An iterative learning control method based on master-slave architecture

Abstract

The application discloses an iterative learning control method based on master-slave architecture, and relates to the technical field of automatic control, which comprises the following steps: establishing a system energy optimal control problem model according to the dynamic model of a master system and a slave system, a relative reference path and system constraint conditions, obtaining system model parameters, a relative reference path signal, an uncertainty boundary and noise covariance information; adopting an alternating direction multiplier method to perform iterative optimization on the relative reference path signal, a feedback gain matrix and a master system tracking error boundary, synchronously updating slave system control input and a master system reference trajectory and judging convergence, and obtaining optimal slave system control input and the master system reference trajectory. The application introduces the alternating direction multiplier method to perform iterative optimization, decomposes a complex optimization problem into sub-problems which can be solved in parallel, improves calculation efficiency, and guarantees strict satisfaction of constraint conditions through projection transformation and a dual variable updating mechanism.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology, and in particular to an iterative learning control method based on a master-slave architecture. Background Technology

[0002] In the field of automatic control, multi-agent system cooperative control technology has made significant progress in recent years, especially in applications such as UAV swarms and collaborative operations of industrial robots. Existing technologies mainly focus on distributed consensus protocols and cooperative tracking algorithms, achieving synchronization and coordination of group behavior by designing control laws based on local information. Mainstream methods include graph-based multi-agent cooperative frameworks, distributed model predictive control strategies, and adaptive robust control algorithms. These technologies can achieve good tracking performance and stability under ideal conditions.

[0003] However, existing technologies have significant limitations in dealing with uncertainties in practical engineering: First, most studies focus on tracking accuracy and stability assurance, lacking comprehensive consideration of system energy consumption optimization, making it difficult to achieve energy-efficient utilization while ensuring performance; Second, existing control strategies are insufficient in robust handling of model uncertainties and external disturbances, often employing conservative robust design methods that lead to decreased control performance, or lacking quantitative analysis of the statistical characteristics of random noise, making it impossible to establish accurate error boundary estimates. Summary of the Invention

[0004] In view of the aforementioned existing problems, the present invention is proposed.

[0005] Therefore, this invention provides an iterative learning control method based on a master-slave architecture to solve the problem that it is difficult to balance tracking accuracy and energy consumption optimization in the collaborative control of master-slave systems under conditions of model uncertainty, random noise interference, and energy constraints.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] In a first aspect, the present invention provides an iterative learning control method based on a master-slave architecture, comprising:

[0008] Based on the dynamic models of the master system and slave system, the relative reference path, and the system constraints, a model for the optimal energy control problem of the system is established, and the system model parameters, relative reference path signals, uncertainty boundaries, and noise covariance information are obtained.

[0009] By utilizing system model parameters, uncertainty boundaries, and noise covariance information, a robust feedback control law for the main system is established by solving a semidefinite programming problem, thereby obtaining the feedback gain matrix and the tracking error boundary of the main system.

[0010] For the relative reference path signal, feedback gain matrix and master system tracking error boundary, the alternating direction multiplier method is used for iterative optimization. The slave system control input and master system reference trajectory are updated synchronously and the convergence is judged to obtain the optimal slave system control input and master system reference trajectory.

[0011] The optimal control input of the slave system and the reference trajectory of the master system are applied to the slave system and the master system respectively. The system output is monitored in real time and the tracking error is calculated. Based on the error evaluation results, it is decided whether to restart the iterative optimization process.

[0012] As a preferred embodiment of the iterative learning control method based on a master-slave architecture described in this invention, the establishment of the system energy optimal control problem model includes the following steps:

[0013] Based on the state-space equations of the master system and the slave system, system model parameters including the system matrix, input matrix, and output matrix are defined.

[0014] Determine the statistical characteristics of process disturbances and measurement noise, and set uncertainty boundaries and energy consumption constraints for the main system control input;

[0015] Based on the tracking requirement of the output difference between the master and slave systems defined by the relative reference path, an optimal control problem model is constructed with the objective function of minimizing the total energy consumption of the master and slave systems and the system dynamics equations and tracking error requirements as constraints.

[0016] As a preferred embodiment of the iterative learning control method based on a master-slave architecture described in this invention, the step of setting the robust feedback control law of the master system includes the following steps.

[0017] By utilizing the system model parameters, uncertainty boundaries, and statistical characteristics of noise, the main system tracking control problem is transformed into a semidefinite programming problem.

[0018] By solving a semidefinite programming problem, the feedback gain matrix that makes the control input of the main system linearly related to the reference trajectory is obtained;

[0019] The tracking error boundary of the main system is determined based on the statistical characteristics of noise.

[0020] As a preferred embodiment of the iterative learning control method based on a master-slave architecture described in this invention, the iterative optimization of the relative reference path signal, feedback gain matrix, and master system tracking error boundary using the alternating direction multiplier method includes the following steps.

[0021] Using the relative reference path signal, feedback gain matrix, and master system tracking error boundary as inputs, initialize the master system reference trajectory, slave system control input, and dual variables;

[0022] In each iteration, the slave system control input, master system reference trajectory, and auxiliary variables are updated sequentially;

[0023] The tracking error constraint is processed by projection transformation, and the dual variables are updated to output the optimal slave system control input and master system reference trajectory.

[0024] As a preferred embodiment of the iterative learning control method based on master-slave architecture described in this invention, the update of the slave system control input refers to obtaining a new control input that reduces the objective function and satisfies the slave system dynamic constraints by solving a regularized least squares problem based on the current master system reference trajectory, auxiliary variables, and dual variable values.

[0025] As a preferred embodiment of the iterative learning control method based on master-slave architecture described in this invention, the update of the master system reference trajectory refers to obtaining a new reference trajectory that reduces the objective function and satisfies the energy consumption constraints of the master system by using the feedback gain matrix and the currently updated slave system control input, auxiliary variables and dual variable values, and solving an optimization problem with regularization terms.

[0026] As a preferred embodiment of the iterative learning control method based on master-slave architecture described in this invention, the update of the auxiliary variable refers to substituting the currently updated slave system control input and master system reference trajectory into the tracking error expression, and constraining the auxiliary variable within the allowable error range through projection transformation, as the relative path tracking accuracy requirement.

[0027] As a preferred embodiment of the master-slave architecture-based iterative learning control method described in this invention, the convergence determination includes the following steps:

[0028] After each update of the system control input, the main system reference trajectory, and auxiliary variables, the expected value of the current relative tracking error is calculated.

[0029] The current expected value of the relative tracking error is compared with the preset accuracy threshold to determine whether to continue iterative optimization or terminate the optimization.

[0030] As a preferred embodiment of the master-slave architecture-based iterative learning control method of the present invention, the step of determining whether to restart the iterative optimization process based on the error evaluation result includes the following steps.

[0031] The optimal slave system control input and master system reference trajectory are applied to the slave system and master system respectively, and the actual output signals of the master and slave systems are continuously monitored.

[0032] The real-time relative tracking error is calculated based on the monitored actual output signal; the real-time relative tracking error is compared with a preset accuracy threshold, and a decision is made on whether to restart the iterative optimization process based on the comparison result.

[0033] As a preferred embodiment of the iterative learning control method based on master-slave architecture described in this invention, the restart of the iterative optimization process refers to using the current system operating state as a new initial condition, re-executing the alternating direction multiplier method optimization process using the feedback gain matrix and error boundary parameters, and generating the optimal slave system control input and master system reference trajectory adapted to the new environmental conditions.

[0034] The beneficial effects of this invention are as follows: By establishing an accurate energy-optimal control problem model, the tracking accuracy requirement is transformed into mathematical constraints, achieving joint optimization of performance indicators and energy consumption indicators, and ensuring that the system minimizes energy consumption while meeting the preset accuracy requirements; a robust feedback control law is designed using a semidefinite programming method, and system uncertainties and noise interference are handled through linear matrix inequalities, significantly enhancing the robustness of the system and ensuring control stability under the presence of model bias and external disturbances; the alternating direction multiplier method is introduced for iterative optimization, decomposing the complex optimization problem into subproblems with multiple variables, which not only improves computational efficiency but also ensures strict satisfaction of constraints through projection transformation and dual variable update mechanisms. Attached Figure Description

[0035] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 This is a flowchart of an iterative learning control method based on a master-slave architecture.

[0037] Figure 2 This is a flowchart for iterative optimization of system control and main system trajectory.

[0038] Figure 3 The flowchart for the convergence judgment logic of iterative optimization.

[0039] Figure 4 Flowchart for system operation monitoring and adaptive optimization restart mechanism. Detailed Implementation

[0040] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0041] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0042] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0043] Reference Figures 1-4 This is one embodiment of the present invention, which provides an iterative learning control method based on a master-slave architecture, including the following steps:

[0044] S1. Based on the dynamic models of the master system and slave system, the relative reference path, and the system constraints, establish a model for the optimal energy control problem of the system, and obtain the system model parameters, relative reference path, uncertainty boundary, and noise covariance information.

[0045] S1.1. Based on the state-space equations of the master system and the slave system, define system model parameters including the system matrix, input matrix, and output matrix.

[0046] Furthermore, the state-space equations of the main system are defined as follows:

[0047] ;

[0048] ;

[0049] Wherein, the superscript 1 represents the main system, and the subscript... Indicates the number of iterations. Indicates a time index. , and These represent the master-slave system in The state at any given moment, the input signal, and the output signal. The input signal is the raw signal entering the main system, and the output signal is the processed signal generated by the main system. The specific form depends on the system being applied. This represents the main system matrix, used to describe the evolution of the system state. This represents the main system input matrix, used to characterize the influence of control inputs on the state. This represents the main system output matrix, used to map internal states to observable outputs. Indicates in Interference during a given process refers to external, uncontrollable input signals that disrupt system stability. Indicates in Measurement noise at any given time, i.e., sensor measurement error;

[0050] The state-space equation of the system is defined as follows:

[0051] ;

[0052] ;

[0053] The superscript 1 indicates from the system. Indicates from the system matrix, This represents the input matrix from the system. This represents the matrix output from the system.

[0054] It should be noted that by accurately establishing the state-space equations of the master-slave system and clarifying the parameterized representations of the system matrix, input matrix, and output matrix, it is possible to accurately describe the system state evolution law, the influence of control input on the state, and the mapping relationship from internal state to observable output.

[0055] S1.2. Determine the statistical characteristics of process disturbances and measurement noise, and set uncertainty boundaries and main system control input energy consumption constraints.

[0056] Furthermore, based on the state-space equations of the master and slave systems, the statistical characteristics of process disturbances and measurement noise are determined. It is assumed that both process disturbances and measurement noise are zero-mean random processes with covariance matrices of... , used to quantify the statistical properties of noise;

[0057] The uncertainty boundary of the system model is set as ,in Indicates system uncertainty. This represents the upper bound of uncertainty, used to describe the range of deviation between the system model and the actual system, while also setting the main system control input to satisfy... The energy consumption constraints, among which This is the upper limit for energy consumption, used to limit the energy consumption of the main system;

[0058] Based on the defined noise characteristics and uncertainty boundaries, a relative reference path is defined. The relative reference path defines the desired relative motion trajectory between the master and slave systems, and establishes tracking accuracy requirements, requiring the master and slave systems to output the difference. Track the relative reference path.

[0059] It should be noted that by determining the statistical characteristics of process disturbances and measurement noise, a quantitative basis is provided for the anti-interference design of the system. Setting the uncertainty boundary of the model can effectively describe the deviation range between the system model and the actual system, and enhance the robustness of the control algorithm. At the same time, setting the energy consumption constraint of the main system control input ensures the energy consumption optimization characteristics of the system from the source. Defining the relative reference path and establishing the tracking accuracy requirements provides a clear control objective for the system.

[0060] S1.3. Based on the relative reference path, define the tracking accuracy requirement of the output difference between the master and slave systems, and construct an optimal control problem model with the objective function of minimizing the total energy consumption of the master and slave systems and the system dynamic equations and tracking error requirements as constraints.

[0061] Furthermore, based on the established tracking requirements and energy consumption constraints, an energy-optimal control problem model is constructed, with the objective function being to minimize the total energy consumption of the master-slave system. The expression for the objective function is as follows:

[0062] ;

[0063] in, This indicates the system's energy consumption. Indicates the main system energy consumption. Indicates the reference trajectory of the main system. This indicates the control input signal from the system;

[0064] Based on the objective function, we introduce the output equations of the master system, the output equations of the slave system, and the energy consumption constraint for tracking accuracy requirements, expressed as follows:

[0065] ;

[0066] ;

[0067] ;

[0068] in, Represents the main system transfer matrix. This represents the combined disturbance term. This represents the ideal output reference trajectory from the system. This represents the matrix transferred from the system. It represents the expected value of a random variable. The preset accuracy threshold is set based on task requirements, system capabilities, and disturbance levels. It is a dimensionless or positive real number with specific physical units. There is no universal value for the specific value; it depends entirely on the actual application scenario, the characteristics of the system itself (the strength of uncertainty, the magnitude of noise), and the degree of energy consumption limitation.

[0069] By solving the energy-optimal control problem model, the optimal combination of solutions that minimizes the objective function is determined, and the output includes the initial settings of the master-slave system model parameters, relative reference path signal, uncertainty boundary and noise covariance information.

[0070] It should be noted that constructing an optimization problem with minimizing the total energy consumption of the master-slave system as the objective function directly reflects the energy optimization design concept of the system. By introducing multiple constraints such as the output equation of the master system, the output equation of the slave system, and the tracking accuracy requirements, multiple considerations of system dynamics, tracking performance, and energy consumption optimization are achieved.

[0071] S2. Using system model parameters, uncertainty boundaries, and noise covariance information, a robust feedback control law for the main system is established by solving a semidefinite programming problem, thereby obtaining the feedback gain matrix and the tracking error boundary of the main system.

[0072] Furthermore, based on the master-slave system model parameters, uncertainty boundaries, and noise covariance information, the master system tracking control problem is transformed into a semidefinite programming problem. The core of this transformation is to reformulate the problem of setting the robust feedback control law into a mathematical framework solvable by convex optimization methods, with the goal of finding the minimized scalar. The solution must satisfy a set of linear matrix inequality constraints, specifically including:

[0073] ;

[0074] ;

[0075] ;

[0076] in, This represents the objective variable, an auxiliary scalar. The value that is ultimately minimized represents the degree to which the overall control problem's optimization objective (in this case, an upper bound on control performance) is achieved. After solving, The specific numerical value is usually not the focus; the focus is on the solutions for other variables. The feedback gain matrix, representing the core objective of the entire optimization problem, is used to construct a robust feedback control law that directly linearly correlates the control input with the reference trajectory. and The auxiliary optimization variable is a slack variable or auxiliary scalar introduced to transform the robust feedback control problem into the standard form of SDP. It has no direct physical meaning in itself, but it is crucial for constructing and solving constraints. This represents the upper bound of the energy consumption constraint, which is the maximum energy allowed for the main system control input. express The vectorized form of the feedback gain matrix serves to transform the feedback gain matrix. Applying this constraint, This indicates the transpose operation. Represents the identity matrix, with dimensions AND Dimensional matching, The nominal transfer matrix of the main system is derived from the derivation or identification of the main system model and is an ideal model of the main system when no disturbance occurs.

[0077] By numerically solving the transformed semidefinite programming problem, the control input of the main system can be obtained. Compared with reference trajectory Feedback gain matrix to achieve linear correlation;

[0078] Based on the determined noise statistical characteristics (covariance matrix) and the solved feedback gain matrix, the statistical boundary of the main system tracking error is analyzed and determined to ensure that the main system tracking error is bounded in the mathematical expectation sense, that is, it satisfies... This allows the main system output to be characterized as the superposition of the reference trajectory and a bounded error term, i.e. ,in, This represents the tracking error vector of the main system. This represents the mathematical expectation of the norm of the main system tracking error. It represents a definite, non-random positive real constant, serving as the theoretical upper bound of the expected value of the error norm.

[0079] It should be noted that formulating the complex robust feedback controller setup problem into a standard mathematical framework solvable by convex optimization methods fundamentally guarantees the global convergence and computational efficiency of the solution process. By handling system uncertainties through linear matrix inequality constraints, the potential pitfalls of traditional methods in getting stuck in local optima are effectively avoided, providing reliable mathematical guarantees for controller design. The feedback gain matrix is ​​obtained by numerically solving a semidefinite programming problem, achieving a linear correlation between the control input and the reference trajectory. This robust feedback control law design significantly simplifies the controller's implementation structure while ensuring system stability and response characteristics. The solution process for the feedback gain matrix fully considers system model parameters, uncertainty boundaries, and noise statistics, ensuring the controller's robust performance under conditions of model bias and external disturbances.

[0080] S3. For the relative reference path signal, feedback gain matrix and master system tracking error boundary, iterative optimization is performed using the alternating direction multiplier method. The slave system control input and master system reference trajectory are updated synchronously and convergence is judged to obtain the optimal slave system control input and master system reference trajectory.

[0081] S3.1. Using the relative reference path signal, feedback gain matrix, and master system tracking error boundary as inputs, set the number of iterations, give the initial master system reference trajectory and initial slave system control input, and initialize the dual variables and auxiliary variables.

[0082] S3.2. Based on the current main system reference trajectory, auxiliary variables, and dual variables, the control input from the system is updated by solving a regularized least squares problem. The update formula is:

[0083] ;

[0084] in, Indicates the first In each iteration, the control input signal of the system is... This represents the penalty parameter, used to adjust the degree to which the constraint condition is satisfied. The higher the value, the greater the penalty for violating the constraint. Indicates the first The Lagrange multiplier vector after each iteration, i.e., the dual variable, contains information about historical constraint violations and is used to drive the solution to satisfy the constraints. Indicates the first The auxiliary variables introduced after the next iteration are used to decouple complex constraints and typically represent an approximation of the tracking error. Indicates the first The main system reference trajectory after the next iteration.

[0085] S3.3. Using the feedback gain matrix and the currently updated slave system control input, auxiliary variables, and dual variables, update the master system reference trajectory by solving an optimization problem with a regularization term. The update formula is:

[0086] ;

[0087] in, Indicates the first The reference trajectory of the main system in the next iteration is the updated reference trajectory of the main system.

[0088] S3.4. Substitute the updated slave system control input and the updated master system reference trajectory into the tracking error expression, and update the auxiliary variables through projection transformation. The expression is:

[0089] ;

[0090] in, Indicates the first Auxiliary variables after the next iteration This represents the projection operator, which projects all the contents within the parentheses onto a convex set. Its purpose is to ensure that the updated auxiliary variables always satisfy the boundary constraints of the tracking error.

[0091] S3.5. Based on the currently updated auxiliary variables, the currently updated slave system control inputs, and the currently updated master system reference trajectory, update the dual variables using the following formula:

[0092] ;

[0093] in, Indicates the first The dual variable after the next iteration.

[0094] S3.6. After each update of the system control input, the main system reference trajectory, and auxiliary variables, calculate the expected value of the current relative tracking error for the iteration. The current expected value of the relative tracking error is compared with the preset accuracy threshold to determine whether it meets the requirements. If the termination condition is not met, return to step S3.2 to continue the next round of iteration optimization; if the termination condition is met, terminate the optimization process and output the current control input and reference trajectory as the optimal solution.

[0095] It should be noted that decomposing the complex joint optimization problem into subproblems with multiple variables allows for simultaneous optimization of the main system reference trajectory and the slave system control input, improving overall optimization efficiency. The application of projection transformation ensures that auxiliary variables always meet preset accuracy requirements, thus rigidly guaranteeing the optimality and feasibility of the solution. The gradient ascent update strategy for dual variables effectively penalizes constraint violations, driving the optimal solution to converge towards the feasible region. When system parameters or the operating environment change, simply restarting the optimization process with the current state quickly generates a new optimal solution. The dynamic update mechanism of the main system reference trajectory overcomes the limitations of traditional fixed trajectories, creating optimization space for reducing overall energy consumption. Cooperative optimization of the slave system control input ensures the minimization of total system energy consumption while satisfying relative tracking accuracy.

[0096] S4. Apply the optimal slave system control input and master system reference trajectory to the slave system and master system respectively, monitor the system output in real time and calculate the tracking error, and decide whether to restart the iterative optimization process based on the error evaluation results.

[0097] S4.1. Continuously apply control input to the slave system. The master system, based on the robust feedback control law in S2, sets a reference trajectory, generates the final control input, and drives the master system to run. During the operation of the master and slave systems, continuously monitor the actual output signals of the master system and the slave system. Based on the monitored actual output signals, calculate the real-time relative tracking error between the master and slave systems. Compare the real-time relative tracking error with a preset accuracy threshold. The comparison process is continuous and aims to evaluate whether the current control performance continuously meets the accuracy requirements of the preset accuracy threshold.

[0098] S4.2. If the real-time relative tracking error is less than or equal to the preset accuracy threshold, the currently applied optimal slave system control input and master system reference trajectory are maintained, and the system continues to operate; if environmental changes, increased disturbances, or component aging cause the real-time relative tracking error to exceed the preset accuracy threshold, the control strategy update mechanism is triggered, and the iterative optimization process is restarted.

[0099] S4.3. When the restart of the iterative optimization process is triggered, the current operating state of the master and slave systems is used as the new initial conditions. The obtained feedback gain matrix and the master system tracking error boundary are used to re-execute the alternating direction multiplier method optimization process to generate the optimal slave system control input and master system reference trajectory adapted to the new environmental conditions.

[0100] S4.4. Apply the optimal slave system control input and master system reference trajectory adapted to the new environmental conditions to the slave system and master system respectively, and re-enter the real-time monitoring loop to ensure that the control strategy can be adjusted and updated online when the dynamic characteristics of the master and slave systems or the external working environment change, continuously ensuring that the relative path tracking accuracy meets the requirements, and significantly reducing the total energy consumption while meeting the accuracy requirements.

[0101] It should be noted that by comparing the relative tracking error with the preset accuracy threshold in real time, the system can promptly detect performance degradation caused by factors such as environmental changes, increased disturbances, or component aging. Once the error exceeds the threshold, a re-optimization process is immediately triggered, using the current operating state as a new initial condition to regenerate the control strategy. This gives the system a strong adaptive capability, enabling it to effectively cope with various uncertainties and maintain stable control performance.

[0102] This embodiment also provides a computer device applicable to the iterative learning control method based on a master-slave architecture, comprising: a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the iterative learning control method based on a master-slave architecture as proposed in the above embodiment.

[0103] The computer device can be a terminal, comprising a processor, memory, communication interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0104] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements the iterative learning control method based on a master-slave architecture as proposed in the above embodiments. The storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read Only Memory (EPROM), Programmable Red-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk.

[0105] In summary, this invention establishes a precise energy-optimal control problem model, transforming the tracking accuracy requirement into mathematical constraints, thereby achieving joint optimization of performance and energy consumption indicators. This ensures that the system minimizes energy consumption while meeting the preset accuracy requirements. A robust feedback control law is designed using semidefinite programming, and system uncertainties and noise interference are handled through linear matrix inequalities, significantly enhancing the system's robustness and ensuring control stability even with model bias and external disturbances. The introduction of the alternating direction multiplier method for iterative optimization decomposes the complex optimization problem into subproblems with multiple variables, improving computational efficiency and ensuring strict constraint satisfaction through projection transformation and dual variable update mechanisms.

[0106] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. An iterative learning control method based on a master-slave architecture, characterized in that: include, Based on the dynamic models of the master system and slave system, the relative reference path, and the system constraints, a model for the optimal energy control problem of the system is established, and the system model parameters, relative reference path signals, uncertainty boundaries, and noise covariance information are obtained. By utilizing system model parameters, uncertainty boundaries, and noise covariance information, a robust feedback control law for the main system is established by solving a semidefinite programming problem, thereby obtaining the feedback gain matrix and the tracking error boundary of the main system. For the relative reference path signal, feedback gain matrix and master system tracking error boundary, the alternating direction multiplier method is used for iterative optimization. The slave system control input and master system reference trajectory are updated synchronously and the convergence is judged to obtain the optimal slave system control input and master system reference trajectory. The iterative optimization of the relative reference path signal, feedback gain matrix, and main system tracking error boundary using the alternating direction multiplier method includes the following steps. Using the relative reference path signal, feedback gain matrix, and master system tracking error boundary as inputs, initialize the master system reference trajectory, slave system control input, and dual variables; In each iteration, the slave system control input, master system reference trajectory, and auxiliary variables are updated sequentially; The tracking error constraint is processed by projection transformation, and the dual variables are updated to output the optimal slave system control input and master system reference trajectory. The optimal control input of the slave system and the reference trajectory of the master system are applied to the slave system and the master system respectively. The system output is monitored in real time and the tracking error is calculated. Based on the error evaluation results, it is decided whether to restart the iterative optimization process.

2. The iterative learning control method based on a master-slave architecture as described in claim 1, characterized in that: The steps involved in establishing the system's optimal energy control problem model are as follows: Based on the state-space equations of the master system and the slave system, system model parameters including the system matrix, input matrix, and output matrix are defined. Determine the statistical characteristics of process disturbances and measurement noise, and set uncertainty boundaries and energy consumption constraints for the main system control input; Based on the tracking requirement of the output difference between the master and slave systems defined by the relative reference path, an optimal control problem model is constructed with the objective function of minimizing the total energy consumption of the master and slave systems and the system dynamics equations and tracking error requirements as constraints.

3. The iterative learning control method based on a master-slave architecture as described in claim 1, characterized in that: The process of setting the robust feedback control law for the main system includes the following steps. By utilizing the system model parameters, uncertainty boundaries, and statistical characteristics of noise, the main system tracking control problem is transformed into a semidefinite programming problem. By solving a semidefinite programming problem, the feedback gain matrix that makes the control input of the main system linearly related to its reference trajectory is obtained; The tracking error boundary of the main system is determined based on the statistical characteristics of noise.

4. The iterative learning control method based on a master-slave architecture as described in claim 1, characterized in that: The updated control input refers to obtaining a new control input that reduces the objective function and satisfies the dynamic constraints of the slave system by solving a regularized least squares problem based on the current master system reference trajectory, auxiliary variables, and dual variable values.

5. The iterative learning control method based on a master-slave architecture as described in claim 1, characterized in that: The update of the master system reference trajectory refers to using the feedback gain matrix and the currently updated slave system control input, auxiliary variables and dual variable values ​​to solve an optimization problem with regularization terms, thereby obtaining a new reference trajectory that reduces the objective function and satisfies the master system energy consumption constraints.

6. The iterative learning control method based on a master-slave architecture as described in claim 1, characterized in that: The update of the auxiliary variables refers to substituting the updated slave system control input and master system reference trajectory into the tracking error expression, and constraining the auxiliary variables within the allowable error range through projection transformation, which serves as the relative path tracking accuracy requirement.

7. The iterative learning control method based on a master-slave architecture as described in claim 1, characterized in that: The convergence determination includes the following steps. After each update of the system control input, the main system reference trajectory, and auxiliary variables, the expected value of the current relative tracking error is calculated. The current expected value of the relative tracking error is compared with the preset accuracy threshold to determine whether to continue iterative optimization or terminate the optimization.

8. The iterative learning control method based on a master-slave architecture as described in claim 1, characterized in that: The decision on whether to restart the iterative optimization process is based on the error assessment results. Includes the following steps, The optimal slave system control input and master system reference trajectory are applied to the slave system and master system respectively, and the actual output signals of the master and slave systems are continuously monitored. Calculate the real-time relative tracking error based on the monitored actual output signal; The real-time relative tracking error is compared with a preset accuracy threshold, and the comparison result determines whether to restart the iterative optimization process.

9. The iterative learning control method based on a master-slave architecture as described in claim 1, characterized in that: The restart iterative optimization process refers to using the current system operating state as a new initial condition, and re-executing the alternating direction multiplier method optimization process using the feedback gain matrix and error boundary parameters to generate the optimal slave system control input and master system reference trajectory adapted to the new environmental conditions.

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