A local linear expansion system identification method based on attention mechanism

Abstract

The present application relates to a local linear expansion system identification method based on an attention mechanism, the method comprising: mathematically describing a discrete general form of nonlinear system, and using a variety of circuit parameters as input and output data of the nonlinear system; constructing a state observer based on the nonlinear system and through the Kalman filter theory; performing a first-order Taylor series expansion on the state equation in the nonlinear system to obtain a locally expanded nonlinear system; constructing a time-local Taylor observer based on the locally expanded nonlinear system and the state observer; fitting the time-local Taylor observer with a deep attention network module to obtain an accurate time-local Taylor observer; inputting the data to be predicted into the accurate time-local Taylor observer to obtain an output prediction value, which is a load voltage prediction value. This method realizes the observation and identification of nonlinear systems with unknown general forms or specific mechanism models.

Description

Technical Field

[0001] The present application relates to the technical field of nonlinear system identification, and in particular to a local linear expansion system identification method based on an attention mechanism. Background Art

[0002] At present, there are still the following problems that cannot be ignored when using traditional gray box identification methods to observe and identify complex nonlinear systems:

[0003] 1. It is impossible to establish an accurate mechanism model for highly complex nonlinear systems: Most of the existing gray box models are designed for special systems with specific forms, such as time-varying systems, Hammerstein systems, and affine systems. Correspondingly, few researchers have proposed generalized and universal system identification methods for nonlinear systems with general forms or unknown mechanism models.

[0004] 2. Traditional gray box identification methods are limited to the neighborhood range of the equilibrium point: Traditional gray box identification methods identify the linearized system by linearizing the nonlinear system in the neighborhood range of the equilibrium point. Therefore, the system identification method with linearization is only effective near the equilibrium point, and some nonlinear terms are ignored during the linearization process, resulting in the loss of some important dynamic characteristics, which leads to a relatively low identification effect.

[0005] 3. Traditional gray box models are difficult to cope with high-dimensional, massive and highly complex big data: In actual engineering application fields, systems often exhibit characteristics such as strong complexity and strong nonlinearity. Traditional gray box identification methods are greatly restricted and difficult to handle high-dimensional, massive, complex nonlinear and spatiotemporal coupled big data, making it difficult for data-driven learning modules to achieve a high degree of fitting. Summary of the invention

[0006] Based on this, it is necessary to provide a local linear expansion system identification method based on an attention mechanism. The method is based on a wireless power transmission system and includes:

[0007] S1: mathematically describe a discrete general nonlinear system and use a variety of circuit parameters as input and output data of the nonlinear system;

[0008] S2: Based on the nonlinear system, a state observer is constructed through Kalman filter theory;

[0009] S3: Perform a first-order Taylor series expansion on the state equation in the nonlinear system to obtain a locally expanded nonlinear system;

[0010] S4: constructing a time-local Taylor observer based on the locally expanded nonlinear system and the state observer;

[0011] S5: Fitting the time-local Taylor observer with the deep attention network module to obtain an accurate time-local Taylor observer;

[0012] S6: Input the data to be predicted into the precise time-local Taylor observer to obtain an output prediction value that can reflect the system state, wherein the output prediction value is a load voltage prediction value.

[0013] Beneficial effects: Based on the principle of Taylor series expansion, this method performs a first-order Taylor expansion on the state observer constructed by a general form of nonlinear system, and performs deep fitting with the deep attention network module to construct a system state observer. The predicted data is predicted through a precise time-local Taylor observer, which realizes the observation and identification of nonlinear systems with unknown general forms or specific mechanism models. At the same time, it gets rid of the limitations of complex nonlinear systems on the neighborhood range of stable points, making the gray box identification method more flexible to apply. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0015] Figure 1 This is a flowchart of a local linear expansion system identification method based on an attention mechanism according to an embodiment of the present application.

[0016] Figure 2 This is a circuit diagram of a WPT system according to an embodiment of the present application.

[0017] Figure 3 Schematic diagram of the convergence of the loss function of an embodiment of the present application.

[0018] Figure 4 Schematic diagram of experimental observation results of an embodiment of the present application. DETAILED DESCRIPTION

[0019] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present application. However, the present application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present application, so the present application is not limited by the specific embodiments disclosed below.

[0020] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of this application, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0021] like Figure 1 As shown, this embodiment provides a local linear expansion system identification method based on an attention mechanism, the method comprising:

[0022] S1: A mathematical description is given to a discrete general nonlinear system, and a plurality of circuit parameters are used as input and output data of the nonlinear system.

[0023] The expression of the nonlinear system is:

[0024] ;

[0025] in, The first k +1 status data at the moment; Represents the nonlinear system k Status data collected at all times, , which contains the internal state information of the system and the association information between different states; Represents the nonlinear system k Input data at time, , which means in k External control or incentives on the system at all times; Represents the nonlinear system k Output data at each moment, ; is the dimension of the state data; is the dimension of the input data; is the dimension of the output data; It means that the nonlinear system Nonlinear mapping of state data at; h (·) represents the output equation of the nonlinear system in The mapping relationship at .

[0026] In this embodiment, the general form of nonlinear system refers to a type of nonlinear system that is difficult to characterize and describe with a specific mathematical formula because the nonlinear system is too complex.

[0027] S2: Based on the nonlinear system, a state observer is constructed through Kalman filter theory.

[0028] For the above-mentioned nonlinear system, its state equation is a generalized function mapping form, which does not represent a relatively clean physical mechanism or biochemical reaction, etc. Therefore, for this type of general nonlinear system identification problem, it is first necessary to construct a suitable nonlinear system observer, which can use the measured input and output data to approximate the state and behavior of the nonlinear system, so as to replace the identification result of the original nonlinear system by identifying the observer.

[0029] Specifically, the Kalman filter theory updates the estimated value of the data by the difference between the actually collected data and the predicted data; based on the expression of the nonlinear system, the state observer is constructed by the Kalman filter theory, and the expression of the state observer is:

[0030] ;

[0031] in, represents the first k +1 status data at the moment; represents the first k Status data at the moment; Represents the nonlinear system k Input data at the moment; Represents the nonlinear system k Output data at each moment; represents the output data predicted by the state observer; L is the steady-state Kalman gain; y Represents the output data predicted by the nonlinear system; Represents the state observer k Output data predicted at each moment; It means that the state observer is Nonlinear mapping of state data at .

[0032] S3: Perform a first-order Taylor series expansion on the state equation in the nonlinear system to obtain a locally expanded nonlinear system.

[0033] Specifically, performing a first-order Taylor series expansion on the state equation in the nonlinear system includes:

[0034] According to the Taylor series expansion principle, select any working point on the working domain of the nonlinear system The state equation in the nonlinear system is expanded by a first-order Taylor series; the locally expanded nonlinear system is expressed as:

[0035] ;

[0036] in, The firstk +1 status data at the moment; Represents the nonlinear system k Status data collected at all times; Represents the nonlinear system k Input data at the moment; Represents the nonlinear system k Output data at each moment; It means that the nonlinear system Nonlinear mapping of state data at; The first k -1 status data at time; Represents the nonlinear system k- Input data at time 1; It means that the nonlinear system Nonlinear mapping of state data at; Represents a nonlinear mapping At the point Right x The partial derivative of Represents a nonlinear mapping At the point Right u The partial derivative of .

[0037] S4: Based on the locally expanded nonlinear system and the state observer, a time-local Taylor observer is constructed.

[0038] Specifically, the step includes:

[0039] Based on the Taylor-expanded state equation of the nonlinear system, select any operating point on the working domain of the time-local Taylor observer The state equation in the state observer is expanded by a first-order Taylor series to obtain a time-local Taylor observer; the expression of the time-local Taylor observer is:

[0040] ;

[0041] ;

[0042] ;

[0043] in, represents the first k +1 status data at the moment; represents the first k Status data at the moment; Represents the nonlinear system k Input data at the moment; Represents the state observer k Output data at each moment; It means that the state observer is Nonlinear mapping of state data at; represents a time-local Taylor observer in Nonlinear mapping of state data at; represents the first partial differential function term of the state equation in the time-local Taylor observer; represents the second partial differential function term of the state equation in the time-local Taylor observer; Represents the nonlinear system k- Input data at time 1; represents the first k -1 status data at time; Represents a nonlinear mapping At the point Right x The partial derivative of Represents a nonlinear mapping At the point Right u The partial derivative of .

[0044] S5: Fit the time-local Taylor observer with the deep attention network module to obtain an accurate time-local Taylor observer.

[0045] Specifically, the step includes:

[0046] The first partial differential function term and the second partial differential function term are fitted by the neural network, activation function and weight parameters in the deep attention network module; the fitting formula is expressed as:

[0047] ;

[0048] in, represents the first partial differential function term of the state equation in the time-local Taylor observer; represents the second partial differential function term of the state equation in the time-local Taylor observer; represents the first deep neural network module in the deep attention network module; Represents the second deep neural network module in the deep attention network module; represents the first k -1 status data at time; Represents the nonlinear system k Input data at the moment; represents the first k Status data at the moment; Represents the nonlinear system k- Input data at time 1; a vector representing weight parameters in the first deep neural network module; a vector representing weight parameters in a second deep neural network module;

[0049] The time-local Taylor observer is reconstructed according to the fitting formula to obtain a second state observer; the expression of the second state observer is:

[0050] ;

[0051] ;

[0052] ;

[0053] in, Represents the change in state data predicted by the state observer; Represents the change in input data of a nonlinear system; Represents the state observer k The output data at the moment; C represents the coefficient matrix of the output equation in the second state observer;

[0054] Continue fitting partial differential terms through the two deep neural networks of the first deep neural network module Get the first fitting result;

[0055] The two deep neural networks of the second deep neural network module continue to fit the partial differential terms A second fitting result is obtained;

[0056] The partial differential terms of the state equation in the second state observer are replaced by the first fitting result and the second fitting result. , partial differential terms , and obtain an accurate time-local Taylor observer.

[0057] In this embodiment, the state data and input data of the nonlinear system are stored in a data set D, and the data set is expressed as:

[0058] ;

[0059] in, Represents the nonlinear system k Input data at the moment; Represents the nonlinear system k Status data collected at all times; N represents the time period.

[0060] Since the actual nonlinear system is relatively complex and has strong nonlinear characteristics, there must be a strong nonlinear correlation between the system input and output data collected from these complex nonlinear systems. At the same time, for data sets with a large acquisition time span, ordinary neural network models may not be able to accurately capture the nonlinear relationship of the system. Therefore, this embodiment prefers to use a deep attention network to construct the required deep attention neural network module so that it can keenly obtain important information between the data.

[0061] The exact time-local Taylor observer expression is:

[0062] ;

[0063] ;

[0064] ;

[0065] ;

[0066] ;

[0067] in, represents the first k +1 status data at the moment; Represents the nonlinear system k Input data at the moment; represents the first k Status data at the moment; represents the first k Output data at each moment; represents the first k -1 status data at time; Represents the nonlinear system k Status data at the moment; Represents the nonlinear system k- Input data at time 1; represents the first fitting result; represents the second fitting result; N represents the time period; represents the first deep neural network module in the deep attention network module; Represents the second deep neural network module in the deep attention network module; a vector representing weight parameters in the first deep neural network module; a vector representing weight parameters in a second deep neural network module; Represents the change in state data predicted by the state observer; Represents the change in input data of a nonlinear system; Indicates that for the first partial differential function term, the state data in the data set A first weight coefficient output by a first deep neural network in a first deep neural network module; Indicates that for the first partial differential function term, the state data in the data set A second weight coefficient output by a second deep neural network in a second deep neural network module; Indicates that for the second partial differential function term, the state data in the data set A third weight coefficient output by the first deep neural network in the first deep neural network module; Indicates that for the second partial differential function term, the state data in the data set The fourth weight coefficient output by the second deep neural network in the second deep neural network module; Sim(·) represents the correlation calculation formula.

[0068] The inherent properties of the Softmax function can highlight the weights of more important elements, which can be further understood as the weight coefficient of the data. The calculation formula is:

[0069] .

[0070] In this embodiment, in order to ensure that the partial differential terms of the state equation fitted by the deep attention neural network module have good accuracy, the two deep neural network models are respectively constructed with their own loss functions according to the gap between the calculation structure of the actual partial differential terms and the fitting results. The loss function can greatly help improve the accuracy of the fitting results.

[0071] A first loss function is calculated according to the first partial differential function term and the first fitting result; the calculation formula is:

[0072] ;

[0073] in, represents the first loss function; represents the square of the Euclidean norm; represents the first fitting result; represents the first deep neural network module in the deep attention network module; represents the first k -1 status data at time; Represents the nonlinear system k Input data at the moment; a vector representing weight parameters in the first deep neural network module;

[0074] According to the second partial differential function term and the second fitting result, a second loss function is calculated; the calculation formula is:

[0075] ;

[0076] in, represents the second loss function; represents the second fitting result; Represents the second deep neural network module in the deep attention network module; represents the first k Status data at the moment; Represents the nonlinear system k -1 Input data at time; a vector representing weight parameters in a second deep neural network module;

[0077] The loss function of the deep attention network module is constructed based on the first loss function and the second loss function; the calculation formula is:

[0078] ;

[0079] in, represents the loss function of the deep attention network module, represents the first weight, represents the second weight;

[0080] The loss function of the deep attention network module is used to back-propagate the deep attention network module, and the Adam gradient optimization algorithm is used to adaptively adjust the network parameters of the deep attention network module until the deep attention network module converges.

[0081] Furthermore, since the state data of complex nonlinear systems is difficult to capture and collect directly, in order to improve the accuracy of the time-local Taylor observer in identifying the system, the first k +1 Status data at the moment Multiply by the coefficient matrix C , to satisfy the output equation of the time-local Taylor observer and obtain the nonlinear system k +1, the output data is the load voltage. In addition, based on the output equation and output data of the time-local Taylor observer, a global loss function is constructed to further train and improve the entire observer model described in this application to obtain a more accurate time-local Taylor observer. The global loss function is calculated based on the output data predicted by the time-local Taylor observer and the output data of the nonlinear system; the calculation formula is:

[0082] ;

[0083] in, represents the global loss function; represents the square of the Euclidean norm; Represents the nonlinear system k -1 The actual output data at the moment; Represents the exact time-local Taylor observer k -1 time instant output data; the global loss function is used to train the overall model of the fitting precise time-local Taylor observer, especially the learnable coefficient matrix C in the fitting output equation.

[0084] S6: Input the data to be predicted into the precise time-local Taylor observer to obtain an output prediction value that can reflect the system state, wherein the output prediction value is a load voltage prediction value.

[0085] The method provided in this embodiment is based on the Taylor series expansion principle. It performs a first-order Taylor expansion on the state observer constructed by a general form of a nonlinear system, and performs deep fitting with a deep attention network module to construct a system state observer. The predicted data is predicted through a precise time-local Taylor observer, thereby realizing the observation and identification of nonlinear systems with unknown general forms or specific mechanism models. At the same time, it gets rid of the limitations of complex nonlinear systems on the neighborhood range of stable points, so that the gray box identification method can be more flexibly applied.

[0086] In this embodiment, the deep attention network module is deeply integrated with the control mechanism to construct a deep attention network module based on the attention mechanism. The two partial differential terms in the state equation of the time-local Taylor observer are fit through the deep attention network module, and the loss function and the global loss function of the deep neural network module are used to assist in training the observer model to obtain a time-local Taylor observer with both nonlinear fitting capability and interpretability.

[0087] This embodiment will consider the prototype of the wireless power transfer system (Wireless Power Transfer, WPT). The working principle of the WPT system not only involves highly nonlinear electrical characteristics and complex magnetic induction principles, but also has many actual circuit components and parameters, resulting in the WPT system being a highly complex nonlinear system with large-scale multi-coupled multi-dimensional data. Therefore, the WPT system can verify the effectiveness of the identification method in this embodiment.

[0088] The circuit diagram of the WPT system is as follows Figure 2As shown, its structure can be divided into three levels, namely, a phase-shift controlled inverter, a resonant cavity and a rectifier. The inverter and the rectifier are respectively composed of four switching tubes S1-S4 and four diodes D1-D4. Other main circuit parameters are shown in Table 1.

[0089] Table 1 shows the main parameters of the WPT system experimental device;

[0090] ;

[0091] In order to evaluate and verify the performance of the method provided in this embodiment, the complex nonlinear system identification method based on the gray box model proposed in this embodiment is tested using the input and output data of the actual WPT system, wherein the input and output data are data collected from the actual WPT system, including the power supply DC power supply and voltage, the continuous dynamic working load voltage V 0 and other important parameters. According to the dynamically sampled data set, the first 70% of the data samples are selected as the training set, and the last 30% of the data samples are selected as the test set. The loss convergence result of the model proposed in the present invention is obtained as follows Figure 3 As shown in the figure, the horizontal axis is "Epoch", which represents the model training round and is a hyperparameter of a neural network model; the vertical axis is "Model Loss", which reflects the calculated loss size and its unit is 1. Figure 3 The loss curve in describes the convergence of the weighted loss values ​​of the deep attention network module loss function and the global loss function on the training set and the test set, respectively, corresponding to the solid line and dotted line in the figure, thus reflecting that the model proposed in this embodiment converges rapidly.

[0092] In addition, the experimental prediction results are as follows Figure 4 As shown, the load voltage value predicted by the innovative observer based on the gray box model proposed in this embodiment maintains good consistency with the actual load voltage value, that is, the solid line is the actual value of the load voltage, and the dotted line is the predicted value of the load voltage, and the two are almost consistent. This proves that the complex nonlinear system identification method based on the gray box model proposed in this embodiment shows good system identification ability under the mutual assistance of the neural network model and the mechanism model.

[0093] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are 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.

[0094] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be construed as limiting the scope of the patent application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent application shall be subject to the attached claims.

Claims

1. A local linear expansion system identification method based on an attention mechanism, based on a wireless power transmission system, the wireless power transmission system includes a plurality of circuit parameters, the plurality of circuit parameters are: the capacitance of a transmitting resonator, the capacitance of a receiving resonator, the capacitance of an output filter, the inductance of a transmitting resonator, the inductance of a receiving resonator, the mutual inductance between the inductance of a transmitting resonator and the inductance of a receiving resonator, the equivalent resistance of a branch where the inductance of a transmitting resonator and the capacitance of a transmitting resonator are located, the equivalent resistance of a branch where the inductance of a receiving resonator and the capacitance of a receiving resonator are located, a working load resistance, a power supply DC power supply and a voltage, characterized in that: include: S1: mathematically describe a discrete general nonlinear system and use a variety of circuit parameters as input and output data of the nonlinear system; The expression of the nonlinear system is: ； in, The first k +1 status data at the moment; Represents the nonlinear system k Status data collected at all times, ; Represents the nonlinear system k Input data at time, ; Represents the nonlinear system k Output data at each moment, ; is the dimension of the state data; is the dimension of the input data; is the dimension of the output data; It means that the nonlinear system Nonlinear mapping of state data at; h (·) represents the output equation of the nonlinear system in The mapping relationship at S2: Based on the nonlinear system, a state observer is constructed through Kalman filter theory; The Kalman filter theory updates the estimated value of the data by the difference between the actual collected data and the predicted data; based on the expression of the nonlinear system, the state observer is constructed by the Kalman filter theory, and the expression of the state observer is: ； in, represents the first k +1 status data at the moment; represents the first k Status data at the moment; represents the output data predicted by the state observer; L is the steady-state Kalman gain; y Represents the output data predicted by the nonlinear system; Represents the state observer k Output data predicted at each moment; It means that the state observer is Nonlinear mapping of state data at; S3: Perform a first-order Taylor series expansion on the state equation in the nonlinear system to obtain a locally expanded nonlinear system, including: According to the Taylor series expansion principle, select any working point on the working domain of the nonlinear system The state equation in the nonlinear system is expanded by a first-order Taylor series; the locally expanded nonlinear system is expressed as: ； in, The first k -1 status data at time; Represents the nonlinear system k- Input data at time 1; It means that the nonlinear system Nonlinear mapping of state data at; Represents a nonlinear mapping At the point Right x The partial derivative of Represents a nonlinear mapping At the point Right u The partial derivative of S4: Based on the locally expanded nonlinear system and the state observer, a time-local Taylor observer is constructed, including: Based on the Taylor-expanded state equation of the nonlinear system, select any operating point on the working domain of the time-local Taylor observer The state equation in the state observer is expanded by a first-order Taylor series to obtain a time-local Taylor observer; the expression of the time-local Taylor observer is: ； ； ； in, represents a time-local Taylor observer in Nonlinear mapping of state data at; represents the first partial differential function term of the state equation in the time-local Taylor observer; represents the second partial differential function term of the state equation in the time-local Taylor observer; represents the first k -1 status data at time; Represents a nonlinear mapping At the point Right x The partial derivative of S5: Fitting the time-local Taylor observer with the deep attention network module to obtain an accurate time-local Taylor observer, including: The first partial differential function term and the second partial differential function term are fitted by the neural network, activation function and weight parameters in the deep attention network module; the fitting formula is expressed as: ； in, represents the first deep neural network module in the deep attention network module; Represents the second deep neural network module in the deep attention network module; a vector representing weight parameters in the first deep neural network module; a vector representing weight parameters in a second deep neural network module; The time-local Taylor observer is reconstructed according to the fitting formula to obtain a second state observer; the expression of the second state observer is: ； ； ； in, Represents the change in state data predicted by the state observer; represents the change of the input data of the nonlinear system; C represents the coefficient matrix of the output equation in the second state observer; Continue fitting partial differential terms through the two deep neural networks of the first deep neural network module Get the first fitting result; The two deep neural networks of the second deep neural network module continue to fit the partial differential terms A second fitting result is obtained; The partial differential terms of the state equation in the second state observer are replaced by the first fitting result and the second fitting result. , partial differential terms , we obtain an accurate time-local Taylor observer; S6: Input the data to be predicted into the precise time-local Taylor observer to obtain an output prediction value that can reflect the system state, wherein the output prediction value is a load voltage prediction value.

2. The local linear expansion system identification method based on the attention mechanism according to claim 1 is characterized in that: The state data and input data of the nonlinear system are stored in the data set D, which is represented as: ； in, Represents the nonlinear system k Input data at the moment; Represents the nonlinear system k Status data collected at all times; N represents the time period.

3. The local linear expansion system identification method based on the attention mechanism according to claim 2 is characterized in that: The exact time-local Taylor observer expression is: ； ； ； ； ； in, represents the first k +1 status data at the moment; Represents the nonlinear system k Input data at the moment; represents the first k Status data at the moment; represents the first k Output data at each moment; represents the first k -1 status data at time; Represents the nonlinear system k Status data at the moment; Represents the nonlinear system k- Input data at time 1; represents the first fitting result; represents the second fitting result; N represents the time period; represents the first deep neural network module in the deep attention network module; Represents the second deep neural network module in the deep attention network module; a vector representing weight parameters in the first deep neural network module; a vector representing weight parameters in a second deep neural network module; Represents the change in state data predicted by the state observer; Represents the change in input data of a nonlinear system; Indicates that for the first partial differential function term, the state data in the data set A first weight coefficient output by a first deep neural network in a first deep neural network module; Indicates that for the first partial differential function term, the state data in the data set A second weight coefficient output by a second deep neural network in a second deep neural network module; Indicates that for the second partial differential function term, the state data in the data set A third weight coefficient output by the first deep neural network in the first deep neural network module; Indicates that for the second partial differential function term, the state data in the data set The fourth weight coefficient output by the second deep neural network in the second deep neural network module; Sim(·) represents the correlation calculation formula.

4. The local linear expansion system identification method based on the attention mechanism according to claim 3 is characterized in that: A first loss function is calculated according to the first partial differential function term and the first fitting result; the calculation formula is: ； in, represents the first loss function; represents the square of the Euclidean norm; represents the first fitting result; represents the first deep neural network module in the deep attention network module; represents the first k -1 status data at time; Represents the nonlinear system k Input data at the moment; a vector representing weight parameters in the first deep neural network module; According to the second partial differential function term and the second fitting result, a second loss function is calculated; the calculation formula is: ； in, represents the second loss function; represents the second fitting result; Represents the second deep neural network module in the deep attention network module; represents the first k Status data at the moment; Represents the nonlinear system k -1 Input data at time; a vector representing weight parameters in a second deep neural network module; The loss function of the deep attention network module is constructed based on the first loss function and the second loss function; the calculation formula is: ； in, represents the loss function of the deep attention network module, represents the first weight, represents the second weight; The loss function of the deep attention network module is used to back-propagate the deep attention network module, and the Adam gradient optimization algorithm is used to adaptively adjust the network parameters of the deep attention network module until the deep attention network module converges.

5. The local linear expansion system identification method based on the attention mechanism according to claim 1, characterized in that: The global loss function is calculated based on the output data predicted by the time-local Taylor observer and the output data of the nonlinear system; the calculation formula is: ； in, represents the global loss function; represents the square of the Euclidean norm; Represents the nonlinear system k -1 The actual output data at the moment; Represents the exact time-local Taylor observer k -1 time instant output data; the global loss function is used to train the overall model of the fitting accurate time-local Taylor observer.

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