

[0097]

[0098]

[0099] To achieve iteration, at each step of the iteration, the second - smallest eigenvalue is maximized, and we discretize the constraints.

[0100] Let d ij (t k ) = ||x i (t k ) - x j (t k )|| 2 , where t k is the k - th sampling time, then

[0101]

[0102] Let where m is the number of iterations, so we have

[0103]

[0104] Simplifying the above formula, we get

[0105] d ij (m + 1)-d ij (m)=2[x i (m + 1)-x i (m)-x j (m + 1)-x j (m)] T [x i (m)-x j (m)] = 2[x i (m + 1)-x j (m + 1)] T [x i (m)-x j (m)]-2[x i (m)-x j (m)] T [xi (m)-x j (m)] = 2[x i (m + 1)-x j (m + 1)] T [x i (m)-x j (m)] - 2d ij (m)

[0106] That is

[0107] d ij (m + 1)+d ij (m) = 2[x i (m + 1)-x j (m + 1)] T [x i (m)-x j (m)]

[0108] Similarly, define d ih (t k ) = ||x i (t k ) - o h (t k )|| 2 It can be obtained that

[0109] d ih (m + 1)+d ih (m) = 2[x i (m + 1)-o h (m + 1)] T [x i (m)-o h (m)]

[0110] Therefore, the non - convex constraints of the previous optimization problem are transformed into:

[0111]

[0112]

[0113] The beneficial effects of the present invention are:

[0114] Considering the channel environment, the present invention explores the conditions for maintaining the system stability of AGV in material transportation and the topology optimization method that can improve the system performance. The final optimization improves the system performance.

[0115] The present invention takes into account the channel environment, time delay, and obstacles, and solves the problem of unsatisfactory stability of multi-agent systems in practical scenarios. In addition, on the premise of ensuring system stability, the present invention uses the method of increasing the second smallest eigenvalue of the Laplacian to make the system have better stability. Description of the Drawings

[0116] Figure 1 It is the overall structure diagram of the scenario provided by the present invention.

[0117] Figure 2 It is the structure diagram of the control process of the multi-AGV collaborative system provided by the present invention.

[0118] Figure 3 It is the schematic diagram of the potential field received by the cluster head provided by the present invention.

[0119] Figure 4 It is the simulation diagram of each stage considering the information interaction of multiple clusters provided by the present invention. Detailed Embodiment

[0120] The following will disclose the embodiments of the present invention with diagrams. For the sake of clarity, many practical details will be described together in the following description. However, it should be understood that these practical details are not used to limit the present invention. That is to say, in some embodiments of the present invention, these practical details are not necessary.

[0121] The present invention takes Figure 1 as the research scenario, that is, the stability analysis model, which is a scenario of multi-agent collaborative transportation tasks. This scenario consists of a device layer, an edge layer, and a cloud layer. The stability of the system is studied, and the topological structures of the device layer and the edge layer are analyzed and optimized emphatically.

[0122] Specifically, the device layer divides several of the AGVs into several clusters to collaboratively complete the material transportation task. Each cluster of AGVs has a cluster head, which conducts information interaction between two clusters and collaboratively completes the calculation task offloading of real-time path planning. The AGVs within the cluster interact with each other's position information to form a formation, and the target point pulls the cluster head to move, and the cluster head further pulls other AGVs to move; the edge layer consists of several edge nodes, and each edge node includes a 5G base station and an MEC. Each edge node manages a region and is only responsible for managing the obstacle information and real-time path planning of the vehicles within the current region, enabling the vehicles to avoid obstacles in real time; the cloud layer is responsible for providing an operation interface for the operators, sending tasks and instructions to the edge nodes, and then allocating tasks to all AGV cluster heads. According to the tasks given by the cloud service layer, the AGVs automatically identify and transfer the materials. By setting the target point to pull the cluster head, after reaching the target point, the operator completes the material registration and extracts the materials, and then the AGV selects whether to continue the distribution or wait in the designated area according to the instructions of the cloud service layer.

[0123] The present invention assumes that the AGVs within the cluster communicate using a ZigBee or Wi-Fi mesh self-organizing network. The cluster heads access the server in the edge layer through 5G. It is assumed in this paper that the AGV with the best selection ability in terms of comprehensive communication computing power and battery capacity, etc. is selected as the cluster head, and the cluster head enables its own camera to determine the position of obstacles in the surrounding environment. The AGVs select to establish connections with the AGVs with better communication quality (i.e., the communication signal-to-noise ratio is greater than a certain threshold) among all the AGVs within the communication range. During the execution of the task, the above judgment is continuously made. If the signal-to-noise ratio between two AGVs is too low due to various reasons during the movement process, the connection is disconnected; if the probability that the signal-to-noise ratio between two AGVs that did not communicate originally is greater than a certain value during the driving process is higher than a certain threshold, a connection is established between the two AGVs. This communication method reduces the excessive requirements for the communication ability of the cluster head compared with the centralized communication architecture, and also makes the structure of the communication topology not fixed and adjustable.

[0124] Based on Figure 1 the scenario shown, the present invention proposes a network topology optimization method for a multi-agent system, including the following steps:

[0125] Step S1: Combine channel fading, antenna gain and other channel environments to set the conditions for establishing connections between AGVs and between the cluster head and the base station, so as to judge the topological connection situations between AGVs and between the cluster head and the base station in different channel environments.

[0126] In the step S1, the elements of the communication quality matrix between the AGVs within the cluster are defined as:

[0127]

[0128] Among them, d ij represents the distance between two AGV vehicles, and the average power of the noise in the wireless channel is σ 2 , and the vehicle is equipped with a directive antenna with a gain of , so that the node has different gains in the directions of other nodes. There is a controllable transmit power P ij in the directions facing different vehicles. n′ represents the path loss exponent, which increases with the increase of obstacles, and its value range is 2 to 6. When it is 2, it represents the free space environment. a ij represents the probability that node i and the node are connected. If it is greater than a certain value, a connection is established. represents the probability that the signal-to-noise ratio between node i and node j is greater than the threshold signal-to-noise ratio γ, and Γ ij represents the signal-to-noise ratio between node i and node j, and t represents the current time.

[0129] For the connection between the cluster head and the base station, the Shannon formula is used to calculate the channel capacity between the cluster head of the i-th cluster and the k-th base station: Among them, W k represents the bandwidth of the k-th base station, Pi represents the transmit power of the vehicle of the cluster head of the i-th cluster, represents the antenna gain of the vehicle of the cluster head of the i-th cluster, d ik represents the distance from the vehicle of the cluster head of the i-th cluster to the k-th base station, C ik represents the channel capacity between the cluster head of the i-th cluster and the k-th base station, and n 0 represents the noise density. We select the base station with a larger corresponding transmission rate for connection by calculating the magnitude of the transmission rate from the cluster head to the base station.

[0130] Step S2: Consider the delay of the AGVs in each cluster transmitting information to the MEC through the cluster head and queuing in the MEC, the delay of the MEC transmitting the calculated data to the cluster head controller through 5G, and the delay of the cluster head controller transmitting the control information to each AGV actuator.

[0131] In the step S2, each agent performs remote operations through the communication network. The information of each vehicle i is sampled by the sampler in the vehicle with a period of h. The sampled data can be sent to other vehicles via Zigbee or Wi-Fi, and sent to the MEC via 5G through the cluster head. Then, after being calculated by the MEC, the information is sent to the controller of the cluster head. Finally, the cluster head controller sends the control information to the actuator in vehicle i. The k-th sampling time is denoted as t k , then 0 < t k+1 - t k = h k ≤ h will generate network delays in information propagation, specifically including:

[0132] ①Currently, the vehicle sends data packets to neighbor nodes through the in-vehicle sampler and also sends them to the MEC through the cluster head. After receiving the data packets, the neighbor nodes also transmit their own data to the MEC through their samplers via the cluster head for calculation. Therefore, it needs to queue in the MEC queue and then be sent to the cluster head controller after calculation. There is a delay in queuing in the MEC during this process. j represents the agent connected to node i, and Ni represents the set of vehicles connected to vehicle i;

[0133] ②The delay that exists during the process of the MEC transmitting the calculated data to the cluster head controller through the 5G network

[0134] ③The cluster head controller also needs to integrate information when transmitting control information to the in-vehicle actuator, and this process also includes a delay.

[0135] So the total delay is Define the total delay of all vehicles in the distributed multi-agent system during the control process at the k-th sampling time as τ k =max i {τ ik |i=1,...,N}, we assume that τ k is also bounded, τ m ≤τ k ≤τ M .

[0136] Step S3: Implement the separation and aggregation principles by setting the ideal distance between each AGV within the cluster and the cluster head and the artificial potential field function, and complete the transportation task while ensuring the stability of the system.

[0137] In the said step S3, an artificial potential field function is set. Consider a multi-agent system consisting of N vehicles, where the dynamic equation of each vehicle is as follows:

[0138]

[0139] Among them, x i (t) represents the position of vehicle i, B ∈ R N×N , and it is a constant matrix, u i (t) represents the externally input control equation.

[0140] By setting the ideal distance from the cluster head for formation control and using the artificial potential field function for obstacle avoidance control, the obtained AGV state equation is as follows:

[0141]

[0142] Among them, t k +τk t ≤ t k+1 + τ k+1 , where K represents the feedback gain matrix, K ∈ R N×N . t k is the k-th sampling time, and τ k is the time delay of the k-sampling time control process, and r i represents the ideal distance between the vehicle i and the cluster head, and r j represents the ideal distance between the vehicle j and the cluster head, so as to form the desired formation. represents that the AGV forms a formation according to the preset ideal distance from the cluster head to form a certain formation. d i represents whether the vehicle i is the cluster head. It is 1 only when i is N, that is, the i-th cluster head, and 0 in other cases. represents the gravitational force exerted on the cluster head vehicle by the target point, which promotes the entire cluster to move towards the target point, thereby completing the transportation task. Then it represents the repulsive force exerted by the AGVs within the cluster to avoid mutual collision, ||X ij (t k )|| represents the distance between vehicle i and vehicle j at the k-th sampling time, and a ij represents the connection situation between vehicle i and vehicle j in the adjacency matrix, and x i represents the position information of vehicle i. Then it is the repulsive force generated when the distance between the AGV and the external obstacle is less than a certain distance for external obstacle avoidance, o h (t k ) represents the position of the obstacle at the k-th sampling time, and ||·|| represents the Euclidean distance between two nodes. and The specific formulas of are as follows:

[0143]

[0144]

[0145] Taking the negative gradient of the above formula, we get

[0146]

[0147] where μ 1 is a constant, t k + τ k ≤ t ≤ t k+1 + τ k+1 . r represents the maximum communication distance of the vehicle, and x tar represents the position information of the target point

[0148] The intra-cluster obstacle avoidance function between AGVs is as follows:

[0149]

[0150] Among them, μ 2 is a constant, t k +τ k ≤t≤t k+1 +τ k+1 , d α is the threshold distance that needs to be avoided between the cars, ||x ij (t k )|| represents the distance between car i and car j at time t k .

[0151] The internal obstacle avoidance control input is defined as:

[0152]

[0153] Among them, ||x ij (t k )|| represents the distance between car i and car j at time t k .

[0154] When performing external obstacle avoidance, that is, the obstacle avoidance control between the car and the obstacle. For the convenience of calculation, all obstacles are set as point masses, ob = {o 1 , o 2 ,..., o n} is the set of obstacle positions. It is set that the distance between the car and the obstacle cannot be less than d β . If the distance between the car and the obstacle is greater than or equal to d β , the repulsive force is 0; if the distance is less than d β , there is a repulsive force.

[0155]

[0156] Among them, μ 3 is a constant, t k +τ k ≤t≤t k+1 +τ k+1 . ||x i (t k ) - o h (t k )|| represents the distance between car i and obstacle h at time t k , so the control equation for the external obstacle avoidance of car i is:

[0157]

[0158] Among them, N io represents the set of obstacles that will exert a force on car i, ||x i(t k )-o h (t k )|| represents the distance between vehicle i and obstacle h at time t k .

[0159] Step S4: Analyze the conditions for the above system to reach stability using the Lyapunov stability theorem, and use LMI to calculate the parameters that meet the conditions.

[0160] In step S4, let

[0161]

[0162]

[0163] Δ = De - A

[0164] D = col{0, 0,..., 0, 1}

[0165]

[0166]

[0167]

[0168] where De is the node degree matrix, A is the node communication quality matrix, Δ is the Laplacian matrix, x(t) represents the position information matrix of each agent at time t, r represents the relative distance matrix between each agent and the cluster head, u α (t) represents the matrix of forces between agents, u β (t) represents the matrix of forces between agents and obstacles, D has only the Nth value as 1, indicating that the Nth agent is the cluster head. In addition, let d(t) = t - t k , from t k + τ k ≤ t ≤ t k+1 + τ k+1 we can get τ k ≤ d(t) ≤ h + τ k+1 , then it can be further seen that τ m ≤ d(t) ≤ h + τ M , for the convenience of analysis, denote d m = τ m , d M = h + τ M , that is, d m ≤ d(t) ≤ d M . Then the state equation of the vehicle can be simplified as:

[0169]

[0170] Δ t For the Laplacian matrix corresponding to time \(t\), set the Lyapunov functional:

[0171] \(V(t)=V\) 1 (x(t),t)+V 2 (x(t),t)+V 3 (x(t),t)

[0172] Where,

[0173] V 1 (x(t),t)=x T (t)Px(t)

[0174]

[0175]

[0176] Where, \(P > 0\), \(Q\) 1 > 0, \(Q\) 2 > 0, \(R\) 1 > 0, \(R\) 2 > 0, \(d\) M > 0, \(d\) m > 0, \(\sigma = d\) M -d m . For simplicity of representation, use \(H\) i to represent a block matrix, For example:

[0177] It has been proven that the stability conditions are as follows:

[0178] Let \(d\) m > 0, \(d\) M > 0. If there exist a real matrix \(P>0\), \(Q\) 1 > 0, \(Q\) 2 > 0, \(R\) 1 > 0, \(R\) 2 > 0, constants \(a,b > 0\), \(\sigma = d\) M -d m , and a real matrix \(S\) of appropriate dimension such that the following inequality holds, then the system is stable.

[0179]

[0180] Where,

[0181]

[0182]

[0183]

[0184] Proof:

[0185] Let

[0186]

[0187] For \(t\in[t k +\tau k ,t k+1 +\tau k+1 ), we have

[0188]

[0189] where

[0190] Define

[0191] \(\psi(t)=[x T (t),x T (t - d(t)),x T (t - d m ),x T (t - d M ),(u ta (t)) T ,(u α (t)) T ,(u β (t)) T T .。

[0192] Lemma 1: If there exist a constant matrix \(R>0\) and \(R\in\mathbb{R} n×n \), a scalar \(\tau>0\), and a vector function such that the following integral inequality holds:

[0193]

[0194] Lemma 2: For given positive integers \(n,m\), a scalar \(\eta\in(0,1)\), and a given matrix \(R>0\), two matrices \(W 1 \) and \(W 2 \), define the function \(f(\eta,R)\) for all vectors in \(\mathbb{R} m \) as: as:

[0195]

[0196] If there exists a matrix \(S\in\mathbb{R} n×n \) such that then the following holds:

[0197]

[0198] From Lemma 1 and Lemma 2, we can obtain: ​

[0199]

[0200]

[0201] Therefore It can be seen that if then while can be transformed into Thus, it is proved.

[0202] Step S5: Optimize the system performance by maximizing the second smallest eigenvalue of the Laplacian matrix. To prevent agents from approaching each other arbitrarily and colliding in the maximization objective, and considering the need for external obstacle avoidance functions in real life, some constraints are imposed on the topology optimization problem.

[0203] In step S5, considering that the second smallest eigenvalue of the Laplacian matrix Δ of the formation topology adjacency matrix is an important indicator affecting the system control stability. Δ = De - A. To prevent agents from approaching each other arbitrarily and colliding in the maximization objective, and considering the need for external obstacle avoidance functions in real life, the topology optimization problem is transformed into the following problem:

[0204]

[0205]

[0206] where i = 1, 2,..., n - 1, j = 2, 3,.., n and i < j. x i represents the position information of vehicle i, x j the position information of vehicle j, d α represents the minimum allowed distance between vehicles, o h represents the position information of obstacle h, d β represents the minimum allowed distance between a vehicle and an obstacle.

[0207] Due to the non - linear correlation between the relative distances of agents and the Laplacian matrix, the above problem is a non - linear optimization problem. For the convenience of analysis, the following two lemmas are used to transform the problem.

[0208] Lemma 3: Consider the m - dimensional subspace i ∈R n formed by vectors p denoted as P = [p 1 , p 2 ,..., p m ∈ R n×m , then the matrix M satisfies: for any non - zero vector x ∈ P, x TMx > 0 if and only if P T holds when MP > 0.

[0209] Lemma 4: For the Laplacian matrix Δ, its second smallest eigenvalue λ 2 (Δ) ≥ 0 is equivalent to P T ΔP ≥ 0, where P = [p 1 , p 2 ,..., p n-1 , and p i ∈ R n , i = 1, 2,..., m are orthonormal vectors, satisfying:

[0210] ① p i T 1 = 0, i = 1, 2,..., n - 1 ② p i T p j = 0, i ≠ j.

[0211] From the above two theorems, we know that x T Δx ≥ 0 can be transformed into P T ΔP ≥ 0, where P is a matrix composed of non - zero vectors of 1 ⊥ . Therefore, the optimization problem can be transformed into the following problem:

[0212]

[0213]

[0214] To achieve iteration, at each step of the iteration, the second smallest eigenvalue is maximized, and we discretize the constraints.

[0215] Let d ij (t k ) = ||x i (t k ) - x j (t k )|| 2 , where t k is the k - th sampling time. Then

[0216]

[0217] Let x(t k ) = x(m), where m is the number of iterations. So we have

[0218]

[0219] Simplifying the above formula, we get

[0220] d ij(m + 1)-d ij (m)=2[x i (m + 1)-x i (m)-x j (m + 1)-x j (m)] T [x i (m)-x j (m)] = 2[x i (m + 1)-x j (m + 1)] T [x i (m)-x j (m)]-2[x i (m)-x j (m)] T [x i (m)-x j (m)] = 2[x i (m + 1)-x j (m + 1)] T [x i (m)-x j (m)]-2d ij (m)

[0221] That is

[0222] d ij (m + 1)+d ij (m)=2[x i (m + 1)-x j (m + 1)] T [x i (m)-x j (m)]

[0223] Similarly, define d ih (t k ) = ||x i (t k )-o h (t k )|| 2 It can be obtained that

[0224] d ih (m + 1)+d ih (m)=2[x i (m + 1)-o h (m + 1)] T [x i (m)-o h (m)]

[0225] Therefore, the non - convex constraints of the previous optimization problem are transformed into:

[0226]

[0227]

[0228] Step S6: Analyze the feasibility of the model established in Steps S1 - S3 through simulation under two scenarios: within a single cluster and considering the information interaction between two clusters, as well as the impact on the system topology and performance under different channel environments. Finally, use the algorithm in Step S4 to obtain the optimized topology and compare its performance with the previous topology to verify the feasibility of the optimization algorithm.

[0229] To illustrate the effectiveness of the method proposed in the present invention, an example is given below. The performance of the proposed algorithm is evaluated through simulation. Consider an industrial park with a size of 200m × 200m, where there are several clusters of small vehicles. Each cluster has its own transportation task, and the small vehicles within the cluster use Zigbee or Wi-Fi for information interaction. There is information interaction between some clusters to cooperate in completing computational task offloading such as real-time path planning. The clusters are connected to the edge layer server through 5G access. In the simulation, obstacles are abstracted as a single point mass and randomly distributed within the industrial park. By setting a target point for each cluster, the target point exerts a gravitational force on the cluster head vehicle, and the cluster head then pulls the entire group of vehicles towards the target point. If an obstacle is encountered during the movement, a repulsive force is exerted between the obstacle and the vehicle to avoid collision. In this process, the topological connection of the cluster may change. Consider the workshop working process when multiple clusters in the industrial park interact with each other. For the convenience of the experiment, we only select the case of two clusters. The specific parameters are shown in Table 1. For the clarity of the simulation diagram, the two base stations are placed at [5, 25] and [25, 25] respectively when generating the simulation diagram, and they are still set at [-85, 100] and [105, 100] in the simulation code. We select a cluster in the industrial park, and the simulation environment is a two-dimensional space of 30m × 40m to verify the stability of the formation system composed of six AGV vehicles and the feasibility of formation transformation according to the channel environment. As Figure 4 shown, it represents the topological structure diagram considering the information interaction between multiple clusters. (I), (II), (III), and (IV) in the figure respectively represent the states of the cluster in the initial state, the small vehicles within the cluster completing the control to avoid in-cluster collision, external obstacle avoidance, and finally reaching the destination.

[0230] Table 1 Simulation parameters

[0231]

[0232]

[0233] The above are only the preferred embodiments of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. Network topology optimization method for multi-agent system based on stability analysis model, Characterized in that: The network topology optimization method includes the following steps: Step 1: Combine the channel environment to set the conditions for establishing connections between automated guided vehicles (AGVs) and between the cluster head and the base station, and judge the topological connection situations between AGVs and between the cluster head and the base station in different channel environments. Among them, several AGVs are divided into several clusters, and each cluster of AGVs has a cluster head; Step 2: Consider the delays of the AGVs in each cluster transmitting information to the mobile edge computing (MEC) through the cluster head for processing and queuing in the MEC, the delay of the MEC transmitting the calculated data to the cluster head controller through 5G, and the delay of the cluster head controller transmitting the control information to each AGV actuator; Step 3: Achieve the separation and aggregation principles by setting the ideal distance between the AGV and the cluster head in each cluster and the artificial potential field function, and complete the transportation task on the premise of ensuring the stability of the system; Step 4: Use the Lyapunov stability theorem to analyze the conditions for the multi-agent system to reach stability, and use LMI to calculate the parameters that meet the conditions; Step 5: Optimize the system performance by maximizing the second smallest eigenvalue of the Laplacian matrix. In order to prevent the agents from approaching each other arbitrarily in the maximization target and causing collisions, and considering the need for external obstacle avoidance functions in real life, some constraints are imposed on the topology optimization problem; Step 6: Analyze the feasibility of the model established in Steps 1-3 from two cases of within a single cluster and considering the information interaction of two clusters through simulation, as well as the influence on the system topology and performance in different channel environments. Finally, use the algorithm in Step 4 to obtain the optimized topology and compare its performance with the previous topology to verify the feasibility of the optimization algorithm.

2. The network topology optimization method for multi-agent system based on stability analysis model according to claim 1, Characterized in that: In the said Step 1, the communication quality matrix elements between AGVs in each cluster are defined as: where d ij represents the distance between two AGV vehicles, σ 2 is the average power of the noise in the wireless channel, n′ represents the path loss exponent, P ij is the controllable transmit power in the direction facing different vehicles, represents the antenna gain, a ij represents the probability that node i and the node are connected. If it is greater than a certain value, a connection is established. represents the probability that the signal-to-noise ratio between node i and node j is greater than the threshold signal-to-noise ratio γ, Γ ij represents the signal-to-noise ratio between node i and node j, and t represents the current time; For the connection between the cluster head and the base station, the Shannon formula is used to calculate the channel capacity between the cluster head of the i-th cluster and the k-th base station: Among which W k represents the bandwidth of the k-th base station, P i represents the transmission power of the i-th cluster head vehicle, represents the antenna gain of the i-th cluster head vehicle, d ik represents the distance from the i-th cluster head vehicle to the k-th base station, C ik represents the channel capacity between the cluster head of the i-th cluster and the k-th base station, n 0 represents the noise density. By calculating the magnitude of the transmission rate from the cluster head to the base station, the base station with a relatively larger corresponding transmission rate is selected for connection.

3. The network topology optimization method for multi-agent system based on stability analysis model according to claim 1, Characterized in that: In step 2, each agent performs remote operations through a communication network. The information of each AGV vehicle i is sampled by a sampler in the vehicle at a period of h. The sampled data is sent to other AGV vehicles via Zigbee or Wi-Fi, and sent to the MEC via the cluster head using 5G. After being calculated by the MEC, the information is then sent to the controller of the cluster head, and finally the control information is sent from the cluster head controller to the actuator in vehicle i. The k-th sampling moment is denoted as t k , then 0 < t k+1 - t k = h k ≤ h will cause network latency in information dissemination, specifically including: ①Currently, the AGV cart sends data packets to neighbor nodes through the in-vehicle sampler and also sends them to the MEC through the cluster head. After receiving the data packets, the neighbor nodes transmit their own data to the MEC through the cluster head via their own samplers for calculation. It needs to queue in the MEC queue and then be sent to the cluster head controller after calculation. There is a delay in queuing in the MEC during this process. j represents the agent connected to node i, N i represents the set of carts connected to cart i; ②The latency that exists during the process of the MEC transmitting the calculated data to the cluster head controller via the 5G network ③ The cluster head controller needs to integrate information when transmitting control information to the actuators in the trolley, and the process includes time delay Total time delay For \(i = 1,\cdots,N\), the total time delay \(\tau\) of all vehicles in the control process at the \(k\)-th sampling time in the distributed multi-intelligent system is defined as k \(=\max\) i \(\{\tau\) ik \(|i = 1,\cdots,N\}\). Assume that \(\tau\) k is bounded, \(\tau\) m \(\leq\tau\) k \(\leq\tau\) M .

4. The network topology optimization method for multi-agent system based on stability analysis model according to claim 1, Characterized in that: Specifically in the said Step 3: Consider a multi-agent system composed of N small vehicles, and the dynamic equation of each small vehicle is as follows: where x i (t) represents the position of cart i, B ∈ R N×N and is a constant matrix, u i (t) represents the control equation of the external input Through setting the ideal distance from the cluster head for formation control and using the artificial potential field function for obstacle avoidance control, the AGV state equation obtained is as follows: where t k + τ k ≤ t ≤ t k+1 + τ k+1 , K represents the feedback gain matrix, K ∈ R n×n , t k is the k-th sampling time, τ k is the total time delay of the control process for k sampling times, r i represents the ideal distance between vehicle i and the cluster head, r j represents the ideal distance between vehicle j and the cluster head, represents that the AGV forms a formation according to the preset ideal distance from the cluster head to form a certain formation, d i represents whether vehicle i is the cluster head, which is 1 only when i is N, that is, the i-th cluster head, and 0 in other cases, represents the gravitational force exerted on the cluster head vehicle by the target point, represents the repulsive force exerted by the AGVs within the cluster to avoid collision with each other, ‖x ij (t k )‖ represents the distance between vehicle i and vehicle j at the k-th sampling time, a ij represents the connection between vehicle i and vehicle j in the adjacency matrix, x i represents the position information of vehicle i, represents the force between vehicle i and vehicle j, is the repulsive force generated when the distance between the AGV and an external obstacle is less than a certain distance, o h (t k ) represents the position of the obstacle at the k-th sampling time, ‖·‖ represents the Euclidean distance between two nodes, and The specific formulas of are as follows: Take the negative gradient of the above formula to get Among them, μ 1 is a constant, t k +τ k ≤t≤t k+1 +τ k+1 , r represents the maximum communication distance of the trolley, and x tar represents the position information of the target point; The intra-cluster obstacle avoidance function between AGVs is as follows: where μ 2 is a constant, t k + τ k ≤ t ≤ t k+1 + τ k+1 , d α is the threshold distance that needs to be avoided between the cars, and ‖x ij (t k )‖ represents the distance between car i and car j at time t k ; The internal obstacle avoidance control input is defined as: When performing external obstacle avoidance, that is, the obstacle avoidance control between the vehicle and the obstacles, for the convenience of calculation, all obstacles are set as particles, and ob = {o 1 , o 2 ,..., o n} is the set of obstacle positions. The distance between the vehicle and the obstacles is set not to be less than d β . If the distance between the vehicle and the obstacles is greater than or equal to d β , the repulsive force is 0; if the distance is less than d β , there is a repulsive force as follows where μ 3 is a constant, t k +τ k ≤t≤t k+1 +τ k+1 ,‖x i (t k )-o h (t k )‖ represents the vehicle i and the obstacle h The distance at time t k ; The control equation for the external obstacle avoidance of the i-th small vehicle is: Among them, N io represents the set of obstacles that exert forces on cart i, and ‖x i (t k ) - o h (t k )‖ represents the distance between cart i and obstacle h at time t k .

5. The network topology optimization method for multi-agent system based on stability analysis model according to claim 4, Characterized in that: Specifically in the said Step 4: Let Δ = De - A D = col{0, 0,..., 0, 1} where \(D_e\) is the node degree matrix, \(A\) is the node communication quality matrix, \(\Delta\) is the Laplacian matrix, \(x(t)\) represents the position information matrix of each agent at time \(t\), \(r\) represents the relative distance matrix between each agent and the cluster head, \(u\) α (t) represents the matrix of the forces between agents, \(u\) β (t) represents the matrix of the forces between agents and obstacles. \(D\) has only the \(N\)-th value of 1, indicating that the \(N\)-th agent is the cluster head. Let \(d(t)=t - t\) k , from \(t\) k +\(\tau\) k \(\leq t\leq t\) k+1 +\(\tau\) k+1 we can obtain \(\tau\) k \(\leq d(t)\leq h+\tau\) k+1 , then it can be further seen that \(\tau\) m \(\leq d(t)\leq h+\tau\) M , for the convenience of analysis, denote \(d\) m =\(\tau\) m , \(d\) M =h+\(\tau\) M , that is, \(d\) m \(\leq d(t)\leq d\) M , then the state equation of the trolley AGV can be simplified as: Δ t represents the Laplacian matrix corresponding to time t, and the Lyapunov functional is set as: V(t) = V 1 (x(t), t) + V 2 (x(t), t) + V 3 (x(t), t) Where, V 1 (x(t),t) = x T (t)Px(t) where P > 0, Q 1 > 0, Q 2 > 0, R 1 > 0, R 2 > 0, d M > 0, d m > 0, σ = d M -d m , for simplicity of representation, use Η i to represent a block matrix, i = 1, 2,... 5, It has been proved that the stability conditions are as follows: Let d m > 0, d M > 0. If there exist real matrices P > 0, Q 1 > 0, Q 2 > 0, R 1 > 0, R 2 > 0, constants a, b > 0, σ = d M -d m and a real matrix S of appropriate dimension such that the following inequality holds, then the system is stable Where, Ξ = BH 1 -KΔ t (H 2 +r)+H 5 +H 6 +H 7 Proof: Let For \(t\in[t k +\tau k ,t k+1 +\tau k+1 ), it can be obtained that Among them, Definition ψ(t) = [x T (t), x T (t - d(t)), x T (t - d m ), x T (t - d M ), (u ta (t)) T , (u α (t)) T , (u β (t)) T T ,​ Lemma 1: If there exists a constant matrix \(R > 0\) and \(R\in\mathbb{R}\) n×n , a scalar \(\tau>0\), and a vector function such that the following integral inequality holds: Lemma 2: For given positive integers n, m, a scalar η in the interval (0, 1), and a given matrix R > 0, two matrices W 1 and W 2 , define the function f(η, R) for all vectors in R m as: ​ If there exists a matrix S ∈ R n×n , such that then the following equation holds: From Lemma 1 and Lemma 2, it can be obtained that: Therefore it can be seen that if then while can be transformed into thus proven.

6. The network topology optimization method of the multi-agent system based on the stability analysis model according to claim 4, characterized in that: In step 5, considering that the second smallest eigenvalue of the Laplacian matrix Δ of the formation topology adjacency matrix is an important index affecting the system control stability, Δ = De - A. To prevent agents from approaching each other arbitrarily in maximizing the objective and colliding, and considering the need for external obstacle avoidance function in real life, the topology optimization problem is transformed into the following problem: where \(i = 1, 2, \ldots, n - 1\), \(j = 2, 3, \ldots, n\) and \(i < j\), \(x\) i represents the position information of cart \(i\), \(x\) j the position information of cart \(j\), \(d\) α represents the minimum allowable distance between carts, \(o\) h represents the position information of obstacle \(h\), \(d\) β represents the minimum allowable distance between a cart and an obstacle; Due to the non-linear correlation between the relative distances between agents and the Laplacian matrix, the above problem is a non-linear optimization problem. For the convenience of analysis, the following two lemmas are used to transform the problem: Lemma 3: Consider the m-dimensional subspace formed by the vectors p i ∈R n , i = 1, 2, ..., m, denoted as P = [p , p 1 , ..., p 2 , ..., p m ∈ R n×m . Then the matrix M satisfies: for any non-zero vector x ∈ P, x T Mx > 0 if and only if P T MP > 0 holds; Lemma 4: For the Laplacian matrix Δ, its second smallest eigenvalue λ 2 (Δ) ≥ 0 is equivalent to P T ΔP ≥ 0, where P = [p 1 , p 2 ,..., p n-1 , and p i ∈ R n , i = 1, 2,..., m are orthonormal vectors satisfying: ① p i T 1 = 0, i = 1, 2, ..., n - 1 ② p i T p j = 0, i ≠ j From the above two theorems, it can be seen that x T Δx≥0 can be transformed into P T ΔP≥0, where P is a matrix composed of non-zero vectors of 1 ⊥ , so the optimization problem can be transformed into the following problem: To achieve iteration, the second smallest eigenvalue is maximized at each step of the iteration, and the constraints are discretized; Let d ij (t k ) = ‖x i (t k ) - x j (t k )‖ 2 where t k is the k-th sampling time, then Let where m is the number of iterations, so we have Simplify the above formula, and there is d ij (m + 1) - d ij (m) = 2[x i (m + 1) - x i (m) - x j (m + 1) - x j (m)] T [x i (m) - x j (m)] = 2[x i (m + 1) - x j (m + 1)] T [x i (m) - x j (m)] - 2[x i (m) - x j (m)] T [x i (m) - x j (m)] = 2[x i (m + 1) - x j (m + 1)] T [x i (m) - x j (m)] - 2d ij (m) That is d ij (m + 1)+d ij (m) = 2[x i (m + 1)-x j (m + 1)] T [x i (m)-x j (m)] Similarly, define d ih (t k ) = ‖x i (t k ) - o h (t k )‖ 2 It can be obtained that d ih (m + 1) + d ih (m) = 2[x i (m + 1) - o h (m + 1)] T [x i (m) - o h (m)] Therefore, the non-convex constraints of the previous optimization problem are transformed into: Where: m represents the iteration.

7. The network topology optimization method of the multi-agent system based on the stability analysis model according to any one of claims 1-6, characterized in that: The stability analysis model is the scenario of the multi-agent collaborative transportation task, specifically including the device layer, the edge layer and the cloud layer. Specifically, The device layer divides several AGVs into several clusters to collaboratively complete the material transportation task. Each cluster of AGVs has a cluster head. The cluster head conducts information interaction between two clusters, collaboratively completes the calculation task offloading of real-time path planning, and the AGVs within the cluster interact with each other's position information to form a formation. The target point pulls the cluster head to move, and the cluster head further pulls other AGVs to move; The edge layer consists of several edge nodes. Each edge node includes a 5G base station and a ME. Each edge node manages a region. The edge node is only responsible for managing the obstacle information and the real-time path planning of the trolley in the current region, so that the trolley can avoid obstacles in real time; The cloud layer is responsible for providing an operation interface for the operator, sending tasks and instructions to the edge nodes, and then allocating tasks to all AGV cluster heads. According to the tasks given by the cloud service layer, the AGVs automatically identify and transfer. By setting the target point to pull the cluster head, after reaching the target point, the operator completes the material registration and extracts the material. Then, the AGV selects whether to continue the distribution or wait in the designated area according to the instructions of the cloud service layer.

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