Excimer lamp cooperative control method based on multi-source data fusion

Abstract

The invention relates to the technical field of control, in particular to an excimer lamp cooperative control method based on multi-source data fusion. The method comprises the steps of 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 a process and measurement noise covariance matrix, obtaining a prediction state mean value and a prediction covariance matrix based on posterior state estimation, and performing calculation innovation. The method comprises the following steps of: calculating a state-measurement cross covariance matrix, updating a process and measuring a noise covariance matrix, calculating a state-measurement cross covariance matrix and a measurement innovation covariance matrix, determining an optimal Tikhonov regularization parameter and calculating a Kalman gain, updating state estimation and the state covariance matrix, and generating an operation instruction of each excimer lamp based on the updated state. According to the scheme, the limitation of a standard unscented Kalman filter can be overcome, and the reliability of Kalman gain is ensured, so that the uniformity and the stability of a system output light field are improved.

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 noise statistical characteristics 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 occur during iteration, leading to numerical instability in the 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: The multi-source sensing data of the excimer lamp system is acquired, an initial system state vector, an initial state covariance matrix, and inverse Wishart distribution prior parameters of process and measurement noise covariance matrices are initialized; based on posterior state estimation of a previous time, a set of Sigma points is generated by using an unscented transformation and the set of Sigma points is processed by a nonlinear state equation to obtain a predicted state mean and a predicted covariance matrix at a current time; the set of Sigma points processed by the nonlinear state equation is converted into predicted measurement values by a measurement equation, and an innovation between the predicted measurement values and actual measurement values 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, covariance matrices of the process and measurement noise are updated, and a state-measurement cross-covariance matrix and a measurement innovation covariance matrix are calculated; an optimal Tikhonov regularization parameter is determined for the measurement innovation covariance matrix by using a generalized cross-validation method, and a Kalman gain is calculated; the state estimation and the state covariance matrix are updated by using the Kalman gain and the innovation, and operation instructions of each excimer lamp are generated by a cooperative control law based on the updated state.

[0007] Preferably, the initializing the initial system state vector, the initial state covariance matrix, and the inverse Wishart distribution prior parameters of the process and measurement noise covariance matrices comprises: taking sensing data of the excimer lamp system at an initial time as an initial value of the system state vector ; initializing the state covariance matrix as a diagonal matrix , wherein is a state vector dimension, is a preset initial variance of the th state vector dimension; setting an inverse Wishart distribution prior degree of freedom parameter of the process noise covariance matrix Q, and a prior scale matrix ; wherein is a predicted process noise covariance matrix, is the inverse Wishart distribution prior degree of freedom parameter of the process noise covariance matrix Q; setting an inverse Wishart distribution prior degree of freedom parameter of the measurement noise covariance matrix R, and a prior scale matrix ; wherein, is the inverse Wishart distribution prior scale matrix of the measurement noise covariance matrix R, is the inverse Wishart distribution prior degree of freedom parameter of the measurement noise covariance matrix R, m is a measurement vector dimension, is a predicted measurement noise covariance matrix.

[0008] 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.

[0009] 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... .

[0010] 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; (b) Calculate the diagonal matrix. The posterior inverse Wishart distribution parameters: The posterior degrees of freedom are set to 1. Update the posterior scaling matrix to satisfy: And calculate its expected value. ;in, For the set posterior degrees of freedom, This is the updated posterior scaling matrix. For the transpose of the given posterior degrees of freedom, Let be the square root of the weighting factor matrix of the Tukey double-weight function. , They are respectively (c) Calculate the expected value of the process noise covariance matrix based on the filtering and smoothing state estimation of the current iteration; calculate the posterior inverse Wishart distribution parameters of the updated process noise covariance matrix: set the posterior degrees of freedom. Update the posterior scaling matrix to satisfy: And calculate its expected value. ;in, To update the expected value of the process noise covariance matrix, This is the updated posterior scaling matrix. For the set posterior degrees of freedom, For the dimension of the state vector, Let be the expected value of the process noise covariance matrix. , They are respectively The posterior degrees of freedom and posterior scale matrix of the process noise covariance matrix at time step 1; repeat steps (a) to (c) until the expected value is obtained. and Convergence is achieved, yielding the measurement innovation covariance matrix, which satisfies: In the formula, To measure the innovation covariance matrix, To update the expected value of the measurement noise covariance matrix.

[0011] Preferably, 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 In the measurement innovation covariance matrix of the nth iteration One diagonal element; the innovative calculation method is as follows: , 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.

[0012] 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.

[0013] 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.

[0014] Preferably, the operation instruction of each excimer lamp is generated by the cooperative control law based on the updated state estimation and the state covariance matrix using the Kalman gain, including: setting the target state reference vector of the excimer lamp system ; calculating the error vector between the updated state estimation value at the current time and the target state reference vector, the formula is: ; in the formula, is the updated state estimation value at the current time, 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 first time.

[0015] 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: by combining the M-estimation using the Tukey double weight function in a variational Bayesian framework, the covariance matrix of the process and the measurement noise can be jointly estimated, 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] Figure 1 A step flowchart of a multi-source data fusion based excimer lamp cooperative control method in the embodiment is schematically shown. DETAILED DESCRIPTION

[0018] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application.

[0019] As Figure 1 ​As shown, the excimer lamp collaborative control method based on multi-source data fusion in this embodiment includes steps S1 to S3: Step S1: Acquire multi-source sensing 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 using a nonlinear state equation to obtain the predicted state mean and predicted covariance matrix at the current time step.

[0020] Multi-source sensor data includes, but is not limited to, the current, voltage, and lamp wall temperature of each excimer lamp tube, as well as the readings of the ultraviolet light intensity sensors arranged on the working plane. Sensor data are selected as needed and normalized separately. The system state vector is initialized. It may contain implicit states that cannot be directly measured, such as the light intensity and aging factor of each excimer lamp tube. Initialize the state covariance matrix. It can reflect the uncertainty of the initial state.

[0021] 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: The sensor data of the excimer lamp system at the initial moment is used as the system state vector. The initial value; The state covariance matrix Initialize as a diagonal matrix ,in For the state vector dimension, For the first Preset initial variance for each dimension of the state vector; Define the prior degrees of freedom parameters of 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 of the inverse Wishart distribution of the process noise covariance matrix Q are given. Define the prior degrees of freedom parameters of the inverse Wishart distribution of the measurement noise covariance matrix R. 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.

[0022] 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 initial pressure estimate is relatively confident, but the temperature estimate 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.

[0023] 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 .

[0024] 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: 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 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.

[0025] Among them, nonlinear state equations 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 predict covariance matrix .

[0026] 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.

[0027] 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.

[0028] The method for obtaining the predicted measurements and the state-measurement cross-covariance matrix is ​​as follows: The state prediction point set 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... .

[0029] 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 cross-covariance between state and measurement are calculated by weighting the seven predicted measurements.

[0030] 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. The current moment; 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; 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 In the measurement innovation covariance matrix of the nth iteration One diagonal element; The innovative calculation method is as follows: , In order to be in Innovation in the relationship between predicted and actual measurements. for actual measurement value of the time instant, for predicted measurement value of the time instant; (b) calculating the posterior inverse Wishart distribution parameters of the updated measurement noise covariance matrix ; setting the posterior degrees of freedom as ; updating the posterior scale matrix, satisfying: ; and calculating its expectation ; wherein, 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 the time instant , respectively; (c) based on the filtering and smoothing state estimates of the current iteration, calculating the expectation of the process noise covariance matrix; calculating the posterior inverse Wishart distribution parameters of the updated process noise covariance matrix: setting the posterior degrees of freedom ; updating the posterior scale matrix, satisfying: ; and calculating its expectation ; wherein, 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 the time instant , respectively; repeating steps (a) to (c) until the expectations and converge, obtaining the measurement innovation covariance matrix, satisfying: ; wherein, is the measurement innovation covariance matrix, is the expectation of the updated measurement noise covariance matrix.

[0031] Suppose that at time k, the predicted measurements are a radiometer reading of 1520 and a pressure gauge reading of 1.22, while the actual received measurements are a radiometer reading of 1530 and a pressure gauge reading of 3.8. The pressure reading of 3.8 differs significantly from the predicted value of 1.22, likely due to a momentary sensor malfunction or outlier. This results in a very large difference between the predicted and actual pressure readings. In the first step of the iterative update, the standardized residual for each measurement component is calculated. Since the residual for the pressure component is enormous, its value will far exceed the threshold of adjustment parameter c equal to 4.685. Therefore, according to the rules of the Tukey double-weight function, the weight of this pressure measurement is assigned. The weight is 0, while the residual of the radiation intensity measurement is within a reasonable range, thus assigning a weight to the radiation intensity measurement. This is a normal value between 0 and 1, which means that abnormal pressure measurement data are completely ignored when updating the measurement noise covariance matrix R in the future. Abnormal pressure measurement data contributes zero to the update of the posterior parameters of the measurement noise covariance matrix R.

[0032] The smoothed state estimate is also used to infer the actual magnitude of the process noise, and this 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, for example, repeated three to five times, until the estimates of both no longer change significantly. Furthermore, through an iterative process insensitive to outliers, a robust measurement innovation covariance matrix S is obtained, representing the true measurement uncertainty at the current moment, without being contaminated by outlier data.

[0033] Step S3: The optimal Tikhonov regularization parameter is determined for the measurement innovation covariance matrix using the generalized cross-validation method, and the Kalman gain is calculated. The state estimate and state covariance matrix are updated using the Kalman gain and innovation, and the operation instructions for each excimer lamp are generated based on the updated state through a cooperative control law.

[0034] The method of using generalized cross-validation to determine the optimal Tikhonov regularization parameter for the measurement innovation covariance matrix and calculating the Kalman gain includes: Construct a generalized cross-validation function with respect to the Tikhonov regularization parameter that satisfies: 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, It is the identity matrix; 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 . ; 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.

[0035] 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.

[0036] 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.

[0037] The method of using Kalman gain and innovation to update the state estimate and state covariance matrix includes: The updated state is estimated to satisfy: In the formula, for State estimation at time 10:00 for the predicted state mean at time k, the regularized Kalman gain, the innovation at time k, the innovation at time k, the updated state covariance matrix is: ; where, the innovation at time k, the state covariance matrix at time k, the predicted covariance matrix, the measurement innovation covariance matrix after convergence of the expectation, the transpose of the regularized Kalman gain.

[0038] Assuming that the predicted state mean , such as the transpose of , and the measurement innovation have been obtained, and the robust and regularized Kalman gain has been calculated, the updated state estimate and state covariance matrix are obtained using the update formula.

[0039] 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 close to the measurement value; on the contrary, if the model prediction is very accurate, the Kalman gain is small, and the state estimate will be more dependent on the predicted value. For example, the updated state estimate may become the transpose of , which is an optimal compromise between the predicted value and the measurement value. At the same time, the uncertainty of the state is reduced by updating the covariance matrix, and the new covariance matrix is the estimation of the system state after obtaining the new measurement information, and the variance is reduced. The updated state estimate and the state covariance matrix are used as the starting point for the next time step .

[0040] The state estimate and the state covariance matrix are updated using the Kalman gain and the innovation, and based on the updated state, the operation instructions of each excimer lamp are generated through the cooperative control law, including: setting the target state reference vector of the excimer lamp system; calculating the error vector between the updated state estimate value at the current time and the target state reference vector, and the formula is: ; where, is the error vector between the updated state estimate value at the current time and the target state reference vector, and the formula is: an error vector between the updated state estimate and a target state reference vector, For the updated state estimate, is the current time; The operation command vector of each excimer lamp is calculated by a proportional-integral cooperative control law, and the calculation formula is: ; in the formula, is the operation command vector of each excimer lamp, is a proportional gain matrix, is an integral gain matrix, is a control period, is the error vector at the kth time.

[0041] A target state reference vector is preset, for example, the expected radiation intensity is 1600 units, the gas pressure is 1.25 atmospheres, and the chamber temperature is 360 Kelvin. The optimal state estimate after filtering and updating at the kth time is The controller first calculates the error vector between the current state and the target state, and the value is The transpose of all three state quantities is slightly lower than the target value; the PI cooperative control law generates an operation command according to the error; the proportional term is multiplied by , and the current error is immediately responded, for example, a positive error will immediately trigger a command to increase the lamp power or adjust the gas flow, thereby rapidly reducing the deviation; the integral term is multiplied by the cumulative sum of all errors from the initial to the current, thereby eliminating the steady-state error that may exist in the system, if the system continues to be lower than the target value for a long time, even if the current error is small, the integral term accumulates into a larger value, thereby generating a continuous correction, ensuring that the target state can be finally reached. The final control command is the sum of the above two components, which is a vector, containing specific adjustment amounts for multiple actuators in the system, such as power supply voltage, gas valve opening, etc., and is issued once every control period, for example, 100 seconds.

[0042] In the description of the present specification, the meaning of "a plurality of" is at least two, for example, two, three or more, etc., unless otherwise explicitly and specifically limited.

[0043] Although the present specification has shown and described several embodiments of the present application, it will be apparent to those skilled in the art that such embodiments are provided only by way of example. Those skilled in the art will think of many changes, changes and alternatives without departing from the idea and spirit 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 predicted point set, 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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