PID control method and system for high-order unknown nonlinear system based on determined learning

Abstract

The application discloses a PID control method and system for a high-order unknown nonlinear system based on DL, and the method comprises the following steps: acquiring an actual high-order state vector of the high-order unknown nonlinear system, establishing a space state mathematical model and a reference motion trajectory model; determining a tracking error according to an actual output and a reference output, inputting the tracking error into an experience-based extended PID controller, and controlling; the construction of the PID controller comprises the following steps: defining a composite filter tracking error term based on the tracking error of the system, deriving and constructing an error system; defining a high-order unknown nonlinear dynamics function, approximating and representing the function by using a RBFNN, and constructing an extended PID controller based on an adaptive RBFNN; and training the adaptive RBFNN according to a determined learning theory, and learning in a closed-loop control. The application can overcome the limitation that a traditional PID controller only relies on a feedback mechanism to resist unknown nonlinearities, and improve overall control performance.

Description

Technical Field

[0001] This invention relates to the field of automation control technology, and in particular to a PID control method and system for high-order unknown nonlinear systems based on deep learning. Background Technology

[0002] The PID (Proportional-Integral-Derivative) controller is a regulator that controls based on proportional, integral, and derivative parameters. As a classic controller widely used in industrial control, the PID controller has advantages such as simple structure, few parameters, and no need for known model information, making it a typical model-free controller and the most widely used controller type in industrial control. However, in today's era of high-performance control, traditional PID controllers also have several problems, such as insufficient control accuracy. Furthermore, existing research on PID control mainly focuses on linear systems, while real-world physical systems are often nonlinear and contain unknown dynamics. Existing PID controller research lacks a general theory for addressing the nonlinearity and uncertainty in real-world systems. The fundamental reason is that traditional PID controllers, relying solely on feedback mechanisms, have limited ability to handle unknown nonlinearities, resulting in certain limitations in their control. Therefore, researching PID-related control algorithms for complex, unknown, and nonlinear systems is highly valuable and significant.

[0003] With the development of artificial intelligence, neural networks have been proposed and widely applied in the control of unknown nonlinear systems. Among them, artificial neural networks, represented by Radial Basis Function Neural Networks (RBFNNs), have the ability to globally approximate any nonlinear function. Therefore, RBFNNs are widely used in the adaptive control of nonlinear systems. However, although adaptive neural network methods have achieved great success in the theoretical field of nonlinear system control, PID controllers are more commonly used in practical industrial control.

[0004] Currently, there is a class of PID control algorithms for unknown nonlinear systems in the standard form of second order. However, this PID control algorithm cannot be extended to nonlinear systems with an order higher than 2 or general systems with a nonlinear rate of change higher than linear, such as complex high-order unknown nonlinear systems (i.e., high-order uncertain nonlinear systems) such as nonlinear coupled mechanical systems and supercritical units. Its limitations are relatively strong. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a PID control method and system for high-order unknown nonlinear systems based on Deterministic Learning (DL). For high-order nonlinear systems with unknown dynamics, an RBF neural network is introduced to compensate for the complex unknown nonlinearities in the controlled system, overcoming the limitation of traditional PID controllers that rely solely on feedback mechanisms to combat unknown nonlinearities. Furthermore, based on Lyapunov theory, not only is system stability and tracking control guaranteed, but the selection of controller parameters is also simplified. Based on deterministic learning theory, the complex unknown nonlinear dynamics are accurately compensated and approximated, and the acquired knowledge is stored in a constant neural network to construct a knowledge-based extended PID controller, thereby improving overall control performance.

[0006] In a first aspect, the present invention provides a PID control method for high-order unknown nonlinear systems based on deep learning.

[0007] A PID control method for high-order unknown nonlinear systems based on deep learning includes: Obtain the actual high-order state vector of a high-order unknown nonlinear system, and establish a spatial state mathematical model and a reference motion trajectory model; Based on the actual and reference outputs of the model, the tracking error of the system is determined. This tracking error is then input into an experience-based extended PID controller, which performs real-time control of the system based on the output control signal. The construction of the experience-based extended PID controller includes: Based on the system's tracking error, a composite filter tracking error term is defined, which is expressed by the derivatives of the tracking error. Differentiate the tracking error term of the composite filter to construct the error system; Define a high-order unknown nonlinear dynamic function in the error system, approximate the function using RBFNN, and then construct an extended PID controller based on adaptive RBFNN. Substitute this controller into the error system to construct a closed-loop error system. Based on deterministic learning theory, the adaptive RBFNN in the closed-loop error system is learned and trained in closed-loop control by using the periodic reference motion trajectory and the corresponding higher-order state vector.

[0008] A further technical solution involves constructing an error system that includes a high-order state vector and a high-order reference output of a high-order unknown nonlinear system. An RBF neural network is then constructed with the high-order state vector and the high-order reference output as inputs to fit and approximate the high-order unknown nonlinear dynamic function in the error system.

[0009] A further technical solution involves introducing adaptive design based on the constructed RBF neural network to build an extended PID controller based on the adaptive RBF neural network. The adaptive RBF neural network weight update rate is set based on Lyapunov stability. An extended PID controller based on an adaptive RBF neural network is substituted into the error system to construct a closed-loop error system; Based on deterministic learning theory, an adaptive RBF neural network in a closed-loop error system is trained using a periodic reference motion trajectory and its corresponding higher-order state vector. The training is completed by learning in the closed-loop control so that the tracking error and weight estimation error converge to a small neighborhood of zero.

[0010] A further technical solution is to store the learned experience in the form of constant neural network weights; Based on stored experiential knowledge, build an experience-based extended PID controller.

[0011] A further technical solution involves transforming the state of the nonlinear terms in the closed-loop error system during training to construct a linear time-varying system. Closed-loop control learning is then performed within this linear time-varying system, causing the tracking error and weight estimation error to converge to a small neighborhood of zero, thus completing the training.

[0012] A further technical solution defines the composite filter tracking error term, expressed in terms of the derivatives of the tracking error, as follows: ; in, The integral representing the tracking error. The derivatives of the tracking error are represented by their respective orders. The set scaling factor.

[0013] A further technical solution involves differentiating the composite filter tracking error term, resulting in: ; definition as well as The error system is organized and constructed as follows: ; in, denoted by , and u represents the input to the controller.

[0014] Secondly, the present invention provides a PID control system for a high-order unknown nonlinear system based on deep learning.

[0015] A high-order unknown nonlinear system PID control system based on deep learning includes: The data acquisition module is used to acquire the actual high-order state vector of a high-order unknown nonlinear system; The model building module is used to establish a spatial state mathematical model and a reference motion trajectory model; The tracking error determination module is used to determine the tracking error of the system based on the actual output and reference output of the model. The control module is used to input the tracking error into an experience-based extended PID controller, and to perform real-time control of the system based on the output control signal; the construction of the experience-based extended PID controller includes: Based on the system's tracking error, a composite filter tracking error term is defined, which is expressed by the derivatives of the tracking error. Differentiate the tracking error term of the composite filter to construct the error system; Define a high-order unknown nonlinear dynamic function in the error system, approximate the function using RBFNN, and then construct an extended PID controller based on adaptive RBFNN. Substitute this controller into the error system to construct a closed-loop error system. Based on deterministic learning theory, the adaptive RBFNN in the closed-loop error system is learned and trained in closed-loop control by using the periodic reference motion trajectory and the corresponding higher-order state vector.

[0016] Thirdly, the present invention also provides an electronic device, including a memory and a processor, and computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the steps of the method described in the first aspect.

[0017] Fourthly, the present invention also provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the steps of the method described in the first aspect.

[0018] The above one or more technical solutions have the following beneficial effects: 1. This invention provides a PID control method and system for high-order unknown nonlinear systems based on deep learning. For high-order nonlinear systems with unknown dynamics, a neural network extended PID control method is adopted. By introducing a radial basis neural network, the high-order unknown nonlinearity is identified, and the complex uncertainty terms of the controlled high-order system in the control process are dynamically compensated. This overcomes the limitation of traditional PID controllers that rely solely on feedback mechanisms to combat system uncertainty and unknown nonlinearity, thereby significantly improving the control performance of traditional PID.

[0019] 2. In this invention, based on the neural network extended PID controller design framework and Lyapunov theory, not only can the stability and tracking control of the system be guaranteed, but the selection of controller parameters is also simplified, which reduces the difficulty of selecting parameters of the extended PID controller to a certain extent.

[0020] 3. This invention introduces a deterministic learning (DL) mechanism, enabling the neural network to accurately identify the closed-loop unknown nonlinear dynamics in high-order systems. This solves the closed-loop learning problem in extended PID control of such high-order uncertain nonlinear systems. Under the adaptive weight law of the neural network based on Lyapunov stability design, the designed radial basis function neural network can accurately approximate the unknown dynamics of the complex unknown nonlinear dynamic system and store the acquired knowledge in a constant neural network, constructing an extended PID controller based on empirical knowledge, thereby improving the overall control performance. When facing the same or similar control tasks, this PID control method can achieve faster convergence speed and tracking accuracy, while saving computational resources and improving the transient performance of the system. Attached Figure Description

[0021] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0022] Figure 1 This is a flowchart of the PID control method for high-order unknown nonlinear systems based on deep learning, as described in an embodiment of the present invention. Figure 2 This is a simulation diagram of state tracking error and trajectory in an embodiment of the present invention; Figure 3 This is a simulation diagram illustrating the convergence of neural network weights in an embodiment of the present invention; Figure 4 This is a simulation diagram of neural network approximation in an embodiment of the present invention; Figure 5 This is a simulation comparison diagram of the control performance of the extended PID controller, the neural network-based extended PID controller, and the experience-based extended PID controller in the embodiments of the present invention. Detailed Implementation

[0023] It should be noted that the following detailed descriptions are exemplary and are intended only to describe specific embodiments and to provide further explanation of the invention, and are not intended to limit the scope of exemplary embodiments of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0024] Example 1 To address the shortcomings of existing technologies, this embodiment provides a neural network-extended PID control method for high-order unknown nonlinear systems based on deterministic learning (DL). Based on the deterministic learning mechanism, it achieves accurate learning and knowledge reuse of the unknown dynamic functions of the system while ensuring stable system control. Furthermore, it proposes an intelligent PID control framework for high-order unknown nonlinear systems, improving overall control performance. Through this PID control method, faster convergence speed and tracking accuracy can be achieved, computational resources can be saved, and the transient performance of the system can be improved.

[0025] A PID control method for high-order unknown nonlinear systems based on deterministic learning (DL), such as Figure 1 As shown, the specific steps include: Step S1: Establish a spatial state mathematical model and a reference motion trajectory model. At the same time, obtain the actual high-order state vector of the high-order unknown nonlinear system.

[0026] For a high-order canonical form nonlinear system (i.e., a controlled system) containing unknown dynamics, the space state expression is established as follows: (1) in, This represents the state vector of the high-order unknown nonlinear system; Indicates the input to the controller; This indicates the output of the system; and This represents the unknown nonlinear function of the system.

[0027] Taking the above-mentioned high-order unknown nonlinear system as the controlled system, the reference motion trajectory model of the controlled system (1) is constructed as follows: (2) in, This represents the system state vector of the reference motion trajectory model; Represent a known smooth nonlinear function; The output of the reference motion trajectory model (2) is called the reference output.

[0028] Furthermore, the controlled system is set to initial values... The system trajectory below is recorded as Furthermore, the system trajectory assumption of this reference motion trajectory model is a cyclic trajectory.

[0029] Step S2: Based on the actual output and reference output of the model, determine the system's tracking error, input the tracking error into the experience-based extended PID controller, and perform real-time control of the system based on the output control signal. The construction of this experience-based extended PID controller specifically includes the following steps: Step S2.1: Construct the system tracking error based on the two models mentioned above, and define the composite filter tracking error term represented by the derivatives of the tracking error.

[0030] Specifically, the tracking error of the system is defined as: (3) in, This is the actual output of the system. This is the output of the reference trajectory model. Numerical simulations were performed on the state tracking error and the output trajectory, and the simulation results are as follows: Figure 2 As shown, Figure 2 (a) is a simulation diagram of the state tracking error. Figure 2 (b) is a simulation diagram of the trajectory.

[0031] Define the composite filter tracking error term as: (4) in, The integral representing the tracking error. The derivatives of the tracking error are represented by their respective orders. This indicates the preset scaling factor.

[0032] Step S2.2: Differentiate the composite filter tracking error term to construct the error system. Specifically, differentiate the composite filter error term (4) as follows: (5) Define nonlinear terms and nonlinear terms The combined error term (5) after integrating the derivatives can be summarized as follows: (6) Step S2.3: Define the high-order unknown nonlinear dynamic function in the error system, approximate the function using RBFNN, and then construct an extended PID controller based on adaptive RBFNN. Substitute this controller into the error system to construct a closed-loop error system.

[0033] Step S2.3.1: The error system constructed above includes the higher-order state vector and higher-order reference output of the higher-order unknown nonlinear system. The unknown nonlinear dynamic function in the error system is defined as: (7) In the above formula, This represents the input to the RBF neural network.

[0034] Step S2.3.2: Construct an RBF neural network with a high-order state vector and a high-order reference output as inputs, and use this RBFNN to fit and approximate the high-order unknown nonlinear dynamic function in the error system. That is, the above-mentioned unknown nonlinear dynamic function (7) can be approximated and represented by an RBF neural network, as follows: (8) in, This represents the ideal weights of the neural network. These are the corresponding radial basis functions. This represents the error in the ideal approximation.

[0035] Step S2.3.3: Introduce adaptive design and construct an extended PID controller based on an adaptive RBF neural network, as follows: (9) in, Indicates the controller gain. This represents the adaptive estimate of the neural network weights. The scaling factor corresponding to the tracking error satisfies the Hurwitz condition.

[0036] Step S2.3.4: Based on Lyapunov stability, set the adaptive RBF neural network weight update rate as follows: (10) in, Represents a positive definite diagonal matrix. .

[0037] Step S2.3.5: Substitute the designed controller (9) into the error system (6) to construct a closed-loop error system, as follows: (11) Step S2.4: Based on the deterministic learning theory, the adaptive RBFNN in the closed-loop error system is trained in the closed-loop control using the periodic reference motion trajectory and the corresponding higher-order state vector. After training, an experience-based extended PID controller is obtained.

[0038] Specifically, according to deterministic learning theory, when the RBF neural network satisfies the persistentexcitation (PE) condition, the estimated weights of the neurons in the neural network can converge to the ideal value. The constructed neural network can achieve accurate approximation of unknown nonlinear dynamics, thereby realizing learning in closed-loop control. Based on Lyapunov stability, under the action of the constructed controller (9), all closed-loop signals of the above system (1) eventually become uniformly bounded, and the tracking error converges to a small neighborhood of zero. This proves that the input of the RBF neural network is... By tracing a cyclic trajectory, and then following the regressor subvector composed of neurons near the cyclic trajectory... Satisfying the continuous incentive condition provides a theoretical basis for the subsequent proof of neural network learning.

[0039] Furthermore, considering the nonlinear terms in the closed-loop error system (11) This might amplify the approximation error, thus hindering learning. To address this issue, this embodiment employs a state transformation method to eliminate the influence of nonlinear terms on learning. Specifically, it uses a transformation function... ,in For nonlinear terms The maximum value of is used to transform the nonlinear term in the closed-loop error model, resulting in the following linear time-varying (LTV) system including tracking error and neural network weight estimation: (12) in, The disturbance term represents the approximation error. This represents the learning gain of neurons near the trajectory. This represents the weight estimation error of the trajectory neuron.

[0040] Based on the exponential theorem for LTV systems and the perturbation theorem for nonlinear systems, the tracking error and the estimated neural network weights are converged to a small neighborhood of zero, yielding the ideal values ​​for the neural network weights and completing the training. The simulation results of the neural network weight convergence and the neural network approximation are as follows: Figure 3 and Figure 4 As shown.

[0041] Furthermore, the learned experience knowledge is stored as constant neural network weights; based on the stored experience knowledge, an experience-based extended PID controller is constructed, and the experience-based extended PID controller is used to perform closed-loop control of the system.

[0042] Specifically, firstly, the learned nonlinear knowledge is stored in the form of a constant neural network, which is represented as follows: (13) in, This represents the time interval after the neural network weights converge. This represents the adaptive estimate of the weights of the RFB neural network.

[0043] Then, based on the stored constant neural network, an empirical extended PID controller is constructed as follows: (14) Finally, an empirically-based extended PID controller is used to perform closed-loop control of the high-order unknown nonlinear system under control.

[0044] By introducing knowledge into the closed-loop control process, the controller can achieve high-performance control without repeated readjustment of network weights when facing the same or similar control tasks, thus greatly saving computing resources and further improving the transient performance of the system.

[0045] To further verify the superiority of the control method proposed in this embodiment, numerical simulations were performed on the extended PID controller (EPID), the neural network-based extended PID controller (NNB-EPID), and the experience-based extended PID controller (EBL-EPID). The comparison of the simulated control performance is shown in the figure below. Figure 5 As shown, it is clear that the experience-based extended PID controller can achieve better control performance, namely, smaller tracking error and better transient performance.

[0046] Example 2 This embodiment proposes a PID control system for a high-order unknown nonlinear system based on deep learning, including: The data acquisition module is used to acquire the actual high-order state vector of a high-order unknown nonlinear system; The model building module is used to establish a spatial state mathematical model and a reference motion trajectory model; The tracking error determination module is used to determine the tracking error of the system based on the actual output and reference output of the model. The control module is used to input the tracking error into an experience-based extended PID controller, and to perform real-time control of the system based on the output control signal; the construction of the experience-based extended PID controller includes: Based on the system's tracking error, a composite filter tracking error term is defined, which is expressed by the derivatives of the tracking error. Differentiate the tracking error term of the composite filter to construct the error system; Define a high-order unknown nonlinear dynamic function in the error system, approximate the function using RBFNN, and then construct an extended PID controller based on adaptive RBFNN. Substitute this controller into the error system to construct a closed-loop error system. Based on deterministic learning theory, the adaptive RBFNN in the closed-loop error system is learned and trained in closed-loop control by using the periodic reference motion trajectory and the corresponding higher-order state vector.

[0047] Example 3 This embodiment provides an electronic device, including a memory and a processor, as well as computer instructions stored in the memory and running on the processor. When the processor executes the computer instructions, it completes the steps in the PID control method for high-order unknown nonlinear systems based on DL as described above.

[0048] Example 4 This embodiment also provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the steps in the PID control method for high-order unknown nonlinear systems based on DL as described above.

[0049] The steps and methods involved in Embodiments 2 to 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0050] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0051] The above description is only a preferred embodiment of the present invention. Although the specific implementation of the present invention has been described in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that, based on the technical solution of the present invention, various modifications or variations that can be made by those skilled in the art without creative effort are still within the scope of protection of the present invention.

Claims

1. A PID control method for high-order unknown nonlinear systems based on deterministic learning, characterized in that, include: To obtain the actual high-order state vector of a high-order unknown nonlinear system, a spatial state mathematical model and a reference trajectory model are established; the expression of the spatial state mathematical model is: in, This represents the state vector of the high-order unknown nonlinear system; Indicates the controller input; This indicates the output of the system; and Represents the unknown nonlinear function of the system; Based on the actual and reference outputs of the model, the tracking error of the system is determined. This tracking error is then input into an experience-based extended PID controller, which performs real-time control of the system based on the output control signal. The construction of the experience-based extended PID controller includes: Based on the system's tracking error, a composite filter tracking error term is defined, which is expressed by the derivatives of the tracking error. Differentiate the tracking error term of the composite filter to construct the error system; A high-order unknown nonlinear dynamic function is defined in the error system. This function is approximated using an RBFNN, and an extended PID controller based on an adaptive RBFNN is constructed. Substituting this approximation into the error system, a closed-loop error system is built. The extended PID controller based on the adaptive RBFNN is: in, Indicates controller gain. r Describe the tracking error term of the composite filter. This represents the adaptive estimate of the neural network weights. These are the corresponding radial basis functions. e Indicates tracking error. The derivatives of the tracking error are represented by their respective orders. The integral of the tracking error is represented by the integral of the tracking error. The scaling factor corresponding to the tracking error satisfies the Hurwitz condition; Based on deterministic learning theory, the adaptive RBFNN in the closed-loop error system is learned and trained in closed-loop control using periodic reference motion trajectories and corresponding higher-order state vectors. Specifically, according to deterministic learning theory, when the RBF neural network meets the continuous excitation condition, the estimated weights of the neurons in the neural network can converge to the ideal value, and the constructed neural network can achieve accurate approximation of unknown nonlinear dynamics.

2. The PID control method for high-order unknown nonlinear systems based on deterministic learning as described in claim 1, characterized in that, The constructed error system includes a high-order state vector and a high-order reference output of a high-order unknown nonlinear system. An RBF neural network is constructed with the high-order state vector and the high-order reference output as inputs to fit and approximate the high-order unknown nonlinear dynamic function of the error system.

3. The PID control method for high-order unknown nonlinear systems based on deterministic learning as described in claim 2, characterized in that, Based on the constructed RBF neural network, adaptive design is introduced to build an extended PID controller based on the adaptive RBF neural network; The adaptive RBF neural network weight update rate is set based on Lyapunov stability. An extended PID controller based on an adaptive RBF neural network is substituted into the error system to construct a closed-loop error system; Based on deterministic learning theory, an adaptive RBF neural network in a closed-loop error system is trained using a periodic reference motion trajectory and its corresponding higher-order state vector. The training is completed by learning in the closed-loop control so that the tracking error and weight estimation error converge to a small neighborhood of zero.

4. The PID control method for high-order unknown nonlinear systems based on deterministic learning as described in claim 3, characterized in that, The learned experience is stored as constant neural network weights. Based on stored experiential knowledge, build an experience-based extended PID controller.

5. The PID control method for high-order unknown nonlinear systems based on deterministic learning as described in claim 3, characterized in that, During training, the nonlinear terms in the closed-loop error system are transformed to construct a linear time-varying system. Closed-loop control learning is then performed in this linear time-varying system to bring the tracking error and weight estimation error to a small neighborhood of zero, thus completing the training.

6. The PID control method for high-order unknown nonlinear systems based on deterministic learning as described in claim 1, characterized in that, a definition is provided. The composite filter tracking error term, expressed in terms of the derivatives of the tracking error, is: ； in, The integral of the tracking error is represented by the integral of the tracking error. The derivatives of the tracking error are represented by their respective orders. The set scaling factor.

7. The PID control method for high-order unknown nonlinear systems based on deterministic learning as described in claim 1, characterized in that, The derivative of the composite filter tracking error term is: ； definition as well as The error system is organized and constructed as follows: ； in, Represents nonlinear terms, u This indicates the input to the controller.

8. A PID control system for a high-order unknown nonlinear system based on deterministic learning, characterized in that, include: The data acquisition module is used to acquire the actual high-order state vector of a high-order unknown nonlinear system; The model building module is used to establish a spatial state mathematical model and a reference motion trajectory model; the expression of the spatial state mathematical model is: in, This represents the state vector of the high-order unknown nonlinear system; Indicates the controller input; This indicates the output of the system; and Represents the unknown nonlinear function of the system; The tracking error determination module is used to determine the tracking error of the system based on the actual output and reference output of the model. The control module is used to input the tracking error into an experience-based extended PID controller, and to perform real-time control of the system based on the output control signal; the construction of the experience-based extended PID controller includes: Based on the system's tracking error, a composite filter tracking error term is defined, which is expressed by the derivatives of the tracking error. Differentiate the tracking error term of the composite filter to construct the error system; A high-order unknown nonlinear dynamic function is defined in the error system. This function is approximated using an RBFNN, and an extended PID controller based on an adaptive RBFNN is constructed. Substituting this approximation into the error system, a closed-loop error system is built. The extended PID controller based on the adaptive RBFNN is: in, Indicates controller gain. r Describe the tracking error term of the composite filter. This represents the adaptive estimate of the neural network weights. These are the corresponding radial basis functions. e Indicates tracking error. The derivatives of the tracking error are represented by their respective orders. The integral of the tracking error is represented by the integral of the tracking error. The scaling factor corresponding to the tracking error satisfies the Hurwitz condition; Based on deterministic learning theory, the adaptive RBFNN in the closed-loop error system is learned and trained in closed-loop control using periodic reference motion trajectories and corresponding higher-order state vectors. Specifically, according to deterministic learning theory, when the RBF neural network meets the continuous excitation condition, the estimated weights of the neurons in the neural network can converge to the ideal value, and the constructed neural network can achieve accurate approximation of unknown nonlinear dynamics.

9. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, complete the steps of a PID control method for a high-order unknown nonlinear system based on deterministic learning as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, Used to store computer instructions, which, when executed by a processor, complete the steps of a PID control method for a high-order unknown nonlinear system based on deterministic learning as described in any one of claims 1-7.

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