Low-carbon energy-saving oriented intelligent factory construction method

Abstract

The invention relates to the field of intelligent construction management, and discloses a low-carbon and energy-saving oriented intelligent factory construction method which comprises the following steps: establishing a state space model of a construction system; constructing a system dynamics and carbon emission objective function based on the state space model; solving an optimal resource scheduling track of carbon emission minimization by utilizing a Hamiltonian system principle and a Pontryagin maximum value principle; introducing a construction constraint condition and optimizing the optimal resource scheduling track through a Lagrange multiplier method; and a feedback control mechanism is constructed, and a Lyapunov function is introduced, so that the stability and robustness of the system under an external disturbance condition are guaranteed. According to the invention, by introducing the Lagrange multiplier method and combining a Lyapunov robust control mechanism, efficient scheduling of construction resources and fine control of carbon emission are realized; the method can stably operate in a dynamic environment, and has good response capability and system adaptability. The construction efficiency and the greening level are remarkably improved, and the method has the advantages of high engineering practicability and intelligence.

Description

Technical Field

[0001] This invention relates to the field of intelligent construction management, specifically to a low-carbon and energy-saving intelligent factory construction method. Background Technology

[0002] In today's rapidly developing industrial and construction sectors, with increasingly stringent environmental regulations, reducing carbon emissions while ensuring project efficiency has become a significant challenge. A common problem in the construction industry is that traditional resource allocation methods often neglect environmental protection factors, resulting in high energy and resource consumption and exceeding carbon emission and energy consumption limits during construction. However, with the promotion of a low-carbon economy, green construction methods are gradually becoming the industry trend. Therefore, there is an urgent need for a new construction method that can effectively reduce carbon emissions while improving construction efficiency, achieving the goals of low-carbon, energy-saving, and environmentally friendly practices.

[0003] Most existing construction methods focus on increasing construction speed and reducing costs, but optimization in areas such as resource scheduling and carbon emission control is insufficient. Many construction management systems employ traditional scheduling algorithms, often relying on simple rules or static models for resource allocation. While these methods improve construction efficiency to some extent, they neglect the variability and complexity of real-world engineering projects. For example, traditional scheduling methods fail to adequately consider platform resource limitations, equipment load capacity, and the impact of environmental changes on the construction process, frequently leading to resource waste, schedule delays, and non-compliance with carbon emission standards in actual operation.

[0004] Furthermore, existing scheduling systems often lack consideration for environmental factors, particularly carbon emission control. Current scheduling optimization methods often aim to minimize costs or construction time, failing to effectively balance environmental protection and construction efficiency. Traditional algorithms, such as genetic algorithms and particle swarm optimization, while providing relatively excellent scheduling solutions in some cases, typically ignore carbon emission constraints and fail to fully consider the dynamically changing construction environment and actual resource availability. Therefore, existing technologies have significant shortcomings in green construction and low-carbon-oriented scheduling, and cannot cope with increasingly complex construction needs and environmental pressures. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a low-carbon and energy-saving intelligent factory construction method, which solves the problems of insufficient resource scheduling and carbon emission control in existing construction methods.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A low-carbon and energy-saving smart factory construction method includes the following steps:

[0008] S1. Establish the state-space model of the construction system;

[0009] S2. Construct system dynamics and carbon emission objective functions based on the state-space model;

[0010] S3. Solve for the optimal resource scheduling trajectory that minimizes carbon emissions using the Hamiltonian system principle and the Pontryagin maximum principle.

[0011] S4. Introduce construction constraints and optimize the optimal resource scheduling trajectory using the Lagrange multiplier method;

[0012] S5. Construct a feedback control mechanism and introduce Lyapunov functions to ensure the stability and robustness of the system under external disturbance conditions.

[0013] Preferably, establishing the state-space model includes:

[0014] Collect construction node information Construct a task dependency graph based on the process flow;

[0015] Configure the types of resources required for each node The corresponding initial inventory With maximum consumption limit ;

[0016] Extracting carbon emission factors from various resources Constructing a total carbon emission boundary ;

[0017] The state vector is defined as ,in Indicates the first A state variable in time The value of .

[0018] Preferably, step S2 includes:

[0019] S2.1, Define the control vector ,in Indicates the first Class resources at any time The delivery rate;

[0020] S2.2, The system dynamics model is established as follows:

[0021] ;

[0022] in:

[0023] This is the system state vector; Input for resource scheduling; The task topology matrix, Resource efficiency matrix; This represents the external disturbance vector.

[0024] Preferably, the carbon emission objective function is defined as:

[0025] ;

[0026] in:

[0027] The objective function is carbon emissions; This refers to the total duration of the construction period; Control cost weight matrix; This is the state cost weight matrix; It is a state vector; For real-time resource access.

[0028] Preferably, step S3 includes the following three sub-steps:

[0029] S3.1 Constructing the Hamiltonian function:

[0030] ;

[0031] in:

[0032] It is a companion variable. It is a state vector; For control input; External disturbance; Here is the state transition matrix. To control the input matrix;

[0033] S3.2, Define the accompanying variable The dynamic equation:

[0034] ;

[0035] in, For Hamiltonian, The changes are obtained through optimality conditions and dynamic equations.

[0036] S3.3, Construct optimality conditions such that Thus, the control input is derived.

[0037] Preferably, the control input The optimal solution is defined as:

[0038] ;

[0039] in: This is the optimal control input; These are costate variables.

[0040] Preferably, the costate variable Solve the following boundary value problem:

[0041] ;

[0042] in:

[0043] For state variables, For costate variables; External disturbance; For control input; Here is the state transition matrix. To control the input matrix.

[0044] Preferably, step S4 includes the following three sub-steps:

[0045] S4.1 sets the total construction time, the upper limit of node resource usage, and the platform equipment capacity as constraints;

[0046] S4.2, Construct the Lagrangian function to introduce the constraints into the objective function;

[0047] S4.3 Optimize the control trajectory based on the Karush-Kuhn-Tucker conditions.

[0048] Preferably, step S5 includes the following three sub-steps:

[0049] S5.1, Constructing Lyapunov functions:

[0050] ;

[0051] in It is a positive definite matrix; This is the system state vector;

[0052] S5.2, Design Feedback Control Items:

[0053] ;

[0054] in This is the feedback gain matrix;

[0055] S5.3, Final Control Input:

[0056] ;

[0057] in, The control input is corrected through feedback control; This is the optimal control input.

[0058] A low-carbon, energy-saving, and intelligent factory construction system, applied to the low-carbon, energy-saving, and intelligent factory construction method according to any one of claims 1-9, characterized in that it comprises:

[0059] The model building module is used to construct the state space and dynamic equations of the construction system;

[0060] The control solution module is used to calculate the control trajectory based on the Hamiltonian system and optimality conditions.

[0061] The constraint optimization module is used to apply resource and time constraints and perform optimization.

[0062] The robust feedback module is used for constructing and controlling Lyapunov functions under disturbances.

[0063] The scheduling and execution module is used to convert control trajectories into platform task instructions and drive field equipment to execute them.

[0064] This invention provides a low-carbon and energy-saving intelligent factory construction method, which has the following beneficial effects:

[0065] 1. This invention employs a scheduling optimization algorithm based on the Lagrange multiplier method. By strictly introducing multiple constraints (such as resource capacity, platform overall scheduling capacity, carbon emissions, etc.), it achieves precise control of resource scheduling in actual construction. Compared with traditional simple scheduling schemes in the prior art, this invention effectively solves the problems of uneven resource allocation and excessive carbon emissions in complex construction environments, achieving more efficient and environmentally friendly construction management.

[0066] 2. This invention employs a Lyapunov robust feedback control strategy, which can automatically adjust the scheduling trajectory based on real-time construction conditions, ensuring system stability even under external disturbances. Compared to existing scheduling systems that struggle to adapt to external changes, this invention solves the instability problem of traditional methods under disturbed environments, thus enhancing system adaptability and reliability.

[0067] 3. This invention successfully solves the problem of balancing multiple mutually restrictive factors (such as maximum resource input, platform capacity, and carbon emission limits) during construction resource scheduling by introducing a technical solution that combines multiple constraints with optimal control. Compared with the simple single optimization methods in existing technologies, this invention significantly improves resource utilization and construction efficiency, while avoiding resource waste and environmental burden.

[0068] 4. The scheduling optimization method of this invention combines a control strategy based on Lyapunov stability theory with actual engineering constraints, effectively integrating theory and practice to ensure control accuracy and system stability during the optimization process. Compared to traditional optimization algorithms, the technical solution of this invention can respond to unexpected situations in different construction scenarios in real time, ensuring the smooth progress of the entire construction process and avoiding the problems of unreasonable scheduling or slow response that may occur in previous technologies. Attached Figure Description

[0069] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0070] Figure 2 This is a schematic diagram of the system architecture of the present invention. Detailed Implementation

[0071] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0072] Please see the appendix Figure 1 This invention provides a low-carbon, energy-saving smart factory construction method, comprising:

[0073] S1. Establish the state-space model of the construction system;

[0074] In this embodiment, the establishment of the state-space model of the construction system includes construction task decomposition, resource type identification, carbon emission factor acquisition, and construction of dynamic equations for state-control relationships. This process not only provides the foundation for the system control model but also clarifies the mapping relationship between resources and construction tasks, laying a structural foundation for subsequent carbon optimization control and robust feedback.

[0075] First, extract the construction node information and construct the task topology graph. A construction node is a finite set of structured task units, denoted as set:

[0076] ;

[0077] in, Indicates the first Each construction process involves a set of steps. If there is a sequential dependency between any two nodes, a directed edge is formed in the directed graph, indicating that the subsequent node can only be executed after the preceding node is completed.

[0078] The adjacency matrix corresponding to the task graph is generated by the structured dependencies, and the state transition matrix is ​​constructed accordingly. Specifically, the definition is:

[0079] ;

[0080] This matrix is ​​used to reflect the coupling dependencies between various construction states and affects the dynamic evolution of the state vector.

[0081] Each node Corresponding to a construction state variable , used to represent the completion level of the node, satisfying:

[0082] ;

[0083] The state vector is defined as:

[0084] ;

[0085] Construction resources include several types, denoted as a set:

[0086] ;

[0087] Each resource It has the following attributes: Initial inventory Maximum delivery rate Unit carbon emission factor The unit is / Unit resources.

[0088] The control input vector is the resource scheduling function:

[0089] ;

[0090] in Indicates the first Resources in time The call intensity (units vary depending on the resource type, such as kW, tons, etc.) meets the requirements. .

[0091] Each construction task node This task may be accomplished by multiple resources working together; define a resource-task mapping matrix. Its elements Indicates unit resources State The efficiency of advancement. If resources Does not apply to nodes ,but .

[0092] The state evolution model is described as follows:

[0093] ;

[0094] in:

[0095] : Indicates the impact of inter-task dependencies;

[0096] This indicates the direct impact of resource scheduling on task progress.

[0097] : Indicates unmodeled disturbance factors, such as material delays, employee absenteeism, etc., whose values ​​can be estimated from historical data or set as a zero-mean stochastic process.

[0098] In the resource-carbon emission mapping, carbon emissions per unit time are expressed as:

[0099] ;

[0100] in .

[0101] The total carbon emissions of the project are:

[0102] ;

[0103] The system should meet carbon emission limits:

[0104] ;

[0105] in, The acceptable total carbon emissions threshold for the platform is determined by government regulations or company-set limits.

[0106] In the process of model implementation, the matrix The matrix can be constructed by combining a topological sorting algorithm with an adjacency list. The generation is determined by the resource allocation scheme, for example:

[0107] If construction task Requires 2 units of concrete (resources) ) and 1 unit of labor (resources) ),but , ,in These are the actual measured or calibrated construction efficiency parameters.

[0108] The aforementioned model can be automatically modeled in simulation platforms such as MATLAB by inputting a structure matrix, or generated after extracting construction process-resource relationships in a BIM platform. The resulting state-control model constitutes a unified input platform for subsequent steps such as objective function construction, optimal control solution, and feedback correction.

[0109] Through the above steps, a precise mapping between construction tasks, resources, and carbon emissions can be achieved, resulting in a clear structure, data-driven approach, and the ability to embed optimization algorithms.

[0110] S2. Constructing system dynamics and carbon emission objective functions based on state space;

[0111] In this embodiment, the dynamic modeling and objective function construction of the construction system are based on the state-space model. Through the construction of the structural matrix and the integration of performance index functions, it is ensured that the subsequent optimization solution has a well-defined input-output channel.

[0112] First, establish the state variables to describe the construction system. This is used to reflect the completion progress of each task node in the system. The state vector form is:

[0113] ;

[0114] in, , indicating the first Each construction node at time The completion rate satisfies the initial conditions. Boundary conditions are .

[0115] Then the control input vector is defined. Used to describe the system at time 0. The amount of various resources allocated:

[0116] ;

[0117] in, , representing the The real-time dispatch rate of resources (such as electricity, water, manpower, etc.) is set in units based on the specific resource, such as kW, L / min, person-times / h, etc.

[0118] There are dependencies between construction tasks. A directed graph topology for the tasks is established, and a state coupling matrix is ​​generated. .matrix The construction method is as follows:

[0119] ;

[0120] matrix This indicates logical coupling between tasks and serves as an intrinsic dependency of the system during state updates.

[0121] The contribution of each resource to different tasks is represented by a resource efficiency matrix. Representation. Element Indicates the first Class of resources for the first The progress rate brought about by the deployment of each construction node unit is expressed as the node completion rate divided by the amount of resource units.

[0122] For example, if node For every unit of concrete used The propulsion speed is 0.2, using 1 unit of human resources. If the propulsion speed is 0.3, then , The rest are 0.

[0123] The dynamic equations formed by the above state-control relationships are as follows:

[0124] ;

[0125] in:

[0126] : System state vector;

[0127] Resource scheduling input;

[0128] Task topology matrix;

[0129] Resource efficiency matrix;

[0130] The disturbance term represents possible construction anomalies in reality (such as equipment delays or changes in the external environment), and can be modeled as a zero-mean Gaussian process or a noise sequence.

[0131] In carbon emission modeling, a resource-carbon emission factor vector is introduced:

[0132] ;

[0133] in, Indicates unit resources The carbon emission intensity, expressed in kgCO2 / unit, is used to quantify the carbon impact of this resource allocation.

[0134] The carbon emission function per unit time is expressed as:

[0135] ;

[0136] That is, every moment The carbon emission intensity at that moment is obtained by multiplying all resource usage by its carbon emission factor.

[0137] The cumulative carbon emissions during the construction period are:

[0138] ;

[0139] in: Total carbon emissions; Construction period; Emission intensity per moment.

[0140] Carbon emissions must meet the system's total limit:

[0141] ;

[0142] in Carbon emission caps set for regulations or project requirements.

[0143] To optimize the overall benefits during the scheduling process, an objective function is further established:

[0144] ;

[0145] In the formula:

[0146] The objective function represents a comprehensive evaluation of resource costs and state deviations.

[0147] This refers to the total duration of the construction period;

[0148] : Control input weight matrix;

[0149] State offset weight matrix;

[0150] For real-time resource allocation;

[0151] This indicates the node's progress status.

[0152] matrix , It is a positive definite matrix, ensuring that the optimization problem has a unique solution. Its elements can be set according to actual scheduling costs and node priorities. For example, high carbon impact resources can be assigned higher values. Weights are allocated more heavily to critical path nodes. .

[0153] The objective function is used to construct the subsequent optimal control problem. Combined with constraints (such as carbon emission limits and not exceeding maximum resource capacity), it forms a standard constrained optimization problem.

[0154] The aforementioned dynamic modeling and objective function construction can be achieved through a control system modeling platform, such as using the Simulink module in MATLAB for system modeling, or using symbolic control libraries (such as CasADi and GEKKO) to achieve objective function-constraint system modeling.

[0155] In construction scheduling practice, this step can be implemented through the following process:

[0156] First, extract the topology and resource allocation parameters of the construction nodes to generate a matrix. , .

[0157] Carbon emission factors were then obtained from the resource inventory. , and construct a carbon emission model.

[0158] Finally, define the optimization time window. Set state constraints, resource allocation constraints, and carbon emission caps. Derive the complete system model and performance index expressions.

[0159] The implementation of this step enables physical-carbon dual-perspective modeling of the dynamic allocation behavior of construction resources, with clear carbon emission mapping and clear state coupling.

[0160] S3. Solve for the optimal resource scheduling trajectory that minimizes carbon emissions using the Hamiltonian system principle and the Pontryagin maximum principle.

[0161] In this embodiment, based on the aforementioned state-space model and carbon emission objective function, a system optimal control problem is constructed. The goal is to minimize carbon emissions and resource scheduling costs while satisfying system dynamic constraints and resource limitations, and to obtain the dynamic construction scheduling trajectory.

[0162] First, based on the system state vector defined in step S2:

[0163] ;

[0164] The control input is a resource scheduling signal:

[0165] ;

[0166] The system dynamic model is as follows:

[0167] ;

[0168] in:

[0169] Construction task dependency matrix;

[0170] Resource utilization efficiency matrix;

[0171] The system disturbance term is often modeled as zero-mean noise.

[0172] Construction status;

[0173] Resource scheduling input.

[0174] The objective function is:

[0175] ;

[0176] in:

[0177] : Control cost weight matrix, reflecting resource scheduling costs;

[0178] State error weight matrix, reflecting the cost of schedule deviation;

[0179] The total duration of the construction project;

[0180] The objective function value measures the overall efficiency of carbon-resource scheduling.

[0181] To solve this optimal control problem, costate variables are introduced. It is used to measure the impact of each state variable on performance metrics. Marginal sensitivity.

[0182] The Hamiltonian function is constructed as follows:

[0183] ;

[0184] in:

[0185] It is a companion variable. It is a state vector; For control input; External disturbance; Here is the state transition matrix. To control the input matrix;

[0186] According to Pontryagin's maximum principle, the optimal control solution must satisfy:

[0187] ;

[0188] ;

[0189] ;

[0190] The optimal control strategy can be obtained:

[0191] ;

[0192] The control input expression indicates that the optimal resource scheduling intensity is determined by the current costate variables and the resource action matrix. The relationship determines this.

[0193] Coupled dynamic equations of state and costate:

[0194] ;

[0195] This system constitutes a typical two-point boundary value problem, where:

[0196] initial value This is given by the current system status or the construction start status;

[0197] The final value is the free boundary or a set target. This can be completed by all nodes, that is... .

[0198] Since the state evolves in a forward direction and the costate evolves in a backward direction, the following approach is required:

[0199] Numerical solutions can be obtained using the forward-backward sweep method or collocation method.

[0200] In the forward-backwardsweep method, a time interval is set. Divided evenly into Segment, step size is The algorithm flow is as follows:

[0201] Initialize costate variables It can be set to zero or random perturbation;

[0202] Positive integral state variable ;

[0203] Inverse integral costate variable ;

[0204] Update the control strategy according to equation (9) ;

[0205] Iterate until the state, costate, and control converge.

[0206] This solution framework can be implemented in platforms such as MATLAB (via ODE45+shootingmethod) and Python (via SciPy+solve_bvp function).

[0207] The obtained control trajectory This is a carbon-optimized scheduling strategy that can be used to generate field control commands.

[0208] For example, let's assume three types of resources. Five construction nodes ,matrix , , It is known that the minimum carbon emission scheduling rate for each type of resource can be obtained at each time step through the above optimal control strategy.

[0209] The final control output is connected to the scheduling execution unit via an interface. The unit maps the control signals into resource allocation instructions for the task platform, thereby enabling the docking of the on-site construction platform with the optimal model.

[0210] This implementation method enables the optimal coupling of carbon emission control and task scheduling, and the system control logic has technical effects such as clear structure, feedback update capability, and stable convergence.

[0211] S4. Introduce construction constraints and optimize the optimal resource scheduling trajectory using the Lagrange multiplier method;

[0212] In this embodiment, considering the constraints such as limited resource supply capacity, limited parallel scheduling capability of equipment, and controlled carbon emissions during actual construction, a set of equality and inequality constraint models are introduced based on the optimal control structure of the system, and a complete constraint optimization structure is established by using the Lagrange multiplier method and KKT conditions.

[0213] First, consider the constraints on individual resource capabilities. The maximum available capacity for each type of resource at any given time is set as follows:

[0214] ;

[0215] in:

[0216] : No. The rate at which resources of this type are deployed;

[0217] : Maximum rate limit set by the platform or construction physical conditions, in units of resources / time.

[0218] The total resource deployment capacity must also meet the physical limits of the platform's concurrent processing capacity, and the following constraints are constructed:

[0219] ;

[0220] in:

[0221] The platform's maximum scheduling capacity.

[0222] Simultaneously considering the carbon emission limits throughout the system's lifecycle, based on the aforementioned defined carbon emission function:

[0223] ;

[0224] The total carbon emissions during the construction period should meet the following requirements:

[0225] ;

[0226] in:

[0227] Carbon emission factors of various resources (units) / unit resources);

[0228] The acceptable upper limit for total carbon emissions.

[0229] To solve the optimal control problem with the above constraints, the Lagrangian Multiplier Method is used for structural modeling.

[0230] First, construct the extended Lagrange function based on the objective function:

[0231] ;

[0232] in:

[0233] The performance objective function defined above;

[0234] : No. Each scheduling constraint (such as resource limit, total scheduling capacity) is in the form of: ;

[0235] : with the The Lagrange multiplier functions corresponding to each constraint;

[0236] : The multiplier of carbon emission constraints.

[0237] The construction scheduling optimization problem is transformed into solving the following set of KKT (Karush-Kuhn-Tucker) conditions:

[0238] ;

[0239] ;

[0240] Based on Pontryagin's maximum principle and the unified framework of constrained optimization, the enhanced Hamiltonian function is constructed as follows:

[0241] ;

[0242] In this structure:

[0243] The first three terms are the original unconstrained Hamiltonians;

[0244] The fourth term is an inequality constraint structure;

[0245] The fifth item is the carbon emission restriction item.

[0246] Enhanced Hamiltonian function Taking the partial derivative with respect to the control quantity, we obtain the optimality condition:

[0247] ;

[0248] Combined with boundary conditions Terminal status (Can be set to complete at all nodes), and at the same time, combine equations (6)–(9) to construct a nonlinear restricted boundary value problem.

[0249] The above problems can be solved using numerical methods such as Sequential Quadratic Programming (SQP), Interior Point Method (IPM), or Augmented Lagrangian Method (ALM), with control variables used during the solution process. Multiplier function , Updated synchronously with state-costate variables.

[0250] The following process can be used in the project:

[0251] First, a discrete-time grid is constructed. Initial estimates are made for the state variables, co-state variables, and multiplier vectors.

[0252] Subsequently, an iterative method was used to perform forward integration of the state and backward integration of the co-state, and the control quantity and multiplier value were corrected at each step using KKT conditions.

[0253] Finally, the scheduling trajectory that satisfies the system constraints is obtained under the convergence condition. The trajectory achieves the minimum objective function value while satisfying platform and carbon emission constraints.

[0254] In system deployment, this structure embeds a scheduling optimization unit. The unit includes:

[0255] Optimize the interface section to connect to modeling input;

[0256] Multiplier Management Department, performing constraint matching;

[0257] The trajectory output unit drives the execution module to send scheduling signals.

[0258] The constrained optimal scheduling model constructed through this implementation method can achieve synchronous control and optimization of carbon constraints, resource capabilities, and platform capacity, and has the technical effects of strong scheduling feasibility, stable control strategy, and closed mathematical structure.

[0259] S5. Construct a feedback control mechanism and introduce Lyapunov functions to ensure the stability and robustness of the system under external disturbance conditions.

[0260] First, the system's dynamic equations are still based on the scheduling model from step S4. The state-space equations describe the system's time... The evolution of the internal state. Assume the dynamic equations of the system are:

[0261] ;

[0262] in:

[0263] It is the system state vector, representing each time step. Below, the system's various scheduling and equipment status information;

[0264] It is the system's control input, i.e., the optimized scheduling trajectory;

[0265] and These are the state transition matrix and the control input matrix, respectively, used to describe the relationship between state changes and control inputs;

[0266] External disturbances represent dynamic environmental changes or unforeseen factors that the system may face.

[0267] To ensure system stability, the Lyapunov function is chosen as the stability analysis tool. The commonly used form of the Lyapunov function is a quadratic form:

[0268] ;

[0269] in:

[0270] It is a symmetric positive definite matrix, representing the weighting coefficients of the system, used to adjust the strength of system stability.

[0271] The derivative of the Lyapunov function is:

[0272] ;

[0273] Substituting into the system dynamic equations, we get:

[0274] ;

[0275] To ensure system stability and eliminate the effects of external disturbances, the Lyapunov derivative... It needs to satisfy negative definiteness, that is:

[0276] ;

[0277] in, The matrix is ​​positive definite, adjusting the system's stability and convergence speed. This condition ensures that the system will not diverge under external disturbances and will converge to a stable state within a certain time.

[0278] To achieve robust control of the system, we designed the control input. As a state feedback controller, the control input takes the following form:

[0279] ;

[0280] in:

[0281] It is the state feedback gain matrix, which determines the response of the control input to the system state;

[0282] The optimal scheduling trajectory obtained in step S4 is used as a reference system objective.

[0283] Through this feedback control structure, the system can adjust according to the current state. and reference trajectory Adjust control input This is to ensure the stable operation of the system.

[0284] In practice, construction systems are often subject to external disturbances. The impact of the disturbance signal. To analyze the robustness of the system, we assume the disturbance signal... The following constraints must be met:

[0285] ;

[0286] here, It represents the maximum amplitude of the disturbance, reflecting the uncertainty of the external environment.

[0287] According to Lyapunov stability theory, robustness conditions must be met when designing a controller:

[0288] ;

[0289] in, It is a constant used to control the degree of influence of disturbances.

[0290] By adjusting and The value of , and the selection of an appropriate feedback gain matrix. The system can effectively cope with external disturbances, maintain stability, and eventually converge to the desired scheduling trajectory.

[0291] The implementation process of this control system is as follows:

[0292] System initialization: Based on the optimal scheduling trajectory obtained in step S4 Initialize the system state vector and control input .

[0293] Constructing the Lyapunov function: Selecting an appropriate positive definite matrix based on system characteristics. Construct Lyapunov functions And calculate its derivative. .

[0294] Feedback Control Design: Design a feedback controller based on Lyapunov stability theory. and adjust The matrix makes the system robust to disturbances.

[0295] System optimization: Based on the disturbance analysis results, further optimize the system parameters to ensure that the system can cope with external disturbances and remain stable during construction.

[0296] To verify the performance of the robust controller, simulation tests were conducted. In the simulation, the disturbance signal... It will be applied to the system according to different patterns (such as periodic disturbances, random disturbances, etc.). This is achieved by monitoring the system's state variables in real time. The response of the control system was evaluated. Experimental results show that the proposed control strategy can stably converge to the optimal scheduling trajectory under disturbances and effectively avoid system instability.

[0297] The low-carbon and energy-saving smart factory construction system described below can be referred to in conjunction with the low-carbon and energy-saving smart factory construction method described above.

[0298] Please see Figure 2 The present invention also provides a low-carbon and energy-saving intelligent factory construction system, comprising:

[0299] The model building module is used to uniformly model resources, tasks, and platform operating status during the construction process, forming a state-space representation, and establishing a dynamic description of the construction system by combining dynamic factors in the construction environment. This module supports multi-source information input, capable of collecting data from field equipment, task scheduling history, and environmental sensors, and automatically generating state variables for scheduling solutions. Through system structure modeling and construction process analysis, this module constructs the basic physical and behavioral framework of system operation, providing a unified data foundation for subsequent control optimization and feedback mechanisms.

[0300] The control solution module calculates the optimal control scheduling trajectory based on the state space provided by the model building module and the task objectives (such as minimum duration and minimum energy consumption). The module integrates a scheduling strategy based on optimality conditions, enabling continuous planning of control inputs within a time period. During the control solution process, the system dynamically adjusts the trajectory solution path based on current task priority, platform availability, and other information. This module emphasizes timeliness and engineering adaptability, ensuring that the theoretically optimal solution is practically feasible.

[0301] The constraint optimization module is used to embed various constraints from real-world construction scenarios, such as maximum equipment load, task time windows, platform scheduling capacity, and carbon emission limits, as hard or soft constraints in the optimization problem. The module supports modeling at multiple constraint levels and has the capability to set differentiated constraints for different resource types (such as machinery, labor, and energy). This module can work in conjunction with the control solver module to detect and correct scheduling paths that do not meet constraints in real time when optimizing the control trajectory, ensuring high executability of the output results and avoiding problems such as resource conflicts, schedule delays, or carbon emission violations.

[0302] The robust feedback module monitors and responds to external disturbances that may occur during actual execution. During operation, the system reads equipment status and environmental data in real time, identifies potential risks of deviating from the planned trajectory, and adjusts accordingly based on preset control strategies. The module incorporates robust control logic, which can quickly invoke adjustment strategies upon detecting disturbances, enabling fine-tuning of the scheduling trajectory. It is particularly suitable for uncontrollable factors commonly encountered in on-site construction, such as sudden task insertions, equipment response delays, and temporary resource unavailability. This module significantly enhances the system's dynamic adaptability and operational stability.

[0303] The scheduling and execution module is responsible for converting the optimized and corrected control trajectory into task instructions that can be executed by the platform. The system supports communication protocol integration with on-site construction equipment, enabling the issuance of specific machinery operation commands, resource scheduling instructions, and personnel task reminders. The module has task execution status tracking capabilities, synchronously collecting equipment feedback to achieve closed-loop task execution. The scheduling and execution module supports data interaction and anomaly feedback mechanisms with the main control system. When scheduling fails to complete or anomalies are reported on-site, it can automatically send back data to trigger a robust module for further correction, forming a complete scheduling control closed loop.

[0304] The device in this embodiment can be used to execute the above method embodiments, and its principle and technical effects are similar, so they will not be described again here.

[0305] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A low-carbon, energy-saving, and intelligent factory construction method, characterized in that, Includes the following steps: S1. Establish the state-space model of the construction system; S2. Construct system dynamics and carbon emission objective functions based on the state-space model; S3. Solve for the optimal resource scheduling trajectory that minimizes carbon emissions using the Hamiltonian system principle and the Pontryagin maximum principle. S4. Introduce construction constraints and optimize the optimal resource scheduling trajectory using the Lagrange multiplier method; S5. Construct a feedback control mechanism and introduce the Lyapunov function to ensure the stability and robustness of the system under external disturbance conditions.

2. The low-carbon, energy-saving-oriented intelligent factory construction method according to claim 1, characterized in that, The establishment of the state-space model includes: Collect construction node information Construct a task dependency graph based on the process flow; Configure the types of resources required for each node The corresponding initial inventory With maximum consumption limit ; Extracting carbon emission factors from various resources Constructing a total carbon emission boundary ; The state vector is defined as ,in Indicates the first A state variable in time The value of .

3. The low-carbon, energy-saving-oriented intelligent factory construction method according to claim 1, characterized in that, Step S2 includes: S2.1, Define the control vector ,in Indicates the first Class resources at any time The delivery rate; S2.2, The system dynamics model is established as follows: ； in: This is the system state vector; Input for resource scheduling; The task topology matrix, Resource efficiency matrix; This represents the external disturbance vector.

4. The low-carbon, energy-saving-oriented intelligent factory construction method according to claim 3, characterized in that, The carbon emission objective function is defined as follows: ； in: The objective function is carbon emissions; This refers to the total duration of the construction period; Control cost weight matrix; This is the state cost weight matrix; It is a state vector; For real-time resource access.

5. The low-carbon, energy-saving-oriented intelligent factory construction method according to claim 1, characterized in that, Step S3 includes the following three sub-steps: S3.1 Constructing the Hamiltonian function: ； in: It is a companion variable. It is a state vector; For control input; External disturbance; Here is the state transition matrix. To control the input matrix; S3.2, Define the accompanying variable The dynamic equation: ； in, For Hamiltonian, The changes are obtained through optimality conditions and dynamic equations; S3.3, Construct optimality conditions such that Thus, the control input is derived.

6. The low-carbon, energy-saving-oriented intelligent factory construction method according to claim 5, characterized in that, The control input The optimal solution is defined as: ； in: For optimal control input; These are costate variables.

7. The low-carbon, energy-saving-oriented intelligent factory construction method according to claim 5, characterized in that, The costate variable Solve the following boundary value problem: ； in: For state variables, For costate variables; External disturbance; For control input; Here is the state transition matrix. To control the input matrix.

8. The low-carbon, energy-saving-oriented intelligent factory construction method according to claim 1, characterized in that, Step S4 includes the following three sub-steps: S4.1 sets the total construction time, the upper limit of node resource usage, and the platform equipment capacity as constraints; S4.2, Construct the Lagrangian function to introduce the constraints into the objective function; S4.3 Optimize the control trajectory based on the Karush-Kuhn-Tucker conditions.

9. The low-carbon, energy-saving-oriented intelligent factory construction method according to claim 1, characterized in that, Step S5 includes the following three sub-steps: S5.1, Constructing Lyapunov functions: ； in It is a positive definite matrix; This is the system state vector; S5.2, Design Feedback Control Items: ； in This is the feedback gain matrix; S5.3, Final Control Input: ； in, The control input is corrected through feedback control; This is the optimal control input.

10. A low-carbon, energy-saving-oriented intelligent factory construction system, applied to the low-carbon, energy-saving-oriented intelligent factory construction method according to any one of claims 1-9, characterized in that, include: The model building module is used to construct the state space and dynamic equations of the construction system. The control solution module is used to calculate the control trajectory based on the Hamiltonian system and optimality conditions. The constraint optimization module is used to apply resource and time constraints and perform optimization. The robust feedback module is used for constructing and controlling Lyapunov functions under disturbances. The scheduling and execution module is used to convert control trajectories into platform task instructions and drive field equipment to execute them.

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