Optimal output tracking control method and system based on fixed convergence speed

Abstract

The application provides an optimal output tracking control method and system based on a fixed convergence speed, and relates to the technical field of industrial process control. A dynamic controller is designed for a linear continuous-time system to generate a control signal, output tracking target trajectory control, and a dynamic error linear system with a fixed convergence speed is constructed. A behavior strategy is designed to operate a dynamic system, and the state of the dynamic system is reconstructed by using input data and output data. The data collected by the behavior strategy applied to the reconstructed dynamic system is iteratively calculated to obtain optimal control gain, and the output of the linear continuous-time system model tracks the target trajectory by using the control signal based on the optimal control gain. The method expands the optimal output tracking control method to linear systems, and the setting of the fixed convergence speed accelerates the convergence of the system, avoids disturbance from external factors, and is beneficial to the smooth progress of industrial production processes.

Description

Technical Field

[0001] This invention relates to the technical field of industrial process control, and more specifically, to an optimal output tracking control method and system based on a fixed convergence rate. Background Technology

[0002] When designing controllers for modern industrial production, it is generally desirable for the output of the controlled system to accurately track the desired trajectory. In actual industrial production processes, this problem is often simplified to an output regulation problem for analysis and solution. The regulation objectives typically include: regulating a stable controller so that the output signal is asymptotically stable within a given reference trajectory error and can overcome the effects of disturbances from external systems. However, solving the output regulation problem usually requires precise knowledge of the system's state parameters, which are often difficult to measure due to the complexity of modern production processes. Therefore, it is desirable to find the optimal control strategy by measuring the system's output information.

[0003] The development of Reinforcement Learning (RL) and Adaptive Dynamic Programming (ADP) theories is of great significance for solving model-free optimal output tracking problems. RL is a machine learning strategy that learns optimal actions or control policies by continuously adjusting actions based on specified rewards through interaction between the agent and the environment. In the absence of an accurate model of the environment or system, ADP approximates the performance index function and control policy in the structure-approximate dynamic programming equations through functional approximation. The emergence of these control algorithms makes it possible to solve optimal control problems without relying on accurate system dynamics, thus expanding the application scope of these techniques.

[0004] Many existing algorithms rely heavily on state feedback learning methods. These methods typically assume access to complete measurements of the system state, which is not always feasible in some engineering scenarios. Furthermore, most learning designs do not consider convergence speed, making the control system more susceptible to disturbances and exhibiting poor stability. To overcome these problems, existing technologies disclose an optimal tracking control method and system with a specified convergence speed. First, a linear discrete-time multi-input multi-output (MIMO) control system model is established, an initial regulator and an initial controller are set, and the Sylvester map of the initial regulator is obtained. A virtual control strategy with a specified convergence speed is added to the established model. Historical data of the MIMO control system model with the added virtual control strategy is collected. Based on the acquired historical data, the initial regulator and initial controller are optimized. Based on the optimized regulator and controller, the optimal tracking controller is obtained, and tracking control is applied to the MIMO control system model. This existing technology, based on data-driven optimal controller design, is applicable to dynamically unknown systems, has a wider range of applications, and can stably track a specified signal while ensuring that the convergence speed of the system output meets requirements during transient response. However, existing technologies only offer methods for solving the tracking control problem of discrete systems. Furthermore, these methods require controller design based on the system's recordable state variables. In many real-world physical control systems, the inherent dynamic characteristics are inherently continuously changing, and intermediate state variables are difficult to measure. For example, in complex chemical reactors, large generator sets, or aircraft engines, engineers can typically only measure some of the system's outputs (such as temperature, speed, and pressure) and inputs, but cannot obtain all the internal state variables that describe the complete dynamics of the system. Summary of the Invention

[0005] To address the problem that existing optimal output tracking control methods in industrial production processes are only applicable to discrete systems and are easily affected by external factors, this invention proposes an optimal output tracking control method and system based on a fixed convergence rate. This applies the optimal output tracking control method to linear systems, improving system stability and ensuring the smooth operation of industrial production processes.

[0006] To achieve the above-mentioned technical effects, the technical solution of the present invention is as follows:

[0007] In the first aspect, this application proposes an optimal output tracking control method and system based on a fixed convergence rate, comprising the following steps:

[0008] S1. Based on the established linear continuous-time system model and target trajectory model, design a dynamic tracking controller, and use the dynamic controller to generate control signals so that the output of the linear continuous-time system model tracks the target trajectory;

[0009] S2. Construct a dynamic error linear system model for tracking the target trajectory, and incorporate a fixed convergence rate into the dynamic error linear system model;

[0010] S3. Design a behavioral strategy for the dynamic error linear system model. Based on the behavioral strategy and the linear continuous-time system model, design a dynamic system model. Use the input data generated by the behavioral strategy to run the dynamic system model and obtain the output data.

[0011] S4. Reconstruct the state of the dynamic system model using input-output data;

[0012] S5. Use the behavior strategy to run the reconstructed dynamic system model, obtain the output data of the dynamic system model, input the output data of the dynamic system model into the constructed calculation equation based on the optimal control gain, and iteratively calculate to obtain the optimal control gain;

[0013] S6. Generate a control signal based on the optimal control gain, and use the control signal to make the output of the linear continuous-time system model track the target trajectory.

[0014] In this technical solution, a dynamic controller is first designed for the linear continuous-time system to generate control signals and output tracking target trajectory control. A dynamic error linear system design behavior strategy incorporating a fixed convergence rate is constructed to operate the dynamic system, and the state of the dynamic system is reconstructed using its input-output data. The behavior strategy is then applied again to the reconstructed dynamic system to collect data, and the optimal control gain is calculated iteratively. Finally, a control signal based on the optimal control gain is used to make the output of the linear continuous-time system model track the target trajectory. This method extends the optimal output tracking control method to linear systems, and the fixed convergence rate accelerates system convergence, avoids disturbances from external factors, and facilitates the smooth operation of industrial production processes.

[0015] Preferably, the expression for the linear continuous-time system model is:

[0016]

[0017]

[0018] in, Indicates the initial state is The state matrix of a linear continuous-time system model. The dimension is , This represents the time derivative of the state matrix of a linear continuous-time system model. Represents the control input matrix. The dimension is , The output matrix of a linear continuous-time system model. The dimension is , The dimension is The system coefficient matrix, The dimension is The input coefficient matrix, The dimension is The output coefficient matrix;

[0019] The expression for the target trajectory model is:

[0020]

[0021]

[0022] in, This represents the state matrix of the target trajectory system model. This represents the derivative of the state matrix of the target trajectory system model with respect to time. This represents the output matrix of the target trajectory model. The dimension is The target trajectory coefficient matrix, The dimension is The target trajectory output coefficient matrix.

[0023] Preferably, the expression for the dynamic tracking controller is:

[0024]

[0025]

[0026] in, This represents the state coefficient matrix of the dynamic tracking controller. This represents the tracking error coefficient matrix. and matrix pairs The smallest p-copy internal model containing matrix S. This represents the intermediate state matrix of the dynamic tracking controller. This represents the derivative of the intermediate state matrix of the dynamic tracking controller with respect to time. Indicates satisfaction observable feedforward gain matrix, and Represents the feedback gain matrix. The tracking error matrix represents the linear continuous-time system model, and the control signal generated by the dynamic controller controls the output of the linear continuous-time system model. Track the target trajectory , .

[0027] Preferably, the expression for the dynamic error linear system model is:

[0028]

[0029]

[0030] in, Represents the state of a linear continuous-time system model With the target trajectory model state The error matrix, , express The derivative with respect to time, , , , This indicates the fixed convergence rate set. , , , The dimension is The identity matrix.

[0031] Preferably, the expression for the behavioral strategy is:

[0032]

[0033]

[0034] in, This represents the internal state of the dynamic controller in the behavioral strategy. This represents the derivative of the internal state with respect to time. Represents the exploration noise matrix. , The free variables representing the exploration noise are combinations of sine and cosine signals with different amplitudes and frequencies;

[0035] The expression for the dynamic system model is:

[0036]

[0037]

[0038] in, This represents the state of a linear continuous-time system operating according to a behavioral strategy. , express The derivative with respect to time, , .

[0039] Preferably, the process of reconstructing the state of the dynamic system model using input data and output data is as follows:

[0040] Input data Inputting the data into the dynamic system model yields the output data. and exploring the noise matrix ;

[0041] Based on input data Output data and exploring the noise matrix Calculate state , , They represent respectively by , and The state of the drive;

[0042] State Substituting into the reconstruction formula, the reconstructed state is calculated. The expression for the reconstructed formula is:

[0043]

[0044] in, This is a parameterized matrix.

[0045] Preferably, the output data of the acquired dynamic system model includes:

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052] in, Indicates the Kronecker product. This indicates the start time for setting data collection. Indicates the end time of data collection. It must be a positive integer and must satisfy the expression:

[0053]

[0054] in, ;

[0055] The process of obtaining the optimal control gain through iterative calculation is as follows:

[0056] S51. Set the initial number of iterations and convergence error Substitute the output data of the dynamic system model into the expression to calculate the control gain. The expression is:

[0057]

[0058]

[0059]

[0060] in, , , ;

[0061] S52. Determine the first... Control gain of the next iteration With the Control gain of the next iteration Do the norms of the error matrices between them satisfy the expression:

[0062]

[0063] If not satisfied, then Return to step S51; if satisfied, proceed to step S53.

[0064] S53. Will As the optimal control gain Based on the optimal control gain, a control signal is generated, and the control signal is used to make the output of the linear continuous-time system model track the target trajectory.

[0065] The expression for the control strategy that generates the control signal based on the optimal control gain is:

[0066]

[0067]

[0068] Secondly, this application also proposes an optimal output tracking control system based on a fixed convergence rate, the system comprising:

[0069] The dynamic tracking controller design unit is used to design a dynamic tracking controller based on the constructed linear continuous-time system model and target trajectory model. The dynamic controller generates control signals to make the output of the linear continuous-time system model track the target trajectory.

[0070] The dynamic error linear system model building unit is used to build a dynamic error linear system model for tracking the target trajectory, and incorporates a fixed convergence rate into the dynamic error linear system model.

[0071] The dynamic system model building and running unit is used to design the behavior strategy of the dynamic error linear system model, design the dynamic system model based on the behavior strategy and the linear continuous time system model, run the dynamic system model using the input data generated by the behavior strategy, and obtain the output data.

[0072] The dynamic system model state reconstruction unit is used to reconstruct the state of the dynamic system model using input-output data.

[0073] The optimal control gain calculation unit is used to run the reconstructed dynamic system model using the behavior strategy, obtain the output data of the dynamic system model, input the output data of the dynamic system model into the constructed calculation equation based on the optimal control gain, and iteratively calculate the optimal control gain.

[0074] The target trajectory output unit is used to generate a control signal based on the optimal control gain, and to use the control signal to make the output of the linear continuous-time system model track the target trajectory.

[0075] Thirdly, this application also proposes a computer device, which includes a memory, a processor, and a computer program stored in the memory that can be run by the processor. The processor executes the computer program to implement the optimal output tracking control method based on a fixed convergence speed.

[0076] Fourthly, this application also proposes a computer storage medium storing a computer program, the computer program including program instructions, which, when executed by a computer, cause the computer to execute the optimal output tracking control method based on a fixed convergence speed.

[0077] Compared with the prior art, the beneficial effects of the present invention are:

[0078] This invention proposes an optimal output tracking control method and system based on a fixed convergence rate. First, a dynamic controller is designed for the linear continuous-time system to generate a control signal, which tracks the target trajectory, thus constructing a dynamic error linear system incorporating a fixed convergence rate. A behavioral strategy is then designed to operate the dynamic system, reconstructing its state using input-output data. The behavioral strategy is applied again to the reconstructed dynamic system to collect data, and the optimal control gain is calculated iteratively. Finally, a control signal based on this optimal control gain is used to make the output of the linear continuous-time system model track the target trajectory. This method extends optimal output tracking control to linear systems, and the fixed convergence rate accelerates system convergence, avoids disturbances from external factors, and facilitates smooth industrial production processes. Attached Figure Description

[0079] Figure 1 This is a flowchart illustrating an optimal output tracking control method based on a fixed convergence rate proposed in Embodiment 1 of the present invention.

[0080] Figure 2 A flowchart illustrating the method for obtaining the optimal control gain through iterative calculation proposed in Embodiment 1 of the present invention;

[0081] Figure 3 A schematic diagram showing the comparison between the convergence error of achieving the optimal control gain and the convergence error of non-optimal control gain proposed in Embodiment 1 of the present invention;

[0082] Figure 4 This diagram illustrates the relationship between the output tracking target trajectory control and time in the linear continuous-time system model proposed in Embodiment 1 of the present invention.

[0083] Figure 5 A schematic diagram illustrating the implementation of the fixed convergence rate proposed in Embodiment 1 of the present invention;

[0084] Figure 6 This diagram illustrates the structure of an optimal output tracking control system based on a fixed convergence rate, as proposed in Embodiment 3 of the present invention.

[0085] Figure 7 This is a schematic diagram of the structure of the computer device proposed in Embodiment 4 of the present invention. Detailed Implementation

[0086] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent.

[0087] To better illustrate this embodiment, some parts of the accompanying drawings may be omitted, enlarged, or reduced, and do not represent the actual dimensions;

[0088] It is understandable to those skilled in the art that some well-known details may be omitted from the accompanying drawings.

[0089] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0090] The positional relationships depicted in the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent.

[0091] Example 1

[0092] This embodiment proposes an optimal output tracking control method based on a fixed convergence rate. A flowchart illustrating this method can be found here. Figure 1 This includes the following steps:

[0093] S1. Based on the established linear continuous-time system model and target trajectory model, design a dynamic tracking controller, and use the dynamic controller to generate control signals so that the output of the linear continuous-time system model tracks the target trajectory;

[0094] S2. Construct a dynamic error linear system model for tracking the target trajectory, and incorporate a fixed convergence rate into the dynamic error linear system model;

[0095] S3. Design a behavioral strategy for the dynamic error linear system model. Based on the behavioral strategy and the linear continuous-time system model, design a dynamic system model. Use the input data generated by the behavioral strategy to run the dynamic system model and obtain the output data.

[0096] S4. Reconstruct the state of the dynamic system model using input-output data;

[0097] S5. Use the behavior strategy to run the reconstructed dynamic system model, obtain the output data of the dynamic system model, input the output data of the dynamic system model into the constructed calculation equation based on the optimal control gain, and iteratively calculate to obtain the optimal control gain;

[0098] S6. Generate a control signal based on the optimal control gain, and use the control signal to make the output of the linear continuous-time system model track the target trajectory.

[0099] In this embodiment, a dynamic controller is first designed for the linear continuous-time system to generate control signals and output control to track the target trajectory, constructing a dynamic error linear system with a fixed convergence rate. A behavioral strategy is then designed to operate the dynamic system, reconstructing its state using input-output data. The behavioral strategy is applied again to the reconstructed dynamic system to collect data, and the optimal control gain is calculated iteratively. Finally, a control signal based on the optimal control gain is used to make the output of the linear continuous-time system model track the target trajectory. This method extends the optimal output tracking control method to linear systems, and the fixed convergence rate accelerates system convergence, avoids disturbances from external factors, and facilitates the smooth operation of industrial production processes.

[0100] In this embodiment, the expression for the linear continuous-time system model is:

[0101]

[0102]

[0103] in, Indicates the initial state is The state matrix of a linear continuous-time system model. The dimension is , This represents the time derivative of the state matrix of a linear continuous-time system model. Represents the control input matrix. The dimension is , The output matrix of a linear continuous-time system model. The dimension is , The dimension is The system coefficient matrix, The dimension is The input coefficient matrix, The dimension is The output coefficient matrix;

[0104] The expression for the target trajectory model is:

[0105]

[0106]

[0107] in, This represents the state matrix of the target trajectory system model. This represents the derivative of the state matrix of the target trajectory system model with respect to time. This represents the output matrix of the target trajectory model. The dimension is The target trajectory coefficient matrix, The dimension is The target trajectory output coefficient matrix.

[0108] Specifically, the following assumptions are made regarding the parameters of the linear continuous-time system model and the target trajectory model:

[0109] 1. It is controllable, meaning that all states within a linear continuous-time system model can be controlled by applying [a certain condition]. Control input to change; It is observable, meaning that all states within a linear continuous-time system model can be analyzed. It can be concluded that;

[0110] 2. Matrix There are no eigenvalues ​​with negative real parts;

[0111] 3. For any ;

[0112] 4. Matrix Dimensions ;

[0113] In this embodiment, the expression for the dynamic tracking controller is:

[0114]

[0115]

[0116] in, This represents the state coefficient matrix of the dynamic tracking controller. This represents the tracking error coefficient matrix. and matrix pairs The smallest p-copy internal model containing matrix S. This represents the intermediate state matrix of the dynamic tracking controller. This represents the derivative of the intermediate state matrix of the dynamic tracking controller with respect to time. Indicates satisfaction observable feedforward gain matrix, and Represents the feedback gain matrix. The tracking error matrix represents the linear continuous-time system model, and the control signal generated by the dynamic controller controls the output of the linear continuous-time system model. Track the target trajectory , .

[0117] In this embodiment, the expression for the dynamic error linear system model is:

[0118]

[0119]

[0120] in, Represents the state of a linear continuous-time system model With the target trajectory model state The error matrix, , express The derivative with respect to time, , , , This indicates the fixed convergence rate set. , , , The dimension is The identity matrix.

[0121] Specifically, the expression for the optimal performance index is:

[0122]

[0123] in, , It is a positive semi-definite matrix. .

[0124] Specifically, the error matrix The expression is:

[0125]

[0126] in, , The dimension is , , The following expression is the only solution:

[0127]

[0128] in, ,

[0129] In this embodiment, the expression for the behavioral strategy is:

[0130]

[0131]

[0132] in, This represents the internal state of the dynamic controller in the behavioral strategy. This represents the derivative of the internal state with respect to time. Represents the exploration noise matrix. , The free variables representing the exploration noise are combinations of sine and cosine signals with different amplitudes and frequencies;

[0133] The expression for the dynamic system model is:

[0134]

[0135]

[0136] in, This represents the state of a linear continuous-time system operating according to a behavioral strategy. , express The derivative with respect to time, , .

[0137] In this embodiment, the process of reconstructing the state of the dynamic system model using input data and output data is as follows:

[0138] Input data Inputting the data into the dynamic system model yields the output data. and exploring the noise matrix ;

[0139] Based on input data Output data and exploring the noise matrix Calculate state , , They represent respectively by , and The state of the drive;

[0140] State Substituting into the reconstruction formula, the reconstructed state is calculated. The expression for the reconstructed formula is:

[0141]

[0142] in, This is a parameterized matrix.

[0143] Specifically, , express The derivative with respect to time; , express The derivative with respect to time; , express The derivative with respect to time, , and The initial values ​​of all states are 0; ;

[0144]

[0145] in, The eigenvalues ​​are all negative real numbers. It is a positive coefficient.

[0146] In this embodiment, the output data of the acquired power system model includes:

[0147]

[0148]

[0149]

[0150]

[0151]

[0152]

[0153] in, Indicates the Kronecker product. This indicates the start time for setting data collection. Indicates the end time of data collection. It must be a positive integer and must satisfy the expression:

[0154]

[0155] in, ;

[0156] Specifically, the expression for the behavioral strategy used when obtaining the output data of the dynamic system model is:

[0157]

[0158] in, , It is stable.

[0159] See the flowchart of the method for obtaining the optimal control gain through iterative calculation. Figure 2 The process is as follows:

[0160] S51. Set the initial number of iterations and convergence error Substitute the output data of the dynamic system model into the expression to calculate the control gain. The expression is:

[0161]

[0162]

[0163]

[0164] in, , , ;

[0165] S52. Determine the first... Control gain of the next iteration With the Control gain of the next iteration Do the norms of the error matrices between them satisfy the expression:

[0166]

[0167] If not satisfied, then Return to step S51; if satisfied, proceed to step S53.

[0168] S53. Will As the optimal control gain Based on the optimal control gain, a control signal is generated, and the control signal is used to make the output of the linear continuous-time system model track the target trajectory.

[0169] The expression for the control strategy that generates the control signal based on the optimal control gain is:

[0170]

[0171]

[0172] Specifically, before reconstructing the dynamic error linear system model using the behavioral strategy, a model-free pre-collection phase is included. In this phase, the dynamic error linear system runs for a sufficiently long time before data collection begins, allowing... .

[0173] Specifically, regarding the state ,definition

[0174]

[0175] For dimension matrix , The definition of is:

[0176]

[0177] For dimension matrix , The definition of is:

[0178]

[0179] Specifically, the comparison graph of the convergence error when achieving the optimal control gain and the convergence error when achieving the non-optimal control gain is shown in the figure below. Figure 3 As shown, the convergence error of the optimal control gain changes at a similar rate as the convergence error of the non-optimal control gain, but the convergence error remains unchanged after obtaining the optimal control gain.

[0180] Specifically, the relationship between the control signal based on optimal control gain and the output of the linear continuous-time system model for tracking the target trajectory and time is as follows: Figure 4 As shown, Figure 4 In the diagram, the vertical axis represents the tracking trajectory control output of the linear continuous-time system model, and the horizontal axis represents time. The output tracking control is the result after applying the optimal control gain control strategy. Complete with target trajectory control same.

[0181] Specifically, the implementation of the fixed convergence rate is as follows: Figure 5 As shown, the vertical axis represents the tracking control output of the linear continuous-time system. Complete with target trajectory control The difference, after 1 second, is the tracking control output of the linear continuous-time system. Control the target trajectory at a fixed convergence rate. Convergence occurs after 6 seconds, with the tracking control output of the continuous-time system reaching its maximum. Complete with target trajectory control same.

[0182] Example 2

[0183] This embodiment proposes an optimal output tracking control method based on a fixed convergence rate, including the following steps:

[0184] S1. Based on the established linear continuous-time system model and target trajectory model, a dynamic tracking controller is designed. The dynamic controller generates control signals to make the output of the linear continuous-time system model track the target trajectory. In this embodiment, the linear continuous-time system is the F-16 aircraft dynamics system.

[0185] S2. Construct a dynamic error linear system model for tracking the target trajectory, and incorporate a fixed convergence rate into the dynamic error linear system model;

[0186] S3. Design a behavioral strategy for the dynamic error linear system model. Based on the behavioral strategy and the linear continuous-time system model, design a dynamic system model. Use the input data generated by the behavioral strategy to run the dynamic system model and obtain the output data.

[0187] S4. Reconstruct the state of the dynamic system model using input-output data;

[0188] S5. Use the behavior strategy to run the reconstructed dynamic system model, obtain the output data of the dynamic system model, input the output data of the dynamic system model into the constructed calculation equation based on the optimal control gain, and iteratively calculate to obtain the optimal control gain;

[0189] S6. Generate a control signal based on the optimal control gain, and use the control signal to make the output of the linear continuous-time system model track the target trajectory.

[0190] In this embodiment, the expression for the linear continuous-time system model is:

[0191]

[0192]

[0193] in, Indicates the initial state is The state matrix of a linear continuous-time system model. The dimension is , This represents the time derivative of the state matrix of a linear continuous-time system model. Represents the control input matrix. The dimension is , The output matrix of a linear continuous-time system model. The dimension is , The dimension is The system coefficient matrix, The dimension is The input coefficient matrix, The dimension is The output coefficient matrix;

[0194] The expression for the target trajectory model is:

[0195]

[0196]

[0197] in, This represents the state matrix of the target trajectory system model. This represents the derivative of the state matrix of the target trajectory system model with respect to time. This represents the output matrix of the target trajectory model. The dimension is The target trajectory coefficient matrix, The dimension is The target trajectory output coefficient matrix.

[0198] In this embodiment, specifically, the expression for the F-16 aircraft dynamics model is:

[0199]

[0200]

[0201] The expression for the target trajectory model is:

[0202]

[0203]

[0204] Specifically, the following assumptions are made regarding the parameters of the linear continuous-time system model and the target trajectory model:

[0205] 1. It is controllable, meaning that all states within a linear continuous-time system model can be controlled by applying [a certain condition]. Control input to change; It is observable, meaning that all states within a linear continuous-time system model can be analyzed. It can be concluded that;

[0206] 2. Matrix There are no eigenvalues ​​with negative real parts;

[0207] 3. For any ;

[0208] 4. Matrix Dimensions ;

[0209] In this embodiment, the expression for the dynamic tracking controller is:

[0210]

[0211]

[0212] in, This represents the state coefficient matrix of the dynamic tracking controller. This represents the tracking error coefficient matrix. and matrix pairs The smallest p-copy internal model containing matrix S. This represents the intermediate state matrix of the dynamic tracking controller. This represents the derivative of the intermediate state matrix of the dynamic tracking controller with respect to time. Indicates satisfaction observable feedforward gain matrix, and Represents the feedback gain matrix. The tracking error matrix represents the linear continuous-time system model, and the control signal generated by the dynamic controller controls the output of the linear continuous-time system model. Track the target trajectory , .

[0213] In this embodiment, the expression for the dynamic error linear system model is:

[0214]

[0215]

[0216] in, Represents the state of a linear continuous-time system model With the target trajectory model state The error matrix, , express The derivative with respect to time, , , , This indicates the fixed convergence rate set. , , , The dimension is The identity matrix.

[0217] Specifically, the expression for the optimal performance index is:

[0218]

[0219] in, , It is a positive semi-definite matrix. .

[0220] In this embodiment, the error matrix The expression is:

[0221]

[0222] in, , The dimension is , , The following expression is the only solution:

[0223]

[0224] in, ,

[0225] In this embodiment, the expression for the behavioral strategy is:

[0226]

[0227]

[0228] in, This represents the internal state of the dynamic controller in the behavioral strategy. This represents the derivative of the internal state with respect to time. Represents the exploration noise matrix. , The free variables representing the exploration noise are combinations of sine and cosine signals with different amplitudes and frequencies;

[0229] The expression for the dynamic system model is:

[0230]

[0231]

[0232] in, This represents the state of a linear continuous-time system operating according to a behavioral strategy. , express The derivative with respect to time, , .

[0233] In this embodiment, the process of reconstructing the state of the dynamic system model using input-output data is as follows:

[0234] Input data Inputting the data into the dynamic system model yields the output data. and exploring the noise matrix ;

[0235] Based on input data Output data and exploring the noise matrix Calculate state , , They represent respectively by , and The state of the drive;

[0236] State Substituting into the reconstruction formula, the reconstructed state is calculated. The expression for the reconstructed formula is:

[0237]

[0238] in, This is a parameterized matrix.

[0239] Specifically, , express The derivative with respect to time; , express The derivative with respect to time; , express The derivative with respect to time, , and The initial values ​​of all states are 0; ;

[0240]

[0241] in, The eigenvalues ​​are all negative real numbers. It is a positive coefficient.

[0242] In this embodiment, the output data of the acquired power system model includes:

[0243]

[0244]

[0245]

[0246]

[0247]

[0248]

[0249] in, Indicates the Kronecker product. This indicates the start time for setting data collection. Indicates the end time of data collection. It must be a positive integer and must satisfy the expression:

[0250]

[0251] in, ;

[0252] Specifically, the expression for the behavioral strategy used when obtaining the output data of the dynamic system model is:

[0253]

[0254] in, , It is stable.

[0255] The process of obtaining the optimal control gain through iterative calculation is as follows:

[0256] S51. Set the initial number of iterations and convergence error Substitute the output data of the dynamic system model into the expression to calculate the control gain. The expression is:

[0257]

[0258]

[0259]

[0260] in, , , ;

[0261] S52. Determine the first... Control gain of the next iteration With the Control gain of the next iteration Do the norms of the error matrices between them satisfy the expression:

[0262]

[0263] If not satisfied, then Return to step S51; if satisfied, proceed to step S53.

[0264] S53. Will As the optimal control gain Based on the optimal control gain, a control signal is generated, and the control signal is used to make the output of the linear continuous-time system model track the target trajectory.

[0265] The expression for the control strategy that generates the control signal based on the optimal control gain is:

[0266]

[0267]

[0268] Specifically, before reconstructing the dynamic error linear system model using the behavioral strategy, a model-free pre-collection phase is included. In this phase, the dynamic error linear system runs for a sufficiently long time before data collection begins, allowing... .

[0269] Specifically, regarding the state ,definition

[0270]

[0271] For dimension matrix , The definition of is:

[0272]

[0273] For dimension matrix , The definition of is:

[0274]

[0275] Specifically, as shown in the comparison diagram of the convergence error when the optimal control gain is reached and the convergence error when the optimal control gain is not reached, the convergence error of the optimal control gain is represented by a triangle point, and the convergence error when the optimal control gain is not reached is represented by a circle point. The two convergence errors change at similar rates, but after obtaining the optimal control gain, the convergence error remains unchanged.

[0276] Specifically, such as Figure 4 As shown, the vertical axis represents the tracking trajectory control output of the linear continuous-time system model, and the horizontal axis represents time. The tracking control output after applying the optimal control gain control strategy is... Complete with target trajectory control The same applies. After applying a control strategy with optimal control gain, the tracking control output of the linear continuous-time system... Complete with target trajectory control same.

[0277] Specifically, such as Figure 5 As shown, the vertical axis represents the tracking control output of the linear continuous-time system. Complete with target trajectory control The difference, after 1 second, is the tracking control output of the linear continuous-time system. Control the target trajectory at a fixed convergence rate. Convergence occurs after 6 seconds, with the tracking control output of the continuous-time system reaching its maximum. Complete with target trajectory control same.

[0278] Example 3

[0279] This embodiment proposes an optimal output tracking control system based on a fixed convergence rate. In this embodiment, the system is used to implement an optimal output tracking control method based on a fixed convergence rate. The structural diagram is shown below. Figure 6 As shown, it includes:

[0280] The dynamic tracking controller design unit is used to design a dynamic tracking controller based on the constructed linear continuous-time system model and target trajectory model, so that the output of the linear continuous-time system model tracks the target trajectory.

[0281] The optimal performance index construction unit is used to construct a dynamic error linear system model for tracking the target trajectory based on the dynamic tracking controller and the linear continuous-time system model, incorporate a fixed convergence rate into the dynamic error linear system model, and set the optimal performance index of the tracking control based on the dynamic error linear system model.

[0282] The dynamic system model building unit is used to design the behavior strategy of the dynamic error linear system model. Based on the behavior strategy and the linear continuous-time system model, the dynamic system model is designed, and the dynamic system is run using the input data generated by the behavior strategy to obtain the output data.

[0283] The dynamic system model reconstruction unit is used to reconstruct the state of the dynamic system model using input-output data, and obtain the reconstructed state of the dynamic system model.

[0284] The optimal control gain calculation unit is used to run the reconstructed state representation of the dynamic system model again using the behavior strategy, collect data and input it into the optimal control gain calculation equation, iteratively calculate the optimal control gain, and use the control signal based on the optimal control gain to make the linear continuous time system model output the target trajectory control.

[0285] Example 4

[0286] In this embodiment, a computer device 100 is proposed. The computer device 100 includes a memory 101, a processor 102, and a computer program stored in the memory 101 that can be executed by the processor. The processor 102 executes the computer program to implement an optimal output tracking control method based on a fixed convergence rate. A schematic diagram of the device structure is shown below. Figure 7 As shown.

[0287] In this embodiment, a computer storage medium is also proposed, on which a computer program is stored. The computer program includes program instructions, which, when executed by a computer, cause the computer to execute the optimal output tracking control method based on a fixed convergence speed.

[0288] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. An optimal output tracking control method based on a fixed convergence rate, characterized in that, Includes the following steps: S1. Based on the established linear continuous-time system model and target trajectory model, design a dynamic tracking controller, and use the dynamic controller to generate control signals so that the output of the linear continuous-time system model tracks the target trajectory; S2. Construct a dynamic error linear system model for tracking the target trajectory, and incorporate a fixed convergence rate into the dynamic error linear system model; The expression for the dynamic error linear system model is: in, Represents the state of a linear continuous-time system model With the target trajectory model state The error matrix, , express The derivative with respect to time, , , , This indicates the fixed convergence rate set. , , , The dimension is The identity matrix, The dimension is The system coefficient matrix, The dimension is The input coefficient matrix, The dimension is The output coefficient matrix, and Represents the feedback gain matrix; S3. Design a behavioral strategy for the dynamic error linear system model. Based on the behavioral strategy and the linear continuous-time system model, design a dynamic system model. Use the input data generated by the behavioral strategy to run the dynamic system model and obtain the output data. The expression for the behavioral strategy is: in, This represents the internal state of the dynamic controller in the behavioral strategy. This represents the derivative of the internal state with respect to time. Represents the exploration noise matrix. , The free variables representing the exploration noise are combinations of sine and cosine signals with different amplitudes and frequencies. and matrix pairs The smallest p-copy internal model containing matrix S. Indicates satisfaction observable feedforward gain matrix, This represents the feedback gain matrix in the k-th iteration; The expression for the dynamic system model is: in, This represents the state of a linear continuous-time system operating according to a behavioral strategy. , express The derivative with respect to time, , ; S4. Reconstruct the state of the dynamic system model using input-output data; The process of reconstructing the state of the dynamic system model using input data and output data is as follows: Input data Inputting the data into the dynamic system model yields the output data. and exploring the noise matrix ; Based on input data Output data and exploring the noise matrix Calculate state , , They represent respectively by , and The state of the drive; State Substituting into the reconstruction formula, the reconstructed state is calculated. The expression for the reconstructed formula is: in, For parameterized matrices; S5. Use the behavior strategy to run the reconstructed dynamic system model, obtain the output data of the dynamic system model, input the output data of the dynamic system model into the constructed calculation equation based on the optimal control gain, and iteratively calculate to obtain the optimal control gain; The output data of the acquired dynamic system model includes: in, Indicates the Kronecker product. This indicates the start time for setting data collection. Indicates the end time of data collection. It must be a positive integer and must satisfy the expression: in, , , , Both represent the dimensions of the matrix; The process of obtaining the optimal control gain through iterative calculation is as follows: S51. Set the initial number of iterations and convergence error Substitute the output data of the dynamic system model into the expression to calculate the control gain. The expression is: in, , , , The dimension is The target trajectory output coefficient matrix, The weight submatrix representing the adjustment error state. , It is a positive semi-definite matrix; S52. Determine the first... Control gain of the next iteration With the Control gain of the next iteration Do the norms of the error matrices between them satisfy the expression: If not satisfied, then Return to step S51; if satisfied, proceed to step S53. S53. Will As the optimal control gain Based on the optimal control gain, a control signal is generated, and the control signal is used to make the output of the linear continuous-time system model track the target trajectory. The expression for the control strategy that generates the control signal based on the optimal control gain is: ； S6. Generate a control signal based on the optimal control gain, and use the control signal to make the output of the linear continuous-time system model track the target trajectory.

2. The optimal output tracking control method based on a fixed convergence rate according to claim 1, characterized in that, The expression for the linear continuous-time system model is: in, Indicates the initial state is The state matrix of a linear continuous-time system model. The dimension is , This represents the time derivative of the state matrix of a linear continuous-time system model. Represents the control input matrix. The dimension is , The output matrix of a linear continuous-time system model. The dimension is , The dimension is The system coefficient matrix, The dimension is The input coefficient matrix, The dimension is The output coefficient matrix; The expression for the target trajectory model is: in, This represents the state matrix of the target trajectory system model. This represents the derivative of the state matrix of the target trajectory system model with respect to time. This represents the output matrix of the target trajectory model. The dimension is The target trajectory coefficient matrix, The dimension is The target trajectory output coefficient matrix.

3. The optimal output tracking control method based on a fixed convergence rate according to claim 2, characterized in that, The expression for the dynamic tracking controller is: in, This represents the state coefficient matrix of the dynamic tracking controller. This represents the tracking error coefficient matrix. and matrix pairs The smallest p-copy internal model containing matrix S. This represents the intermediate state matrix of the dynamic tracking controller. This represents the derivative of the intermediate state matrix of the dynamic tracking controller with respect to time. Indicates satisfaction observable feedforward gain matrix, and Represents the feedback gain matrix. The tracking error matrix represents the linear continuous-time system model, and the control signal generated by the dynamic controller controls the output of the linear continuous-time system model. Track the target trajectory , .

4. An optimal output tracking control system based on a fixed convergence rate, characterized in that, The system includes: The dynamic tracking controller design unit is used to design a dynamic tracking controller based on the constructed linear continuous-time system model and target trajectory model. The dynamic controller generates control signals to make the output of the linear continuous-time system model track the target trajectory. The dynamic error linear system model building unit is used to build a dynamic error linear system model for tracking the target trajectory, and incorporates a fixed convergence rate into the dynamic error linear system model. The expression for the dynamic error linear system model is: in, Represents the state of a linear continuous-time system model With the target trajectory model state The error matrix, , express The derivative with respect to time, , , , This indicates the fixed convergence rate set. , , , The dimension is The identity matrix, The dimension is The system coefficient matrix, The dimension is The input coefficient matrix, The dimension is The output coefficient matrix, and Represents the feedback gain matrix; The dynamic system model building and running unit is used to design the behavior strategy of the dynamic error linear system model, design the dynamic system model based on the behavior strategy and the linear continuous time system model, run the dynamic system model using the input data generated by the behavior strategy, and obtain the output data. The expression for the behavioral strategy is: in, This represents the internal state of the dynamic controller in the behavioral strategy. This represents the derivative of the internal state with respect to time. Represents the exploration noise matrix. , The free variables representing the exploration noise are combinations of sine and cosine signals with different amplitudes and frequencies. express and matrix pairs The smallest p-copy internal model containing matrix S. Indicates satisfaction observable feedforward gain matrix, This represents the feedback gain matrix in the k-th iteration; The expression for the dynamic system model is: in, This represents the state of a linear continuous-time system operating according to a behavioral strategy. , express The derivative with respect to time, , ; The dynamic system model state reconstruction unit is used to reconstruct the state of the dynamic system model using input-output data. The process of reconstructing the state of the dynamic system model using input data and output data is as follows: Input data Inputting the data into the dynamic system model yields the output data. and exploring the noise matrix ; Based on input data Output data and exploring the noise matrix Calculate state , , They represent respectively by , and The state of the drive; State Substituting into the reconstruction formula, the reconstructed state is calculated. The expression for the reconstructed formula is: in, For parameterized matrices; The optimal control gain calculation unit is used to run the reconstructed dynamic system model using the behavior strategy, obtain the output data of the dynamic system model, input the output data of the dynamic system model into the constructed calculation equation based on the optimal control gain, and iteratively calculate the optimal control gain. The output data of the acquired dynamic system model includes: in, Indicates the Kronecker product. This indicates the start time for setting data collection. Indicates the end time of data collection. It must be a positive integer and must satisfy the expression: in, , , , Both represent the dimensions of the matrix; The process of obtaining the optimal control gain through iterative calculation is as follows: Set the initial number of iterations. and convergence error Substitute the output data of the dynamic system model into the expression to calculate the control gain. The expression is: in, , , , The dimension is The target trajectory output coefficient matrix, The weight submatrix representing the adjustment error state. , It is a positive semi-definite matrix; Judge the first Control gain of the next iteration With the Control gain of the next iteration Do the norms of the error matrices between them satisfy the expression: If not satisfied, then Return to step S51; if satisfied, proceed to step S53. Will As the optimal control gain Based on the optimal control gain, a control signal is generated, and the control signal is used to make the output of the linear continuous-time system model track the target trajectory. The expression for the control strategy that generates the control signal based on the optimal control gain is: ； The target trajectory output unit is used to generate a control signal based on the optimal control gain, and to use the control signal to make the output of the linear continuous-time system model track the target trajectory.

5. A computer device, characterized in that, The computer device includes a memory, a processor, and a computer program stored in the memory that can be executed by the processor, wherein the processor executes the computer program to implement the method according to any one of claims 1 to 3.

6. A computer storage medium, characterized in that, It stores a computer program, which includes program instructions that, when executed by a computer, cause the computer to perform the method described in any one of claims 1 to 3.

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