A control-twin collaborative resource allocation method and system for an industrial digital twin system

Abstract

The application discloses a control-twin collaborative resource allocation method and system for an industrial digital twin system, comprising: constructing an industrial digital twin system model, the system containing multiple industrial applications, each industrial application being composed of a main control task and a digital twin sub-task; establishing a communication and calculation resource constraint model of an edge computing network; and adopting an offline-online two-stage collaborative scheduling strategy for resource allocation: in the offline stage, reserving static resources for each digital twin sub-task according to the historical triggering frequency of the digital twin sub-task, and determining a fixed resource allocation scheme of the main control task with the aim of minimizing the control deviation of the main control task and the total processing time delay of all tasks; and in the online stage, keeping the fixed resource allocation scheme of the main control task unchanged, and utilizing the remaining resources to perform dynamic scheduling on the digital twin sub-task in an event-triggered manner.

Description

Technical Field

[0001] This invention relates to the field of industrial cyber-physical systems, and in particular to a control-twin collaborative resource allocation method and system for industrial digital twin systems. Background Technology

[0002] With the continuous development of intelligent manufacturing and the Industrial Internet, industrial cyber-physical systems are evolving towards higher complexity and intelligence. New service models, represented by digital twins, construct high-fidelity virtual mappings of physical objects and continuously integrate real-time operational data to achieve online perception, predictive analysis, and decision support for system status, demonstrating significant value in improving the operational efficiency, maintainability, and intelligence level of industrial systems. However, compared to traditional control-centric industrial applications, digital twin services place higher demands on data acquisition frequency, model computational complexity, and the timeliness of status synchronization, significantly increasing resource consumption at the communication and computing levels. In industrial scenarios with multiple tasks running in parallel, the differentiated requirements of heterogeneous tasks for latency, computing power, and bandwidth are constantly compounded, making traditional resource management methods, which are statically configured or single-objective-oriented, ineffective in supporting stable system operation. Edge computing, by deploying computing power closer to physical devices, can alleviate the latency and load pressure brought by centralized architectures to a certain extent and has become an important infrastructure for applications such as real-time control and digital twins. However, under the end-edge collaborative operation mode, how to meet the performance requirements of multiple types of tasks simultaneously under limited resources still faces a severe challenge.

[0003] On the other hand, in industrial digital twin systems, real-time control tasks typically have strict latency constraints and high reliability requirements, while digital twin model update tasks are characterized by computational intensity, frequent updates, but relatively higher latency tolerance. When these two types of tasks share communication and computing resources at the edge, without a reasonable collaborative scheduling and resource allocation mechanism, resource contention can easily occur under high load scenarios, leading to problems such as increased control task response latency, decreased control accuracy, and even affecting system stability. Simultaneously, the complex and variable industrial environment, with its fluctuating network load, limited computing resources, and uncertain equipment operating status, makes the system more prone to latency jitter, task blocking, or execution failures in actual operation. In this context, simply applying the same scheduling strategy or synchronous execution method to digital twin model updates and control tasks not only fails to guarantee the deterministic performance of the control loop but may also waste resources and reduce overall system efficiency. Therefore, in edge environments with limited communication and computing resources, how to reasonably coordinate the resource consumption of digital twin model update tasks while ensuring real-time control performance, and improve system stability and operational robustness, has become a critical technical problem that urgently needs to be solved. Summary of the Invention

[0004] In view of the above-mentioned deficiencies of the prior art, the technical problem to be solved by the present invention is that most existing industrial digital twin system scheduling methods focus on the synchronization accuracy and update efficiency of the twin model itself, or focus on the resource allocation of general computing tasks, but fail to effectively coordinate high-priority real-time control tasks and computationally intensive twin update tasks. In resource-constrained edge environments, this can easily lead to resource competition, resulting in increased control latency and decreased accuracy, thereby damaging the overall performance and stability of the system.

[0005] To achieve the above objectives, the present invention provides a control-twin collaborative resource allocation method for industrial digital twin systems, comprising: An industrial digital twin system model is constructed, the system comprising multiple industrial applications, each of which consists of a main control task and a digital twin subtask, and the main control task has a higher real-time priority than the digital twin subtask. Establish a communication and computing resource constraint model for edge computing networks; Resource allocation is performed using a two-stage offline-online collaborative scheduling strategy: During the offline phase, static resources are reserved for each digital twin subtask based on the historical trigger frequency of the digital twin subtask. A fixed resource allocation scheme for the main control task is determined with the goal of minimizing the control deviation of the main control task and the total processing latency of all tasks, so as to ensure the deterministic latency performance of the main control task in a resource contention environment. During the online phase, the fixed resource allocation scheme of the main control task remains unchanged, and the remaining resources are used to dynamically schedule the digital twin sub-tasks for event triggering. When the digital twin sub-task that triggers the update has insufficient remaining resources on the current server, it is migrated to other servers with sufficient remaining resources, thereby prioritizing the real-time performance of the main control task.

[0006] This invention proposes a control-twin offline-online collaborative scheduling strategy, which ensures the performance of control tasks through a static resource reservation mechanism and optimizes twin model updates by combining a dynamic migration strategy, thereby achieving system-level collaborative allocation of communication and computing resources.

[0007] A hierarchical optimization framework is adopted to decompose the problem into two stages: offline and online. In the offline stage, the control deviation and the total processing latency of all tasks are jointly minimized, forming a mixed-integer nonlinear programming problem. In the online stage, after reserving the necessary resources for the control task, the remaining resources are used to dynamically schedule the twin update task to minimize its update latency, thereby balancing control performance and model fidelity at the global level.

[0008] This invention achieves efficient utilization of system resources to support the updating of digital twin models while ensuring determinism and low latency for time-sensitive control tasks. It avoids control performance degradation and system instability caused by disorderly competition for resources, thereby improving the overall efficiency and reliability of cyber-physical fusion systems.

[0009] Furthermore, during the online phase, when a digital twin subtask cannot be executed on the current server due to insufficient resources, the system calculates the total completion latency of migrating the task to each candidate server. The total completion latency includes migration waiting latency, transmission latency, and computation latency. The system then selects the target server that minimizes the total completion latency to perform the migration. If all servers are unable to accommodate the digital twin task, the update request is discarded to absolutely guarantee the resource supply for the main control task.

[0010] Furthermore, in the offline phase, a joint optimization model is constructed to collaboratively optimize the control accuracy of the main control task, the model fidelity of the digital twin sub-tasks, and the total system processing latency; the objective function of the joint optimization model is:

[0011] Among them, the first item The first term is the control deviation term, used to quantify the impact of the sampling period on control accuracy; the second term is the total processing delay per unit time, including transmission delay. Controlling computation delay And based on trigger probability Weighted twin computation latency , To control the task sampling period, the objective function is constrained by computational resource constraints, bandwidth resource constraints, and sampling period constraints, and is used to maximize the efficiency of the twin service while ensuring the bottom line of control performance.

[0012] Furthermore, the control deviation With sampling period The quantization relationship between them is an exponential decay function:

[0013] in, For amplitude coefficient, The attenuation rate is used to quantitatively characterize the sensitivity of the sampling frequency to control accuracy.

[0014] Furthermore, the digital twin sub-task is updated using an event-triggered mechanism, with the trigger condition being the current model deviation. Exceeding the preset threshold The model bias With the current equivalent sampling interval The quantification relationship between them is a logarithmic function:

[0015] in The equivalent sampling interval for the twin task at the current moment. and These are the fitting parameters calibrated based on historical data from a specific twin model.

[0016] On the other hand, a control-twin collaborative resource allocation system for industrial digital twin systems according to the first aspect includes: The system modeling module is used to build an industrial digital twin system model that includes the main control task and digital twin sub-tasks; The constraint modeling module is used to establish communication and computing resource constraint models for edge computing networks; The offline scheduling module is used to reserve static resources based on the historical triggering frequency of digital twin subtasks, and generate a fixed resource allocation scheme for the main control task with the goal of minimizing control deviation and total processing latency. The online scheduling module is used to maintain the fixed resource allocation of the main control task and make dynamic scheduling and migration decisions for digital twin subtasks triggered by events by utilizing the remaining resources. The offline scheduling module and the online scheduling module are integrated into an end-to-end solver based on a multi-agent large language model.

[0017] Existing scheduling strategies typically employ fixed or simple synchronous update mechanisms when coordinating control and twin tasks. They fail to conduct in-depth quantitative analysis of the differential impact of different sampling frequencies on control accuracy and twin model fidelity. Therefore, they cannot achieve a fine-grained trade-off and adaptive optimization between the two under dynamically changing system load and resource conditions.

[0018] This invention proposes a joint optimization model that integrates control deviation, twin model fidelity, and overall time delay, and designs a matching dynamic twin model update mechanism to achieve quantitative characterization and collaborative optimization of the intrinsic coupling relationship between control accuracy and model update performance.

[0019] The scheduling model explicitly characterizes the impact of the sampling frequency of the control task on its tracking accuracy, and the impact of the twin model's update frequency on its simulation fidelity. By incorporating these two key performance indicators along with task processing latency into a unified objective function for optimization, and combining this with a dynamic update mechanism, the scheduling strategy can adaptively adjust resource allocation and task parameters based on the real-time system state, maximizing the service efficiency of the digital twin while ensuring the baseline control performance.

[0020] This invention achieves refined management and dynamic balance of the relationship between control accuracy, twin model fidelity, and system resource efficiency. Compared to baseline methods, this strategy maintains high control accuracy and high model fidelity while achieving better overall latency performance, enabling the system to adaptively cope with load fluctuations and significantly improving the overall efficiency of resource utilization.

[0021] Furthermore, the multi-agent large language model solver includes: Management agents are used to activate offline or online schedulers according to the scheduling phase and coordinate the collaborative processes of various specialized agents. A solution-generating agent is used to generate candidate scheduling schemes based on the problem description and existing solution set during the offline phase; A feasibility check agent is used to verify whether candidate solutions meet all constraints and output a structured error report when they do not. The error report includes a natural language description, a LaTeX constraint expression, and a diagnostic explanation. A feasibility correction agent is used to correct a minimum number of decision variables based on the error report to restore the feasibility of the solution. Code editing agent, code verification agent, and code correction agent are used to transform mathematical models into executable code and perform correctness verification and correction during the online phase; The solver continuously corrects the intermediate results generated by the large language model through a closed-loop iterative refinement mechanism to eliminate "illusion" outputs that do not conform to actual constraints, and finally generates a feasible scheduling scheme.

[0022] Furthermore, the offline scheduling module executes the following closed-loop iterative process to generate the optimal baseline scheduling scheme: Step 1: The management agent activates the offline scheduler, and the solution generation agent generates a candidate solution based on the current problem description and the existing solution set. Step 2: The feasibility checking agent verifies whether the candidate solution satisfies all constraints. If it is not feasible, a structured error report is output. Step 3: The feasibility correction agent, based on the error report, modifies the minimum number of variable values ​​to restore feasibility while maintaining the optimality of the objective function; Step 4: Repeat steps 1 to 3 until a feasible solution is obtained, and retain the solution with a better objective function value in each iteration. Compared with the standard mathematical programming solver, the optimal scheduling scheme output by the solver has an optimality gap of less than 3% and a solution time that is reduced by more than two orders of magnitude.

[0023] Furthermore, the online scheduling module executes the following closed-loop iterative process to generate a real-time migration and resource reallocation scheme: Step 1: The management agent activates the online scheduler, and the code editing agent generates code snippets corresponding to the equations and constraints in the online scheduling mathematical model in sequence. Step two: The code verification agent immediately verifies the functional correctness of each code segment and its conformity to the mathematical model; Step 3: If a problem is found during verification, the code correction agent will only make minimal corrections to the problematic code segment without changing the correct segment; Step four: All verified code snippets are integrated into the final scheduling code; When the system receives an event trigger signal from a digital twin subtask, it executes the final scheduling code and outputs a real-time task migration decision and resource reallocation scheme.

[0024] Existing methods for solving complex coupled scheduling problems mostly rely on traditional mathematical programming or single intelligent algorithms, which suffer from high solution complexity, poor adaptability to dynamic constraints, and difficulty in effectively handling the multi-objective coupling relationship in control-twin collaborative scheduling. At the same time, existing large language models are prone to producing "illusionary" results that do not conform to actual constraints when solving specialized scheduling problems, and lack an effective closed-loop correction mechanism, making it difficult to guarantee the feasibility of the generated scheme.

[0025] This invention proposes an end-to-end solver based on a multi-agent large language model. It decomposes the complex coupled scheduling problem into multiple specialized sub-tasks through a multi-layer hierarchical agent structure and introduces a closed-loop iterative optimization mechanism to ensure the high quality and feasibility of the generated strategy.

[0026] A hierarchical collaborative framework composed of multiple agents is constructed. The high-level agent is responsible for problem decomposition and coordination, while the low-level specialized agents handle sub-problems such as resource allocation, task sequencing, and constraint satisfaction. By designing a closed-loop feedback and iterative refinement process, the "illusions" or unconstrained intermediate results that may be generated by the large language model are continuously corrected, thereby reliably generating feasible optimization schemes that simultaneously meet the real-time constraints of the control task and the fidelity requirements of the twin task.

[0027] This invention can efficiently solve NP-hard control-twin collaborative scheduling problems, generating high-quality end-to-end solutions with an optimality gap of less than 3% compared to standard solvers. It also ensures the feasibility of offline solutions and supports online dynamic scheduling, providing a scalable and intelligent solution tool for integrated control-twin collaboration in complex industrial scenarios.

[0028] Furthermore, the communication and computing resource constraint model of the edge computing network includes: Unloading constraint: Each master control task and its corresponding digital twin subtask must and can only be assigned to the same MEC server, in binary variables. and Represent the allocation relationship, satisfying: ; Computational resource constraints: The total computing resources used by all tasks on any given server shall not exceed its capacity. ; Bandwidth resource constraint: The total bandwidth allocated to any server cannot exceed its capacity. ; Transmission delay is calculated using Shannon's formula:

[0029] in, For transmission power, For channel gain, This represents noise power.

[0030] Technical effect

[0031] From a technical perspective, this solution systematically addresses the resource contention between real-time control tasks and digital twin model update tasks in industrial edge computing scenarios. Through a two-stage collaborative scheduling strategy that combines offline static resource reservation with online dynamic migration, it achieves efficient twin model updates while ensuring strict latency and high reliability of control tasks. This effectively avoids the performance degradation caused by disorderly resource preemption in traditional methods.

[0032] In terms of performance metrics, simulation experiments show that, under different communication bandwidth and computing resource conditions, the average task processing latency of the proposed scheme is significantly better than existing baseline methods such as fixed sampling scheduling, conflict avoidance scheduling, and pure offline scheduling. At the same time, the proposed multi-agent large language model solver improves the computational efficiency by more than two orders of magnitude compared to the tens of thousands of seconds required by standard mathematical programming solvers (such as Gurobi), and the optimality gap is controlled within 3%, which has the dual advantages of solution speed and solution quality.

[0033] From a production implementation perspective, this method does not rely on specific hardware equipment. It only requires deploying the corresponding scheduling software module on existing edge servers and industrial equipment to run. It has good compatibility with mainstream industrial IoT and industrial automation systems, and its implementation cost is low and its integrability is strong. In terms of industrial applications, this technology can be widely used in industrial fields with high requirements for real-time performance and reliability, such as intelligent manufacturing, robot collaborative control, and energy system management. It is particularly suitable for digital twin-enabled scenarios with multi-task parallelism in edge computing environments, and has a clear commercialization path and high technology transformation value.

[0034] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0035] Figure 1 This is a preferred embodiment of the industrial digital twin system architecture diagram of the present invention; Figure 2 This is a flowchart of an end-to-end solution based on a multi-agent large language model, which is a preferred embodiment of the present invention. Detailed Implementation

[0036] The following description, with reference to the accompanying drawings, illustrates several preferred embodiments of the present invention to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms, and the scope of protection of the present invention is not limited to the embodiments mentioned herein.

[0037] In the accompanying drawings, components with the same structure are indicated by the same numerical designation, and components with similar structures or functions are indicated by similar numerical designations. The dimensions and thicknesses of each component shown in the drawings are arbitrary, and the present invention does not limit the dimensions and thicknesses of each component. To make the illustrations clearer, the thickness of some components has been appropriately exaggerated in the drawings.

[0038] In this embodiment, the industrial digital twin system architecture diagram is as follows: Figure 1 As shown, the end-to-end solution flowchart based on a multi-agent large language model is as follows: Figure 2 As shown.

[0039] Step 1: Perform system modeling for the industrial digital twin system oriented towards control tasks, such as... Figure 1As shown, the system comprises three layers: the device layer, the edge layer, and the service layer. The device layer contains multiple industrial devices (sensors and actuators, such as machine tools, robots, and cameras); the edge layer contains multiple MEC servers, providing computing services for industrial applications; in the service layer, each industrial application consists of a main control task (responsible for real-time feedback control, such as robot arm trajectory tracking) and a digital twin subtask (responsible for the dynamic updating of the digital twin model, such as model identification based on least squares support vector machines). The system has a total of... Each industrial application (i.e., task), each task Use a tuple It means that, among them For the size of the input data, and These represent the computational workload (CPU cycles) required for the main control task and the twin task, respectively. The edge layer has a total of... One MEC server, each server Use a tuple It means that, among them Communication bandwidth capacity (MHz). Computing power (G CPU cycles).

[0040] Step 2: Establish the edge offloading and computational constraint model. Each industrial task consists of a main control task and a digital twin subtask, both of which need to be offloaded to the same MEC server for processing. Define binary variables. and Representing tasks Whether the control section and twin section are assigned to the server A value of 1 indicates assignment, otherwise 0. Each control task must be assigned to one server, and the same applies to twin tasks.

[0041] set up and Assigned to tasks respectively The control and twin parts are on the server On computing resources, and These represent the computational workload required for each of the two parts. The computational delay is then calculated. and satisfy:

[0042] The total computing resources used by all tasks on the edge server cannot exceed its capacity:

[0043] Step 3: Establish a wireless communication model. (When the task...) Data needs to be transmitted to the server. At that time, the system allocates bandwidth to it. Then the transmission rate Given by Shannon's formula:

[0044] in For transmission power, For channel gain, This refers to noise power. (Task) The input data size is The transmission delay is:

[0045] Each edge server Total bandwidth capacity is (Unit: MHz), therefore, bandwidth allocation must meet the following requirements:

[0046] Step 4: Select the sampling period. To avoid data backlog in the buffer, control the sampling period of the task. It needs to accommodate a complete data transmission and calculation process:

[0047] The length of the sampling period directly affects control performance. Define the control deviation. The difference between the actual discrete control performance and the continuous optimal control performance can be approximated as an exponentially decaying function of the sampling period:

[0048] in For amplitude coefficient, This is the attenuation rate (reflecting the sensitivity of the sampling period to the control accuracy). A smaller sampling period reduces control deviation but increases resource consumption, so a trade-off must be struck between the two.

[0049] Step 5: Constructing the Objective Function for the Offline Phase. The objective of the offline phase is to jointly minimize the control bias and the total processing latency per unit time, while reserving resources for online scheduling, given the unknown prior information regarding the triggering of the twin task event. Since it is impossible to predict when the twin task will be triggered, a probability is introduced. (Based on historical trigger frequency statistics) the probability of the twin task being triggered is estimated for resource reservation. Offline optimization issues are as follows:

[0050] in, The set of decision variables. The first term of the objective function. The second metric for measuring control accuracy is the total processing delay per unit time, including transmission delay. Controlling computation delay And the latency of twin computation with probability weights The problem is subject to all constraints in steps 2 through 4, and due to the inclusion of binary variables and nonlinear constraints, it is a mixed-integer nonlinear programming problem.

[0051] Step 6: Dynamic Resource Allocation and Migration Model in the Online Phase. During the online operation phase, the scheduling of the main control task maintains the static reservation determined offline. The digital twin subtasks are dynamically scheduled based on event trigger signals, utilizing the remaining resources beyond the reservation. Define the time frame. server Bandwidth occupied by the main control task and computing resources :

[0052] in For a unit step function, when If the value is 1, then the value is 0; otherwise, the value is 0. Then the remaining bandwidth Remaining computing resources When the twin task needs to be updated, the newly allocated bandwidth... and computing resources Must meet:

[0053] The twin model updates employ an event-triggered mechanism. Let... Indicates time Whether to trigger an update depends on the model bias from the previous time step. Exceeding the preset threshold :

[0054] The relationship between model bias and sampling interval was fitted using a logarithmic model, which was derived from actual experimental data:

[0055] in The equivalent sampling interval for the twin task at the current moment. and These are the fitting parameters calibrated based on historical data from a specific twin model. (This is relevant to the twin task.) At any moment If an update is triggered and current server resources are insufficient, consider migrating it to another server. The total latency for completing the task after migration. Defined as:

[0056] in For the initially assigned server, For the servers actually used after the migration, This represents the task completion time after migration. The system selects the target server that minimizes the total latency for migration.

[0057] If all servers are unable to accommodate additional twin tasks, the control task will be prioritized.

[0058] Step 7: Development and Implementation of the Multi-Agent Solver. This embodiment uses a multi-agent end-to-end solver to solve the above-mentioned offline and online optimization problems. The solution process is as follows: Figure 2As shown. First, problem preprocessing is performed: the mathematical models from steps 1 to 6 are described in natural language, and key components (problem background, parameters, decision variables, constraints, objective function) are extracted and organized into a structured input in JSON format. In the offline scheduling phase, the management agent activates the offline scheduler, which coordinates three dedicated agents for closed-loop iterative refinement: the solution generation agent generates a new candidate solution based on the current problem description and existing solution sets; the feasibility checking agent verifies whether the solution satisfies all constraints, and if infeasible, outputs a structured error report (including natural language description, LaTeX constraint expressions, and diagnostic explanations); the feasibility correction agent modifies a minimum number of variable values ​​based on the error report to restore feasibility. This process is repeated until a feasible solution is obtained, and solutions with better objective values ​​in each iteration are retained. The algorithm terminates and outputs the optimal baseline scheduling scheme. During the online scheduling phase, the management agent activates the online scheduler, which coordinates the code editing agent, code verification agent, and code correction agent to transform the mathematical model from step 6 into executable code: the code editing agent generates code fragments corresponding to each equation in sequence; the code verification agent immediately verifies the functional correctness and conformity to the mathematical model of each fragment; if a problem is found during verification, the code correction agent only makes minimal corrections to the problematic fragments. The verified code fragments are integrated into the final scheduling code. At runtime, when an event trigger signal is received, this code is executed, outputting a real-time twin task migration and resource reallocation scheme.

[0059] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A control-twin collaborative resource allocation method for industrial digital twin systems, characterized in that, include: An industrial digital twin system model is constructed, the system comprising multiple industrial applications, each of which consists of a main control task and a digital twin subtask, and the main control task has a higher real-time priority than the digital twin subtask. Establish a communication and computing resource constraint model for edge computing networks; Resource allocation is performed using a two-stage offline-online collaborative scheduling strategy: During the offline phase, static resources are reserved for each digital twin subtask based on the historical trigger frequency of the digital twin subtask. A fixed resource allocation scheme for the main control task is determined with the goal of minimizing the control deviation of the main control task and the total processing latency of all tasks, so as to ensure the deterministic latency performance of the main control task in a resource contention environment. During the online phase, the fixed resource allocation scheme of the main control task remains unchanged, and the remaining resources are used to dynamically schedule the digital twin subtasks for event triggering. When the digital twin subtask that triggers the update has insufficient remaining resources on the current server, it is migrated to another server with sufficient remaining resources, thereby prioritizing the real-time performance of the main control task.

2. The control-twin collaborative resource allocation method for industrial digital twin systems as described in claim 1, characterized in that, During the online phase, when a digital twin subtask cannot be executed on the current server due to insufficient resources, the system calculates the total completion latency of migrating the task to each candidate server. The total completion latency includes migration waiting latency, transmission latency, and computation latency. The system then selects the target server that minimizes the total completion latency to perform the migration. If all servers are unable to accommodate the digital twin task, the update request is discarded to absolutely guarantee the resource supply for the main control task.

3. The control-twin collaborative resource allocation method for industrial digital twin systems as described in claim 1, characterized in that, The offline phase employs a joint optimization model to collaboratively optimize the control accuracy of the main control task, the model fidelity of the digital twin sub-tasks, and the total system processing latency. The objective function of the joint optimization model is: Among them, the first item The first term is the control deviation term, used to quantify the impact of the sampling period on control accuracy; the second term is the total processing delay per unit time, including transmission delay. Controlling computation delay And based on trigger probability Weighted twin computation latency , To control the task sampling period, the objective function is constrained by computational resource constraints, bandwidth resource constraints, and sampling period constraints, and is used to maximize the efficiency of the twin service while ensuring the bottom line of control performance.

4. The control-twin collaborative resource allocation method for industrial digital twin systems as described in claim 1, characterized in that, The control deviation With sampling period The quantization relationship between them is an exponential decay function: in, For amplitude coefficient, The attenuation rate is used to quantitatively characterize the sensitivity of the sampling frequency to control accuracy.

5. The control-twin collaborative resource allocation method for industrial digital twin systems as described in claim 1, characterized in that, The digital twin subtask is updated using an event-triggered mechanism, with the trigger condition being the current model deviation. Exceeding the preset threshold The model bias With the current equivalent sampling interval The quantification relationship between them is a logarithmic function: in The equivalent sampling interval for the twin task at the current moment. and These are the fitting parameters calibrated based on historical data from a specific twin model.

6. A control-twin collaborative resource allocation system for industrial digital twin systems according to any one of claims 1-5, characterized in that, include: The system modeling module is used to build an industrial digital twin system model that includes the main control task and digital twin sub-tasks; The constraint modeling module is used to establish communication and computing resource constraint models for edge computing networks; The offline scheduling module is used to reserve static resources based on the historical triggering frequency of digital twin subtasks, and generate a fixed resource allocation scheme for the main control task with the goal of minimizing control deviation and total processing latency. The online scheduling module is used to maintain the fixed resource allocation of the main control task and make dynamic scheduling and migration decisions for digital twin subtasks triggered by events by utilizing the remaining resources. The offline scheduling module and the online scheduling module are integrated into an end-to-end solver based on a multi-agent large language model.

7. The control-twin collaborative resource allocation system for industrial digital twin systems as described in claim 6, characterized in that, The multi-agent large language model solver includes: Management agents are used to activate offline or online schedulers according to the scheduling phase and coordinate the collaborative processes of various specialized agents. A solution-generating agent is used to generate candidate scheduling schemes based on the problem description and existing solution set during the offline phase; A feasibility check agent is used to verify whether candidate solutions meet all constraints and output a structured error report when they do not. The error report includes a natural language description, a LaTeX constraint expression, and a diagnostic explanation. A feasibility correction agent is used to correct a minimum number of decision variables based on the error report to restore the feasibility of the solution. Code editing agent, code verification agent, and code correction agent are used to transform mathematical models into executable code and perform correctness verification and correction during the online phase; The solver continuously corrects the intermediate results generated by the large language model through a closed-loop iterative refinement mechanism to eliminate "illusion" outputs that do not conform to actual constraints, and finally generates a feasible scheduling scheme.

8. The control-twin collaborative resource allocation system for industrial digital twin systems as described in claim 6, characterized in that, The offline scheduling module executes the following closed-loop iterative process to generate the optimal baseline scheduling scheme: Step 1: The management agent activates the offline scheduler, and the solution generation agent generates a candidate solution based on the current problem description and the existing solution set. Step 2: The feasibility checking agent verifies whether the candidate solution satisfies all constraints. If it is not feasible, a structured error report is output. Step 3: The feasibility correction agent, based on the error report, modifies the minimum number of variable values ​​to restore feasibility while maintaining the optimality of the objective function; Step 4: Repeat steps 1 to 3 until a feasible solution is obtained, and retain the solution with a better objective function value in each iteration. Compared with the standard mathematical programming solver, the optimal scheduling scheme output by the solver has an optimality gap of less than 3% and a solution time that is reduced by more than two orders of magnitude.

9. The control-twin collaborative resource allocation system for industrial digital twin systems as described in claim 6, characterized in that, The online scheduling module executes the following closed-loop iterative process to generate a real-time migration and resource reallocation scheme: Step 1: The management agent activates the online scheduler, and the code editing agent generates code snippets corresponding to the equations and constraints in the online scheduling mathematical model in sequence. Step two: The code verification agent immediately verifies the functional correctness of each code segment and its conformity to the mathematical model; Step 3: If a problem is found during verification, the code correction agent will only make minimal corrections to the problematic code segment without changing the correct segment; Step four: All verified code snippets are integrated into the final scheduling code; When the system receives an event trigger signal from a digital twin subtask, it executes the final scheduling code and outputs a real-time task migration decision and resource reallocation scheme.

10. The control-twin collaborative resource allocation system for industrial digital twin systems as described in any one of claims 6-9, characterized in that, The communication and computing resource constraint model of the edge computing network includes: Unloading constraint: Each master control task and its corresponding digital twin subtask must and can only be assigned to the same MEC server, in binary variables. and Represent the allocation relationship, satisfying: ； Computational resource constraints: The total computing resources used by all tasks on any given server shall not exceed its capacity. ； Bandwidth resource constraint: The total bandwidth allocated to any server cannot exceed its capacity. ； Transmission delay is calculated using Shannon's formula: in, For transmission power, For channel gain, This represents noise power.

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