A kind of excimer lamp collaborative control method based on multi-source data fusion

Abstract

The application relates to the technical field of control, in particular to a kind of excimer lamp cooperative control method based on multi-source data fusion.The method comprises the following steps: obtaining the multi-source sensing data of excimer lamp system, initializing system state vector, state covariance matrix and the inverse Wishart distribution prior parameter of process and measurement noise covariance matrix, obtaining predicted state mean and predicted covariance matrix based on posterior state estimation, calculating innovation, updating process and measurement noise covariance matrix, calculating state-measurement mutual covariance matrix and measurement innovation covariance matrix, determining optimal gihonov regularization parameter and calculating kalman gain, updating state estimation and state covariance matrix, and generating operation instruction of each excimer lamp based on the updated state.The scheme of the application can overcome the limitations of standard unscented kalman filter, ensure the reliability of kalman gain, and thus improve the uniformity and stability of system output light field.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of control. More particularly, the present application relates to a kind of excimer lamp collaborative control method based on multi-source data fusion. BACKGROUND

[0002] In order to meet the needs of large-area processing or high-intensity irradiation, it is usually necessary to deploy multiple excimer lamps to form an array system and to collaboratively control them to ensure the uniformity and stability of the output light field. However, the operating state of excimer lamps is affected by multiple factors such as lamp aging, gas composition changes, power fluctuations, and environmental temperature and humidity. Moreover, when multiple excimer lamps work collaboratively, the mutual influence between units and environmental changes can further exacerbate the control difficulty, thereby leading to a decline in the overall performance of the system.

[0003] In order to realize the state perception and collaborative control of the excimer lamp system, a model-based filtering estimation algorithm can be used. In terms of processing nonlinear systems, the unscented Kalman filter (UKF) can avoid the complex Jacobian matrix derivation in the extended Kalman filter (EKF) by using unscented transformation (UT) to approximate the probability density of nonlinear functions, thereby having better applicability.

[0004] However, the performance of UKF is highly dependent on the accurate prior setting of the process noise and measurement noise covariance matrix. However, in complex systems such as excimer lamps, the statistical characteristics of noise are often unknown and time-varying. Sensors may produce outliers or non-Gaussian heavy-tailed noise, which can seriously contaminate the state estimation results when the standard UKF faces such abnormal values. In addition, during the filtering iteration process, the measurement innovation covariance matrix may become singular due to model errors or data correlation, leading to numerical instability in its inverse operation, and thereby affecting the calculation of the Kalman gain.

[0005] Therefore, there is an urgent need for a filtering method that can suppress abnormal interference and ensure numerical stability to meet the requirements of collaborative control of multiple excimer lamp systems. SUMMARY

[0006] The present application aims to provide a kind of excimer lamp collaborative control method based on multi-source data fusion to solve the technical problems that the standard unscented Kalman filter in the prior art relies on noise prior information, the singular or ill-conditioned measurement innovation covariance matrix may appear in iteration, leading to numerical instability in its inverse operation, thereby failing to guarantee the uniformity and stability of the output light field of multiple excimer lamp systems. To this end, the present application provides an excimer lamp collaborative control method based on multi-source data fusion, which comprises:

[0007] Acquire multi-source sensor data of the excimer lamp system, initialize the system state vector, state covariance matrix, and inverse Wishart distribution prior parameters of the process and measurement noise covariance matrices; based on the posterior state estimate of the previous time step, generate a Sigma point set using unscented transformation and process the Sigma point set through a nonlinear state equation to obtain the predicted state mean and predicted covariance matrix at the current time step; transform the Sigma point set processed by the nonlinear state equation through the measurement equation to obtain the predicted measurement value, and calculate the innovation between the predicted measurement value and the actual measurement value; within a variational Bayesian framework of fixed-point iteration, based on the innovation and combined with M estimation using Tukey's double-weight function, update the process and measurement noise covariance matrices, and simultaneously calculate the state-measurement cross-covariance matrix and the measurement innovation covariance matrix; use the generalized cross-validation method to determine the optimal Tikhonov regularization parameter for the measurement innovation covariance matrix, and calculate the Kalman gain; use the Kalman gain and innovation to update the state estimate and state covariance matrix, and based on the updated state, generate the operation instructions for each excimer lamp through a cooperative control law.

[0008] Preferably, the initialization of the system state vector, state covariance matrix, and inverse Wishart distribution prior parameters of the process and measurement noise covariance matrices includes: using the sensor data of the excimer lamp system at the initial moment as the system state vector. The initial values; the state covariance matrix Initialize as a diagonal matrix ,in For the state vector dimension, For the first Preset initial variance for each state vector dimension; set prior degrees of freedom parameters for the inverse Wishart distribution of the process noise covariance matrix Q. Prior scale matrix ;in For the estimated process noise covariance matrix, The prior degrees of freedom parameters for the inverse Wishart distribution of the process noise covariance matrix Q are set; the prior degrees of freedom parameters for the inverse Wishart distribution of the measurement noise covariance matrix R are set. Prior scale matrix ;in, The inverse Wishart distribution prior scale matrix of the given measurement noise covariance matrix R. Let m be the prior degrees of freedom parameter of the inverse Wishart distribution of the measurement noise covariance matrix R, and m be the dimension of the measurement vector. This is the estimated measurement noise covariance matrix.

[0009] Preferably, the step of generating a Sigma point set using an unscented transformation based on the posterior state estimate of the previous time step and processing the Sigma point set using a nonlinear state equation to obtain the predicted state mean and predicted covariance matrix at the current time step includes: based on Posterior state estimation at time 1 and posterior covariance matrix Generate 2n+1 Sigma point sets Where n is the dimension of the state vector; substitute each Sigma point in the Sigma point set into the nonlinear state equation. The process is performed to obtain the state prediction point set. The predicted points in the state prediction point set are weighted and calculated to obtain the result. The predicted state mean and predicted covariance matrix at time t; where This refers to the current moment.

[0010] Preferably, the method for obtaining the predicted measurement values ​​and the state-measurement cross-covariance matrix is ​​as follows: [The text abruptly ends here, likely due to an incomplete sentence or a formatting error.] Substitute into the measurement equation The conversion is performed to obtain the measurement prediction point set. We perform weighted calculations on the predicted points in the measurement prediction point set to obtain the predicted measurement mean, the measurement prediction covariance matrix, and the state-measurement cross-covariance matrix. The predicted measurement mean is denoted as... .

[0011] Preferably, the method for calculating the measurement innovation covariance matrix is ​​as follows: In the i-th iteration: (a) Calculate the measurement innovation covariance matrix of the previous iteration, satisfying: In the formula, For the first The measurement innovation covariance matrix of the next iteration. To measure the predicted covariance matrix, For the first The expected value of the measurement noise covariance matrix in the next iteration. At the current time; calculate the weighting factor matrix of the Tukey double-weight function, satisfying: ,in In the formula, Let be the weighting factor matrix of the Tukey double-weight function. For the first Standardized residuals for each measurement vector dimension The first The, the Weights of each measurement vector dimension, To adjust the parameters, m is the dimension of the measurement vector. (a) Calculate the updated measurement noise covariance matrix; the posterior degrees of freedom of the updated measurement noise covariance matrix ; the posterior scale matrix of the updated measurement noise covariance matrix is updated to satisfy: ; and the expectation of the updated measurement noise covariance matrix is calculated as: ; wherein is the set posterior degrees of freedom of the measurement noise covariance matrix, is the posterior scale matrix of the measurement noise covariance matrix, is the transpose of the set posterior degrees of freedom of the measurement noise covariance matrix, is the square root of the weighting factor matrix of the Tukey biweight function, , are the posterior degrees of freedom and the posterior scale matrix of the measurement noise covariance matrix at time ; (c) based on the filtered and smoothed state estimates of the current iteration, the expectation of the process noise covariance matrix is calculated; the posterior inverse Wishart distribution parameters of the updated process noise covariance matrix are calculated: the posterior degrees of freedom of the updated process noise covariance matrix is set; the posterior scale matrix of the updated process noise covariance matrix is updated to satisfy: ; and the expectation of the updated process noise covariance matrix is calculated as: ; wherein is the expectation of the updated process noise covariance matrix, is the posterior scale matrix of the updated process noise covariance matrix, is the set posterior degrees of freedom of the process noise covariance matrix, is the dimension of the state vector, is the expectation of the process noise covariance matrix, , are the posterior degrees of freedom and the posterior scale matrix of the process noise covariance matrix at time ; steps (a) to (c) are repeated until the expectations converge, and the measurement innovation covariance matrix is obtained to satisfy: ; wherein is the measurement innovation covariance matrix, is the expectation of the updated measurement noise covariance matrix.

[0012] Preferably, the normalized residual is calculated as: ; wherein is the normalized residual of the th measurement vector dimension; is the innovation between the predicted measurement value and the actual measurement value of the th measurement vector dimension at time ; and is the th diagonal element of the measurement innovation covariance matrix of the th iteration; the innovation is calculated as: , In order to be in Innovation in the relationship between predicted and actual measurements. for The actual measured value at time, for Predicted measurements at any given time.

[0013] Preferably, the step of using generalized cross-validation to determine the optimal Tikhonov regularization parameter for the measurement innovation covariance matrix and calculating the Kalman gain includes: constructing a generalized cross-validation function with respect to the Tikhonov regularization parameter, satisfying: Where m is the dimension of the measurement vector. For innovation, The measurement innovation covariance matrix after the expected value converges. For the trace operation of a matrix, The square of the L2 norm of the vector. For Tikhonov regularization parameters, For the current moment, Given an identity matrix; within a predefined search range for regularization parameters, a numerical optimization method is used to find a matrix that... The Tikhonov regularization parameter with the smallest function value is taken as the optimal Tikhonov regularization parameter, denoted as . Using the optimal Tikhonov regularization parameter, the regularized Kalman gain is calculated using the following formula: In the formula, The regularized Kalman gain. For the state-measurement cross-covariance matrix, This is the optimal Tikhonov regularization parameter.

[0014] Preferably, the step of updating the state estimate and state covariance matrix using Kalman gain and innovation includes: the updated state estimate satisfies: In the formula, for State estimation at time 10:00 for The mean of the predicted state at time t, The regularized Kalman gain. In order to be in The innovation between the predicted and actual measured values ​​at each moment; the updated state covariance matrix is: In the formula, for The state covariance matrix at time t, To predict the covariance matrix, The measurement innovation covariance matrix after the expected value converges. is the transpose of the regularized Kalman gain.

[0015] Preferably, the operation instruction of each excimer lamp is generated by the cooperative control law based on the updated state, including: setting the target state reference vector of the excimer lamp system ; the error vector between the updated state estimation value at the current time and the target state reference vector is calculated, and the formula is: ; in the formula, is the error vector between the updated state estimation value at the current time and the target state reference vector, is the updated state estimation value at the current time, is the current time; the operation instruction vector of each excimer lamp is calculated by using the proportional-integral cooperative control law, and the calculation formula is: ; in the formula, is the operation instruction vector of each excimer lamp, is the proportional gain matrix, is the integral gain matrix, is the control period, is the error vector at the kth time. The multi-source sensing data includes the current, voltage, lamp wall temperature of each excimer lamp tube and the reading of the ultraviolet light intensity sensor arranged on the working plane.

[0016] The beneficial effects of the present application are: the present application can jointly estimate the covariance matrix of process and measurement noise by combining the M-estimation using Tukey double weight function in a variational Bayesian framework, thereby overcoming the limitation of the standard unscented Kalman filter which depends on the noise prior information; moreover, by using the generalized cross-validation Tikhonov regularization method, the singular or ill-conditioned problem that may occur in the iteration of the measurement innovation covariance matrix is specially processed, the numerical stability of the inverse operation is ensured, the reliability of the Kalman gain calculation is ensured, and the uniformity and stability of the output light field of the multi-excitation lamp system are improved. BRIEF DESCRIPTION OF DRAWINGS

[0017]

[0018] Figure 1 The step flow chart of the excimer lamp cooperative control method based on multi-source data fusion in the embodiment is schematically shown. DETAILED DESCRIPTION

[0019] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application.

[0020] As Figure 1 ​​​As shown, the method for collaborative control of excimer lamps based on multi-source data fusion in the embodiment includes steps S1 to S3:

[0021] In step S1, multi-source sensing data of the excimer lamp system is acquired, the system state vector, the state covariance matrix, and the inverse Wishart distribution prior parameters of the process and measurement noise covariance matrix are initialized; based on the posterior state estimation of the last moment, Sigma point set is generated by using unscented transformation and the Sigma point set is processed through a nonlinear state equation to obtain the predicted state mean and the predicted covariance matrix at the current moment.

[0022] The multi-source sensing data includes but is not limited to the current, voltage, lamp wall temperature of each excimer lamp tube, and the reading of the ultraviolet light intensity sensor arranged on the working plane, and the sensing data is selected as needed and normalized respectively. The system state vector may contain the light intensity, aging factor and other hidden states of each excimer lamp tube which cannot be directly measured. The state covariance matrix can reflect the uncertainty of the initial state.

[0023] The initialization of the system state vector, the state covariance matrix, and the inverse Wishart distribution prior parameters of the process and measurement noise covariance matrix includes:

[0024] The sensing data of the excimer lamp system at the initial moment is taken as the initial value of the system state vector ;

[0025] The state covariance matrix is initialized as a diagonal matrix , wherein is the dimension of the state vector, is the preset initial variance of the th state vector dimension;

[0026] The inverse Wishart distribution prior degree of freedom parameter of the process noise covariance matrix Q is set to , and the prior scale matrix is ; wherein is the estimated process noise covariance matrix, is the inverse Wishart distribution prior degree of freedom parameter of the process noise covariance matrix Q;

[0027] The inverse Wishart distribution prior degree of freedom parameter of the measurement noise covariance matrix R is set to , and the prior scale matrix is Let m be the prior degrees of freedom parameter of the inverse Wishart distribution of the measurement noise covariance matrix R, and m be the dimension of the measurement vector. This is the estimated measurement noise covariance matrix.

[0028] Specifically, assuming the excimer lamp system's state has three dimensions: radiation intensity, gas pressure, and chamber temperature, then n equals 3; the measured values ​​come from two dimensions: an external radiometer and a pressure gauge, then m equals 2. At startup, the first set of sensor data acquired is a radiation intensity of 1500 units, a gas pressure of 1.2 atmospheres, and a chamber temperature of 350 Kelvin. The initial state vector of the system is... That is, set as The transpose of the equation. Simultaneously, the uncertainty of the initial state is set empirically. For example, if the estimate of the initial pressure is relatively confident, but the estimate of the temperature has greater uncertainty, then the initial state covariance matrix can be... Set as a diagonal matrix , which represents the initial variance of each state vector dimension.

[0029] Furthermore, to model the dynamic disturbances and sensor measurement errors during system operation, prior statistical properties of the noise are defined. For example, for the case where the state vector dimension n equals 3, the prior degrees of freedom of the inverse Wishart distribution of the process noise covariance matrix are defined. If the predicted process noise covariance matrix is ​​5, then... diagonal matrix Then its prior scale matrix for ,Right now Similarly, for the case where the measurement vector dimension m equals 2, the prior degrees of freedom of the inverse Wishart distribution of the measurement noise covariance matrix are set. If the estimated measurement noise covariance matrix is ​​4, diagonal matrix Let represent the noise variance of the radiometer and pressure gauge, then its prior scale matrix is... for ,Right now .

[0030] The posterior state estimation based on the previous time step involves generating a Sigma point set using an unscented transformation and processing the Sigma point set using a nonlinear state equation to obtain the predicted state mean and predicted covariance matrix at the current time step, including:

[0031] based on Posterior state estimation at time 1 and posterior covariance matrix Generate 2n+1 Sigma point sets , where n is the dimension of the state vector;

[0032] Substitute each Sigma point in the Sigma point set into the nonlinear state equation. The process is performed to obtain the state prediction point set. ;

[0033] The weighted calculation is performed on the prediction points in the state prediction point set to obtain The predicted state mean and predicted covariance matrix at time t; where This refers to the current moment.

[0034] Among them, the nonlinear state equation This represents the evolution of the lamp's light intensity, aging, and other states over time. The results are calculated by weighted summation of the processed Sigma point set. mean of predicted state at time 1 and the predicted covariance matrix .

[0035] Using the data from the previous example, with a state vector dimension n of 3, 7 Sigma points will be generated. Assuming in... The posterior state estimates obtained at time k are a radiation intensity of 1510 units, a pressure of 1.21 atmospheres, and a temperature of 352 Kelvin, along with a corresponding posterior covariance matrix. The unscented transformation selects seven representative state points, the Sigma point set. These seven Sigma points are input one by one into the nonlinear state equation of the excimer lamp physical process. For example, the state equation might represent the radiation intensity at the next time step as a complex function of the current intensity, pressure, and temperature. Through nonlinear processing, seven new points are obtained, forming the state prediction point set. A weighted sum of these seven prediction points yields the predicted state mean at time k, which might be a radiation intensity of 1508 units, a pressure of 1.20 atmospheres, and a temperature of 355 Kelvin. Simultaneously, the dispersion of these prediction points determines the prediction covariance matrix.

[0036] Step S2 involves transforming the Sigma point set processed by the nonlinear state equation into predicted measurement values ​​using the measurement equation, and calculating the innovation between the predicted and actual measurement values. Within a fixed-point iterative variational Bayesian framework, based on the innovation and combined with M-estimation using Tukey's double-weight function, the covariance matrix of the process and measurement noise is updated, and the state-measurement cross-covariance matrix and the measurement innovation covariance matrix are calculated simultaneously.

[0037] The method for obtaining the predicted measurements and the state-measurement cross-covariance matrix is ​​as follows:

[0038] The state prediction point set Substitute into the measurement equation The conversion is performed to obtain the measurement prediction point set. ;

[0039] We perform weighted calculations on the predicted points in the measurement prediction point set to obtain the predicted measurement mean, the measurement prediction covariance matrix, and the state-measurement cross-covariance matrix. The predicted measurement mean is denoted as... .

[0040] Substitute the seven state prediction points obtained in step S1 into the nonlinear measurement equation, such as the measurement equation describing how the sensor converts real physical quantities into measured readings, and then use the measurement equation... The seven state prediction points are transformed to obtain seven predicted measurements; the predicted measurement mean, measurement prediction covariance, and state-measurement cross-covariance are calculated by weighting the seven predicted measurements.

[0041] The method for calculating the measurement innovation covariance matrix is ​​as follows:

[0042] In the i-th iteration:

[0043] (a) Calculate the measurement innovation covariance matrix of the previous iteration, satisfying: In the formula, For the first The measurement innovation covariance matrix of the next iteration. To measure the predicted covariance matrix, For the first The expected value of the measurement noise covariance matrix in the next iteration. The current moment;

[0044] Calculate the weighting factor matrix of the Tukey double-weight function, satisfying: ,in In the formula, Let be the weighting factor matrix of the Tukey double-weight function. For the first Standardized residuals for each measurement vector dimension The first The, the Weights of each measurement vector dimension, To adjust the parameters, m is the dimension of the measurement vector. It is a diagonal matrix;

[0045] The standardized residual is calculated as follows: In the formula, For the first Standardized residuals for each measurement vector dimension; In order to be in At that moment, the Innovation between predicted and actual measurements across a single measurement vector dimension; For the first the th diagonal element of the measurement innovation covariance matrix in the th iteration;

[0046] The innovation is calculated as: , is the innovation between the predicted measurement and the actual measurement at time is the actual measurement at time is the predicted measurement at time

[0047] (b) Calculate the posterior inverse Wishart distribution parameters of the updated measurement noise covariance matrix Set the posterior degrees of freedom as ; update the posterior scale matrix to satisfy: ; and calculate its expectation ; where is the set posterior degrees of freedom, is the updated posterior scale matrix, is the transpose of the set posterior degrees of freedom, is the square root of the weighting factor matrix of the Tukey biweight function, , are the posterior degrees of freedom and the posterior scale matrix of the measurement noise covariance matrix at time

[0048] (c) Based on the filtering and smoothing state estimates of the current iteration, calculate the expectation of the process noise covariance matrix

[0049] Calculate the posterior inverse Wishart distribution parameters of the updated process noise covariance matrix: set the posterior degrees of freedom ; update the posterior scale matrix to satisfy: ; and calculate its expectation ; where is the expectation of the updated process noise covariance matrix, is the updated posterior scale matrix, is the set posterior degrees of freedom, is the dimension of the state vector, is the expectation of the process noise covariance matrix, , are the posterior degrees of freedom and the posterior scale matrix of the process noise covariance matrix at time

[0050] Repeat steps (a) to (c) until the expectations and ​​​​converges to a measured innovation covariance matrix S satisfying: ; where, is the measured innovation covariance matrix, is the expected value of the updated measurement noise covariance matrix.

[0051] Suppose at time k, the predicted measurement values are radiometer reading 1520 and pressure gauge reading 1.22, while the actual received measurement values are radiometer reading 1530 and pressure gauge reading 3.8. The pressure reading 3.8 is quite different from the predicted value 1.22, and is likely to be an outlier or abnormal value caused by a transient fault of the sensor, and the calculated measurement innovation, i.e., the difference between the prediction and the actual value, will be very large in the pressure component. In the first step of the iterative update, the standardized residual of each measurement component is calculated, and since the residual of the pressure component is huge, its value will be far beyond the threshold value of the adjustment parameter c equal to 4.685, at this time, according to the rule of Tukey double weight function, the weight of the pressure measurement is 0, while the residual of the radiation intensity measurement is within a reasonable range, and the weight of the radiation intensity measurement is a normal value between 0 and 1, so that in the subsequent update of the measurement noise covariance matrix R, the abnormal pressure measurement data is completely ignored, and the contribution of the abnormal pressure measurement data to the posterior parameter update of the measurement noise covariance matrix R is zero.

[0052] The smoothed state estimation is also used to back-propagate the actual size of the process noise, and it is used to update the process noise covariance matrix Q. The process of updating the measurement noise covariance matrix R and the process noise covariance matrix Q is iterated several times, such as three to five times, until the estimated values of the two do not change significantly. Further, through the iteration process insensitive to outliers, a robust measurement innovation covariance matrix S is obtained, representing the real measurement uncertainty at the current time without being polluted by abnormal data.

[0053] In step S3, the optimal Tikhonov regularization parameter is determined for the measurement innovation covariance matrix by using a generalized cross-validation method, and the Kalman gain is calculated; the state estimation and the state covariance matrix are updated by using the Kalman gain and the innovation, and based on the updated state, the operation instructions of each quasi-molecular lamp are generated through a cooperative control law.

[0054] The optimal Tikhonov regularization parameter is determined for the measurement innovation covariance matrix by using a generalized cross-validation method, and the Kalman gain is calculated, including:

[0055] A generalized cross-validation function about the Tikhonov regularization parameter is constructed, satisfying: ; where, m is the dimension of the measurement vector, is the innovation, The measurement innovation covariance matrix after the expected value converges. For the trace operation of a matrix, The square of the L2 norm of the vector. For Tikhonov regularization parameters, For the current moment, It is the identity matrix;

[0056] Within the preset search range for regularization parameters, numerical optimization methods are used to find the optimal regularization parameter. The Tikhonov regularization parameter with the smallest function value is taken as the optimal Tikhonov regularization parameter, denoted as . ;

[0057] Using the optimal Tikhonov regularization parameter, the regularized Kalman gain is calculated using the following formula: In the formula, The regularized Kalman gain. For the state-measurement cross-covariance matrix, This is the optimal Tikhonov regularization parameter.

[0058] In some cases, such as when the measurements from two sensors are highly correlated or when one sensor has extremely low noise, the measurement innovation covariance matrix S may become nearly singular or ill-conditioned. Directly inverting this matrix can lead to significant errors in the calculation results, causing the entire filtering process to diverge. To avoid this, this embodiment employs Tikhonov regularization.

[0059] Specifically, first define a regularization parameter. The search range is, for example, from one in a million to one. Then, a generalized cross-validation function is constructed. By employing numerical optimization algorithms such as the golden section search or grid search, an optimal regularization parameter can be found within this range. Value, denoted as ,pass The function can balance the model's fitting residuals and complexity; its minimum point corresponds to... It can stably calculate the inverse matrix without excessively distorting the original information; assuming that the optimal parameters are calculated. The value is 0.01, using the optimal Tikhonov regularization parameter. Calculate Kalman gain Then it will no longer directly target Instead of finding the inverse, it calculates... add Multiplying by the inverse of the regularized matrix, which is the identity matrix, ensures that even... Even under ill-conditioning conditions, a smooth and reliable Kalman gain can be obtained, preventing the measurement innovation covariance matrix S from becoming numerically unstable and causing the entire filtering process to diverge.

[0060] The state estimate and the state covariance matrix are updated using the Kalman gain and the innovation, including:

[0061] The updated state estimate satisfies: ; where is the state estimate at time , is the predicted state mean at time , is the regularized Kalman gain, is the innovation between the predicted measurement and the actual measurement at time ; and

[0062] The updated state covariance matrix is: ; where is the state covariance matrix at time , is the predicted covariance matrix, is the measurement innovation covariance matrix after convergence of the expectation value, is the transpose of the regularized Kalman gain.

[0063] Assuming that the predicted state mean , such as the transpose of , and the measurement innovation have been obtained, and that the regularized and robust Kalman gain has been calculated, the updated state estimate and the state covariance matrix are obtained using the update equations.

[0064] The Kalman gain determines how much the new measurement data should be trusted. Specifically, if the measurement noise is small, the Kalman gain is large, and the state estimate will be more pulled towards the measurement. Conversely, if the model prediction is very accurate, the Kalman gain is small, and the state estimate will be more dependent on the prediction. For example, the updated state estimate may become the transpose of , which is an optimal compromise between the prediction and the measurement. At the same time, the uncertainty of the state is reduced by updating the covariance matrix, and the new covariance matrix makes the estimation of the system state more certain after the new measurement information is obtained, and the variance is reduced. The updated state estimate and the state covariance matrix serve as the starting point for the next time step .

[0065] The process of using Kalman gain and innovation to update the state estimate and state covariance matrix, and generating operating instructions for each excimer lamp based on the updated state through a cooperative control law, includes:

[0066] Set the target state reference vector of the excimer lamp system ;

[0067] The error vector between the updated state estimate and the target state reference vector at the current time is calculated using the following formula: In the formula, for The error vector between the updated state estimate and the target state reference vector at each time step. for The state estimate after each update. The current moment;

[0068] The proportional-integral (PI) coordinated control law is used to calculate the operation command vector of each excimer lamp. The calculation formula is as follows: In the formula, This refers to the operation command vector for each excimer lamp. It is a proportional gain matrix. Here is the integral gain matrix. To control the cycle, For the first Error vector at time step.

[0069] Pre-defined target state reference vector For example, the desired radiation intensity is 1600 units, the gas pressure is 1.25 atmospheres, and the chamber temperature is 360 Kelvin. At time k, the optimal state estimate after filtering and updating... for The transpose of the target state. The controller first calculates the error vector between the current state and the target state. Its value is The transpose of the equation results in all three state variables being slightly below the target value; the PI collaborative control law generates operating commands based on the error; the proportional term... Multiply It responds instantly to current errors; for example, a positive error will immediately trigger a command to increase lamp power or adjust gas flow, thereby rapidly reducing the deviation; the integral term Multiplying by the cumulative sum of all errors from the initial state to the current state eliminates any potential steady-state errors. If the system remains below the target value for an extended period, even if the current error is small, the integral term accumulates into a large value, resulting in a continuous correction to ensure the target state is eventually reached. The final control command... is the sum of the two components, and is a vector containing the specific adjustments to multiple actuators in the system, such as power supply voltage, gas valve opening, etc., and is issued once every control period, e.g., 100 seconds.

[0070] In the description of the present specification, the meaning of "a plurality of" is at least two, such as two, three or more, etc., unless explicitly specifically limited.

[0071] While the present specification has shown and described a number of embodiments of the present application, it is to be understood that such embodiments are merely illustrative of and not restrictive on the present application. Many modifications, changes, and substitutions can now occur to one skilled in the art without departing from the spirit and scope of the present application.

Claims

1. A method for collaborative control of excimer lamps based on multi-source data fusion, characterized in that, The method comprises the following steps: obtaining multi-source sensing data of an excimer lamp system, initializing a system state vector, a state covariance matrix, and inverse Wishart distribution prior parameters of process and measurement noise covariance matrices; based on the posterior state estimation of the last moment, generating a Sigma point set by using an unscented transformation and processing the Sigma point set by a nonlinear state equation to obtain a predicted state mean value and a predicted covariance matrix at the current moment; the Sigma point set processed by the nonlinear state equation is converted into a predicted measurement value by a measurement equation, and the innovation between the predicted measurement value and the actual measurement value is calculated; in a fixed point iteration variational Bayesian framework, based on the innovation, and combined with M-estimation using a Tukey double weight function, the covariance matrices of the process and the measurement noise are updated, and the state-measurement mutual covariance matrix and the measurement innovation covariance matrix are calculated; the optimal Tikhonov regularization parameter of the measurement innovation covariance matrix is determined by using a generalized cross-validation method, and the Kalman gain is calculated; the state estimation and the state covariance matrix are updated by using the Kalman gain and the innovation, and the operation instructions of each excimer lamp are generated by a cooperative control law based on the updated state. 2.The method of claim 1, wherein, The initialization of the system state vector, the state covariance matrix, and the inverse Wishart distribution prior parameters of the process and measurement noise covariance matrices comprises: The sensor data of the excimer lamp system at the initial time is taken as the initial value of the system state vector ; Initialize the state covariance matrix to a diagonal matrix where is the dimension of the state vector, is the preset initial variance of the th dimension of the state vector; Setting the inverse Wishart distribution prior degrees of freedom parameter of the process noise covariance matrix Q , prior scale matrix ; wherein is an estimated process noise covariance matrix, is the inverse Wishart distribution prior degrees of freedom parameter of the set process noise covariance matrix Q a priori degree of freedom parameter of an inverse Wishart distribution of a set measurement noise covariance matrix R , a priori scale matrix ; wherein is a priori scale matrix of an inverse Wishart distribution of a set measurement noise covariance matrix R, is a priori degree of freedom parameter of an inverse Wishart distribution of a set measurement noise covariance matrix R, m is a measurement vector dimension, is an estimated measurement noise covariance matrix. 3.The method of claim 1, wherein, The method for obtaining the predicted measurement value and the state-measurement mutual covariance matrix comprises: Based on a posteriori state estimate and a posteriori covariance matrix generating 2n+1 sets of Sigma points where n is the dimension of the state vector; substituting each Sigma point of the set of Sigma points into the nonlinear state equations performing processing to obtain a set of state prediction points ; The prediction points in the state prediction point set are weighted and calculated to obtain a prediction state mean value and a prediction covariance matrix at the time instant; wherein is the current time instant. 4.The method of claim 3, wherein, The method for calculating the measurement innovation covariance matrix comprises: the state prediction point set substituting into the measurement equation performing a conversion to obtain a measurement prediction point set ; The predicted measurement mean, the measurement prediction covariance matrix and the state-measurement cross-covariance matrix are obtained by weighted calculation of the predicted points in the set of measurement prediction points, and the predicted measurement mean is denoted as .

5. The method according to claim 4, wherein, In the i-th iteration: (c) based on the filtering and smoothing state estimation of the current iteration, the expected value of the process noise covariance matrix is calculated; (a) compute a measurement innovation covariance matrix for the last iteration, satisfying: ; where is the measurement innovation covariance matrix for the th iteration, is the measurement prediction covariance matrix, is the measurement noise covariance matrix for the th iteration, and is the current time instant; Calculate the weighting factor matrix of the Tukey double-weight function, satisfying: ,in In the formula, Let be the weighting factor matrix of the Tukey double-weight function. For the first Standardized residuals for each measurement vector dimension The first The, the Weights of each measurement vector dimension, To adjust the parameters, m is the dimension of the measurement vector. It is a diagonal matrix; (b) compute the updated measurement noise covariance matrix of the posterior inverse Wishart distribution parameter: set the posterior degrees of freedom to ; The posterior scale matrix is updated to satisfy: ; and the expected value thereof is calculated ; wherein is a set posterior degree of freedom, is an updated posterior scale matrix, is a transpose of the set posterior degree of freedom, is a square root of a weighting factor matrix of a Tukey double weighting function, , are respectively a posterior degree of freedom and a posterior scale matrix of a measurement noise covariance matrix at a time instant The method for determining the optimal Tikhonov regularization parameter of the measurement innovation covariance matrix by using the generalized cross-validation method and calculating the Kalman gain comprises: Compute the posterior inverse Wishart distribution parameters of the updated process noise covariance matrix: set the posterior degrees of freedom ; update the posterior scale matrix, satisfying: ; and compute its expectation ; where is the expectation of the updated process noise covariance matrix, is the updated posterior scale matrix, is the set posterior degrees of freedom, is the state vector dimension, is the expectation of the process noise covariance matrix, , are the posterior degrees of freedom and the posterior scale matrix of the process noise covariance matrix at time , respectively. Steps (a) to (c) are repeated until a desired value and converge to obtain a measurement innovation covariance matrix satisfying: ; where is the measurement innovation covariance matrix, is the expected value of the updated measurement noise covariance matrix. 6.The method of claim 5, wherein, The normalized residual is calculated as follows: ; where, is the normalized residual of the th measurement vector dimension; is the innovation between the predicted and actual measurement values of the th measurement vector dimension at time is the th diagonal element of the measurement innovation covariance matrix at the th iteration;​ The innovation is calculated as: The innovation is calculated as the difference between the predicted measurement and the actual measurement at time t, The actual measurement at time t, The predicted measurement at time t.​​​​ 7.The method of claim 1, wherein, The method for updating the state estimation and the state covariance matrix by using the Kalman gain and the innovation comprises: The generalized cross-validation function about the Tikhonov regularization parameter is constructed, satisfying: ; wherein m is a measurement vector dimension, is an innovation, is a measurement innovation covariance matrix after convergence of an expectation value, is a trace operation of a matrix, is a square of an L2 norm of a vector, is a Tikhonov regularization parameter, is a current time, is an identity matrix; In the preset regularization parameter search interval, a Tikhonov regularization parameter that makes the function value minimum is found as an optimal Tikhonov regularization parameter by a numerical optimization method, and is denoted as . ; With the optimal Tikhonov regularization parameter, the regularized Kalman gain is calculated, and the calculation formula is: ; wherein, is the regularized Kalman gain, is the state-measurement cross-covariance matrix, is the optimal Tikhonov regularization parameter. 8.The method of claim 1, wherein, The method for updating the state estimation and the state covariance matrix by using the Kalman gain and the innovation, and generating the operation instructions of each excimer lamp by a cooperative control law based on the updated state comprises: The updated state estimate satisfies: where, is the state estimate at time is the predicted state mean at time is the innovation between the predicted measurement at time and the actual measurement at time is the regularized Kalman gain, is the innovation between the predicted measurement at time and the actual measurement at time The updated state covariance matrix is: ; where, is the state covariance matrix at time, is the prediction covariance matrix, is the measurement innovation covariance matrix after convergence of the expectation value, is the transpose of the regularized Kalman gain. 9.The method of claim 1, wherein, The multi-source sensing data comprises the current, voltage, and lamp wall temperature of each excimer lamp tube, and the readings of the ultraviolet light intensity sensors arranged on the working plane. Setting a target state reference vector for an excimer lamp system ; An error vector between the state estimation value updated at the current time and the target state reference vector is calculated, and the formula is: ; wherein, is the error vector between the state estimation value updated at the current time and the target state reference vector, is the state estimation value updated at the current time, is the current time; The operation instruction vector of each excimer lamp is calculated by using proportional-integral cooperative control law, and the calculation formula is: ; wherein, is the operation instruction vector of each excimer lamp, is a proportional gain matrix, is an integral gain matrix, is a control period, is an error vector at the moment. 10.The method of claim 1, wherein, ​

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