A predictive control method and device based on an unknown parameter model

Abstract

The application relates to a predictive control method and device based on an unknown parameter model, wherein the method comprises the following steps: parameter setting is performed on an unknown parameter model used for simulating a controlled real system to obtain model parameters; the model parameters of the unknown parameter model are updated through an adaptive observer, and a terminal domain of the unknown parameter model is calculated; based on the model parameters of the unknown parameter model, the adaptive observer and the terminal domain of the unknown parameter model, iterative calculation of a control quantity of the controlled real system is repeatedly performed, and when the number of times of the iterative calculation reaches a preset total iteration number, an optimal control quantity of the controlled real system is obtained. Through the application, the problem of how to perform predictive control based on an unknown parameter model is solved, the model parameters are updated based on the adaptive observer and are input into the unknown parameter model, the best control quantity is calculated by the model using the terminal domain, the robustness of the system is improved, and good control performance is achieved under the condition that the model parameters are unknown.

Description

Technical Field

[0001] This application relates to the field of model prediction technology for control, and in particular to a predictive control method and apparatus based on an unknown parameter model. Background Technology

[0002] Model predictive control (MDI) is a model-based control technique that was proposed in the 1970s based on optimization theory. MDI is widely used in practical engineering fields such as oil refining, petrochemicals, power generation, papermaking, and robotics.

[0003] Since the introduction of model predictive control, a number of step response models and impulse response models based on dynamic matrix control and other related algorithms have been developed. However, model-based predictive control requires knowledge of the specific parameters of the model, and the control performance also depends on the accuracy of the model. If the model parameters are unknown, model predictive control cannot be used.

[0004] Currently, no effective solution has been proposed for the problem of predictive control based on unknown parameter models in related technologies. Summary of the Invention

[0005] This application provides a predictive control method and apparatus based on an unknown parameter model, so as to at least solve the problem of how to perform predictive control based on an unknown parameter model in related technologies.

[0006] In a first aspect, embodiments of this application provide a predictive control method based on an unknown parameter model, the method comprising:

[0007] The unknown parameter model is configured with parameters to obtain model parameters, wherein the unknown parameter model is used to simulate the real controlled system;

[0008] Repeatedly perform iterative calculations of the control quantity of the controlled real system. When the number of iterative calculations reaches the preset total number of iterations, the optimal control quantity of the controlled real system is obtained.

[0009] The iterative calculation of the control quantity of the controlled real system includes:

[0010] The model parameters of the unknown parameter model are updated using an adaptive observer;

[0011] Calculate the terminal domain of the unknown parameter model;

[0012] Based on the terminal domain and the updated model parameters, the control quantity of the controlled real system is calculated;

[0013] The state variables of the controlled real system are calculated based on the control variables, and the unknown parameter model is adjusted by feedback of the state variables.

[0014] In some embodiments, the unknown parameter model used to simulate the controlled real system includes:

[0015] The model formula for simulating the real controlled system by setting unknown parameters is as follows:

[0016]

[0017] Where t represents the data sampling time, x represents the state variable of the controlled real system, and u represents the control variable of the controlled real system. Let θ represent the first derivative of the state variables of the controlled real system, and let θ represent the unknown parameters of the controlled real system. T The unknown parameter is represented by the transpose of the unknown parameter. g(u, x, t) represents a known function of the controlled real system, and f(x, u, t) also represents a known function of the controlled real system.

[0018] In some embodiments, the controlled real system is a nonlinear continuous system containing linear unknown parameters.

[0019] In some embodiments, parameters are set for the unknown parameter model to obtain model parameters including:

[0020] Based on the fact that the unknown parameters of the controlled real system are linear unknown parameters, through θ=(θ1, θ2, …, θ…), n The model parameters of the unknown parameter model are set to n unknown linear parameters.

[0021] In some embodiments, updating the model parameters of the unknown parameter model via an adaptive observer includes:

[0022] The model formula for the adaptive observer is:

[0023]

[0024] in, For the observed state variables of the controlled real system, Let be the estimated parameters of the controlled real system, t represent the data sampling time, x represent the state variables of the controlled real system, u represent the control variables of the controlled real system, g(u, x, t) represent the known functions of the controlled real system, and f(x, u, t) also represent the known functions of the controlled real system. Here, k1≥1 represents the observation parameter, k2>0 represents the observation parameter, and 0<α<1 represents the observation parameter. For symbolic functions, For the error of the adaptive observer, The first derivative of the estimated parameter;

[0025] The model parameters of the unknown parameter model are updated based on the model formula of the adaptive observer.

[0026] In some embodiments, calculating the terminal domain of the unknown parameter model includes:

[0027] The formula Ω=[x] is used for calculation. s -r|x s -x(t k )|,x s +r|x s -x(t k )|] Calculate the terminal domain of the unknown parameter model, where Ω is the terminal domain, x s Let x(t) be the target state variable of the controlled real system, 0 < r < 1 be the contraction factor, and x(t) be the target state variable of the controlled real system. k (t) represents the sampling time. k The state variables of the controlled real system;

[0028] Determine whether the terminal domain Ω calculated by the formula is less than Y. If so, then the terminal domain Ω = x. s If not, the terminal field Ω retains its original value.

[0029] In some embodiments, the control quantities of the controlled real system are calculated based on the terminal domain and the updated model parameters, including:

[0030] Based on the terminal domain and the updated model parameters, the model formula for the updated unknown parameter model is obtained:

[0031]

[0032] Where τ represents the prediction time of the unknown parameter model, t k Let represent the current sampling time, x represent the state variable of the controlled real system, and u represent the control variable of the controlled real system. This represents the model parameters updated by the adaptive observer. Let g(u, x, t) represent the state variables of the controlled real system at the current sampling time, g(u, x, t) represent the known functions of the controlled real system, and f(x, u, t) also represent the known functions of the controlled real system.

[0033] The control quantity of the controlled real system is calculated using the model formula of the updated unknown parameter model.

[0034] In some embodiments, after obtaining the optimal control quantity of the controlled real system, the method includes:

[0035] The first control component of the optimal control quantity is applied to the controlled real system.

[0036] In some embodiments, after obtaining the model parameters, the method includes:

[0037] Initialize the estimated parameters Initialize the current iteration count k = 0, set the preset total iteration count to M, and set the terminal domain shrinkage threshold to Y.

[0038] In a second aspect, embodiments of this application provide an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method described in the first aspect above.

[0039] Compared to related technologies, this application provides a predictive control method and apparatus based on an unknown parameter model. The method involves setting parameters for an unknown parameter model used to simulate a real controlled system to obtain model parameters; updating the model parameters of the unknown parameter model using an adaptive observer and calculating the terminal domain of the unknown parameter model; and repeatedly performing iterative calculations of the control quantity of the real controlled system based on the model parameters, the adaptive observer, and the terminal domain of the unknown parameter model. When the number of iterations reaches a preset total number of iterations, the optimal control quantity of the real controlled system is obtained. This solves the problem of how to perform predictive control based on an unknown parameter model, enabling the observation of the state of the real controlled system using an adaptive observer, updating the model parameters based on the observed state and inputting them into the unknown parameter model. The model then uses the terminal domain to calculate the optimal control quantity, improving the robustness of the system and achieving good control performance even when the model parameters are unknown. Attached Figure Description

[0040] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0041] Figure 1 This is a flowchart of the steps of a predictive control method based on an unknown parameter model according to an embodiment of this application;

[0042] Figure 2 This is a structural block diagram of a predictive control system based on an unknown parameter model according to a specific embodiment of this application;

[0043] Figure 3 This is a flowchart illustrating a predictive control method based on an unknown parameter model according to a specific embodiment of the application.

[0044] Figure 4 This is a schematic diagram of the internal structure of an electronic device according to an embodiment of this application. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this application clearer, the application is described and illustrated below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application. All other embodiments obtained by those skilled in the art based on the embodiments provided in this application without inventive effort are within the scope of protection of this application.

[0046] Obviously, the accompanying drawings described below are merely some examples or embodiments of this application. Those skilled in the art can apply this application to other similar scenarios based on these drawings without any inventive effort. Furthermore, it is understood that although the efforts made in this development process may be complex and lengthy, for those skilled in the art related to the content disclosed in this application, any changes to design, manufacturing, or production based on the technical content disclosed in this application are merely conventional technical means and should not be construed as insufficient disclosure of the content of this application.

[0047] In this application, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment that is mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this application may be combined with other embodiments without conflict.

[0048] Unless otherwise defined, the technical or scientific terms used in this application shall have the ordinary meaning understood by one of ordinary skill in the art to which this application pertains. The terms “a,” “an,” “an,” “the,” and similar words used in this application do not indicate quantity limitation and may indicate singular or plural. The terms “comprising,” “including,” “having,” and any variations thereof used in this application are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or device that includes a series of steps or modules (units) is not limited to the listed steps or units, but may also include steps or units not listed, or may include other steps or units inherent to these processes, methods, products, or devices. The terms “connected,” “linked,” “coupled,” and similar words used in this application are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. “Multiple” used in this application refers to two or more. “And / or” describes the relationship between related objects, indicating that three relationships may exist; for example, “A and / or B” can represent: A alone, A and B simultaneously, and B alone. The character " / " generally indicates that the preceding and following objects are in an "or" relationship. The terms "first," "second," and "third" used in this application are merely to distinguish similar objects and do not represent a specific ordering of the objects.

[0049] This application provides a predictive control method based on an unknown parameter model. Figure 1 This is a flowchart illustrating the steps of a predictive control method based on an unknown parameter model according to an embodiment of this application, as follows: Figure 1 As shown, the method includes the following steps:

[0050] Step S102: Set the parameters of the unknown parameter model to obtain the model parameters, wherein the unknown parameter model is used to simulate the real controlled system;

[0051] Specifically, in step S102, the controlled real system is a nonlinear continuous system containing linear unknown parameters.

[0052] The model formula for simulating the controlled real system by setting unknown parameters is as follows:

[0053]

[0054] Where t represents the data sampling time, x represents the state variable of the controlled real system, and u represents the control variable of the controlled real system. Let θ represent the first derivative of the state variables of the controlled real system, and let θ represent the unknown parameters of the controlled real system. TThe unknown parameter is represented by the transpose of the unknown parameter. g(u, x, t) represents a known function of the controlled real system, and f(x, u, t) also represents a known function of the controlled real system.

[0055] Based on the fact that the unknown parameters of the controlled real system are linear unknown parameters, θ = (θ1, θ2, ..., θ... n The model parameters of the unknown parameter model are set to n unknown linear parameters.

[0056] Following step S102, step S103 is also included to initialize the estimated parameters. Initialize the current iteration count k = 0, set the preset total iteration count to M, and set the terminal domain shrinkage threshold to Y.

[0057] Step S104: Update the model parameters of the unknown parameter model using an adaptive observer;

[0058] Specifically, in step S104, the model formula for the adaptive observer is:

[0059]

[0060] in, For the observed state variables of the controlled real system, Let be the estimated parameters of the controlled real system, t represent the data sampling time, x represent the state variables of the controlled real system, u represent the control variables of the controlled real system, g(u, x, t) represent the known functions of the controlled real system, and f(x, u, t) also represent the known functions of the controlled real system. Here, k1≥1 represents the observation parameter, k2>0 represents the observation parameter, and 0<α<1 represents the observation parameter. For symbolic functions, For the error of the adaptive observer, The first derivative of the estimated parameter;

[0061] Based on the model formula of the adaptive observer mentioned above, the model parameters of the unknown parameter model are updated.

[0062] Step S106: Calculate the terminal domain of the unknown parameter model;

[0063] Specifically, step S106 involves calculating the formula:

[0064] Ω=[x s -r|x s -x(t k )|,x s +r|x s -x(t k )|]

[0065] Calculate the terminal domain of the model with unknown parameters, where Ω is the terminal domain and x s Let x(t) be the target state variable of the controlled real system, 0 < r < 1 be the contraction factor, and x(t) be the target state variable of the controlled real system. k (t) represents the sampling time. k The state variables of the controlled real system;

[0066] Determine if the terminal domain Ω calculated by the formula is less than Y. If so, then the terminal domain Ω = x. s If not, the terminal field Ω retains its original value.

[0067] Step S108: Calculate the control quantity of the controlled real system based on the terminal domain and the updated model parameters.

[0068] Specifically, step S108 involves obtaining the model formula for the updated unknown parameter model based on the terminal domain and the updated model parameters:

[0069]

[0070] Where τ represents the prediction time of the unknown parameter model, t k Let represent the current sampling time, x represent the state variable of the controlled real system, and u represent the control variable of the controlled real system. This represents the model parameters updated by the adaptive observer. Let g(u, x, t) represent the state variables of the controlled real system at the current sampling time, g(u, x, t) represent the known functions of the controlled real system, and f(x, u, t) also represent the known functions of the controlled real system.

[0071] The control quantity of the controlled real system is calculated using the updated model formula of the unknown parameter model.

[0072] Step S110: Calculate the state variables of the controlled real system based on the control variables, and adjust the unknown parameter model through state variable feedback.

[0073] Step S112: Determine whether the number of iterations has reached the preset total number of iterations. If not, repeat the iterative calculation of the control quantity of the controlled real system from step S104 to step S110. If yes, obtain the optimal control quantity of the controlled real system.

[0074] After step S112, the method further includes: applying the first control component of the optimal control quantity to the actual controlled real system.

[0075] Through steps S102 to S112 in the embodiments of this application, the problem of how to perform predictive control based on an unknown parameter model is solved. It realizes the observation of the state of the controlled real system by an adaptive observer, updates the model parameters according to the observed state and inputs them into the unknown parameter model. The model uses the terminal domain to calculate the optimal control quantity, improves the robustness of the system, and achieves good control performance when the model parameters are unknown.

[0076] This application provides a predictive control method based on an unknown parameter model, and a corresponding predictive control system based on an unknown parameter model.

[0077] Figure 2 This is a structural block diagram of a predictive control system based on an unknown parameter model according to a specific embodiment of this application, such as... Figure 2 As shown, the system includes an actual system (the controlled real system), an adaptive observer, and a model predictive controller, wherein the model predictive controller is a model predictive controller based on an unknown parameter model.

[0078] Figure 3 This is a flowchart illustrating a predictive control method based on an unknown parameter model according to a specific embodiment of the application, such as... Figure 3 As shown, the method includes the following steps:

[0079] Step one: The controlled real system is specifically the vehicle speed control system. The model formula for simulating this controlled real system using an unknown parameter model (system dynamics model) is as follows:

[0080]

[0081] Where a, b, and c are unknown inherent parameters of the vehicle speed control system (equivalent to θ above), and it is known that |b| < 1, |a| < 1, |c| < 2, x is the vehicle speed to be controlled, and u is the control variable. Assume b = 0.0021, a = -0.0002, and c = -0.98.

[0082] Step 2: Initialize the estimated parameters Initialize the current iteration count k = 0, set the preset total iteration count to M, and set the terminal domain shrinkage threshold to Y.

[0083] Step 3, the model formula for designing the adaptive finite-time observer is as follows:

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] in, This represents the error between the observer's state and the actual state. Therefore, the estimated parameters of the system can be obtained from the observer. and (equivalent to the above) ).

[0090] Step four: Then, the estimated system parameters obtained in step three are input into the model predictive controller based on the unknown parameter model (system dynamics model) to update the current sampling time t. k The unknown parameter model (system dynamics model) in the controller is as follows:

[0091]

[0092] in, Let τ represent the system state of the prediction model, and τ represent the time of the prediction model.

[0093] Step 5: Perform parameter initialization settings: With k = 0 and xs = 25, we then determine whether k is less than M. If it is, we use an adaptive finite-time observer to iteratively update the system parameters btk, atk, and ctk. Finally, we input the estimated parameters into the prediction model in the model predictive controller to obtain a new prediction model.

[0094] Step six, then calculate the terminal domain in the model predictive controller to ensure that the control system can eventually converge xs, and determine |x s -x(t k If Ω is less than Y, then let Ω = xs; if it is not less than Y, then Ω = [xs]. s -r|x s -x(t k )|,x s +r|x s -x(t k )|].

[0095] Step 7: Solve the optimization problem based on the obtained reference model and the calculated terminal domain to obtain the optimal control. Apply the first control component of the sequence to the real system. The real system applies the input tk+1) to the prediction model at the next sampling time to achieve rolling optimization.

[0096] It should be noted that the steps shown in the above process or in the flowchart of the accompanying figures can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0097] This embodiment also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program and the processor is configured to run the computer program to perform the steps in any of the above method embodiments.

[0098] Optionally, the electronic device may further include a transmission device and an input / output device, wherein the transmission device is connected to the processor and the input / output device is connected to the processor.

[0099] It should be noted that the specific examples in this embodiment can refer to the examples described in the above embodiments and optional implementations, and will not be repeated here.

[0100] Furthermore, in conjunction with the predictive control method based on an unknown parameter model in the above embodiments, this application embodiment can provide a storage medium for implementation. This storage medium stores a computer program; when executed by a processor, the computer program implements any of the predictive control methods based on an unknown parameter model in the above embodiments.

[0101] In one embodiment, a computer device is provided, which may be a terminal. The computer device includes a processor, memory, a network interface, a display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The network interface is used to communicate with an external terminal via a network connection. When the computer program is executed by the processor, it implements a predictive control method based on an unknown parameter model. The display screen may be a liquid crystal display (LCD) or an e-ink display. The input devices may be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0102] In one embodiment, Figure 4 This is a schematic diagram of the internal structure of an electronic device according to an embodiment of this application, such as... Figure 4 As shown, an electronic device is provided, which can be a server, and its internal structure diagram can be as follows. Figure 4As shown, the electronic device includes a processor, a network interface, internal memory, and non-volatile memory connected via an internal bus. The non-volatile memory stores the operating system, computer programs, and a database. The processor provides computing and control capabilities, the network interface communicates with external terminals via a network connection, the internal memory provides an environment for the operation of the operating system and computer programs, the computer programs are executed by the processor to implement a predictive control method based on an unknown parameter model, and the database stores data.

[0103] Those skilled in the art will understand that Figure 4 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the electronic device to which the present application is applied. The specific electronic device may include more or fewer components than shown in the figure, or combine certain components, or have different component arrangements.

[0104] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. This computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc.

[0105] Those skilled in the art should understand that the technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments have been described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0106] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A predictive control method based on an unknown parameter model, characterized in that, The method includes: The unknown parameter model is configured with parameters to obtain model parameters, wherein the unknown parameter model is used to simulate the real controlled system; Repeatedly perform iterative calculations of the control quantity of the controlled real system. When the number of iterative calculations reaches the preset total number of iterations, the optimal control quantity of the controlled real system is obtained. The iterative calculation of the control quantity of the controlled real system includes: The model parameters of the unknown parameter model are updated using an adaptive observer; Calculate the terminal domain of the unknown parameter model; Based on the terminal domain and the updated model parameters, the control quantity of the controlled real system is calculated; The state variables of the controlled real system are calculated based on the control variables, and the unknown parameter model is adjusted by feedback of the state variables.

2. The method according to claim 1, characterized in that, The unknown parameter model used to simulate the controlled real system includes: The model formula for simulating the real controlled system by setting unknown parameters is as follows: Where t represents the data sampling time, x represents the state variable of the controlled real system, and u represents the control variable of the controlled real system. Let θ represent the first derivative of the state variables of the controlled real system, and let θ represent the unknown parameters of the controlled real system. T The unknown parameter is represented by the transpose of the unknown parameter. g(u, x, t) represents a known function of the controlled real system, and f(x, u, t) also represents a known function of the controlled real system.

3. The method according to claim 1 or 2, characterized in that, The controlled real system is a nonlinear continuous system containing linear unknown parameters.

4. The method according to claim 3, characterized in that, By setting parameters for the unknown parameter model, the model parameters are obtained, including: Based on the fact that the unknown parameters of the controlled real system are linear unknown parameters, through θ=(θ1, θ2, …, θ…), n The model parameters of the unknown parameter model are set to n unknown linear parameters.

5. The method according to claim 1, characterized in that, Updating the model parameters of the unknown parameter model using an adaptive observer includes: The model formula for the adaptive observer is: in, For the observed state variables of the controlled real system, Let be the estimated parameters of the controlled real system, t represent the data sampling time, x represent the state variables of the controlled real system, u represent the control variables of the controlled real system, g(u, x, t) represent the known functions of the controlled real system, and f(x, u, t) also represent the known functions of the controlled real system. Here, k1≥1 represents the observation parameter, k2>0 represents the observation parameter, and 0<α<1 represents the observation parameter. For symbolic functions, For the error of the adaptive observer, The first derivative of the estimated parameter; The model parameters of the unknown parameter model are updated based on the model formula of the adaptive observer.

6. The method according to claim 1, characterized in that, The calculation of the terminal domain of the unknown parameter model includes: Calculate the terminal domain of the unknown parameter model through the calculation formula Ω = [x s - r|x s - x(t k )|, x s + r|x s - x(t k )|], where Ω is the terminal domain, x s is the target state quantity of the controlled real system, 0 < r < 1 is the contraction factor, and x(t k ) is the state quantity of the controlled real system at the sampling time t k ; Determine whether the terminal domain Ω calculated by the formula is less than Y. If so, then the terminal domain Ω = x. s If not, the terminal field Ω retains its original value.

7. The method according to claim 1, characterized in that, Based on the terminal domain and the updated model parameters, the control quantities of the controlled real system are calculated as follows: Based on the terminal domain and the updated model parameters, the model formula for the updated unknown parameter model is obtained: Where τ represents the prediction time of the unknown parameter model, t k Let represent the current sampling time, x represent the state variable of the controlled real system, and u represent the control variable of the controlled real system. This represents the model parameters updated by the adaptive observer. Let g(u, x, t) represent the state variables of the controlled real system at the current sampling time, g(u, x, t) represent the known functions of the controlled real system, and f(x, u, t) also represent the known functions of the controlled real system. The control quantity of the controlled real system is calculated using the model formula of the updated unknown parameter model.

8. The method according to claim 1, characterized in that, After obtaining the optimal control input for the controlled real system, the method includes: The first control component of the optimal control quantity is applied to the controlled real system.

9. The method according to claim 1, characterized in that, After obtaining the model parameters, the method includes: Initialize the estimated parameters Initialize the current iteration count k = 0, set the preset total iteration count to M, and set the terminal domain shrinkage threshold to Υ.

10. An electronic device comprising a memory and a processor, characterized in that, The memory stores a computer program, and the processor is configured to run the computer program to perform the method of any one of claims 1 to 9.

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