Prediction and control method of blast furnace ironmaking based on deep auxiliary typical variable analysis

Abstract

The present invention discloses a prediction and control method for blast furnace ironmaking based on deep auxiliary typical variable analysis, the steps of which include determining model input, state estimation, objective function establishment and prediction control strategy; wherein, the model input is determined, and the influential controllable variables are determined as model input by using partial least squares regression (PLSR); for nonlinear BFIP, a nonlinear state space model is proposed, and the state estimation is performed by using the deep learning assisted typical variable analysis DLaCVA method; the corresponding optimization target and learning gradient are obtained by modeling in the auxiliary state space using the deep learning method; and a prediction control strategy based on the quadratic performance index is designed to achieve the best molten iron quality control performance. Experiments on the actual blast furnace ironmaking process show that compared with other methods, DLaCVA provides better modeling accuracy and excellent control effect.

Description

Technical Field

[0001] The invention relates to a blast furnace ironmaking prediction and control method based on deep auxiliary typical variable analysis. Background Art

[0002] As the main method of steel smelting, the closed-loop automatic control technology research of blast furnace ironmaking has been highly valued by many experts and scholars at home and abroad. The main product of the blast furnace ironmaking process is molten iron, and the quality of molten iron directly affects the product quality and energy consumption of the subsequent steelmaking process. Therefore, in order to produce qualified molten iron and achieve sustainable utilization of energy, it is necessary to establish an accurate molten iron quality model and effectively monitor and control it. However, due to the complex characteristics of the blast furnace ironmaking process, it is difficult to establish a molten iron quality parameter model that is directly applied to the actual molten iron quality control optimization, and the control optimization and operation means for the blast furnace still rely on the experience and knowledge judgment of the operator, the production efficiency cannot be improved, and the production cost and product quality are difficult to achieve stable control. Therefore, it is necessary to study the modeling and control of the molten iron quality in the blast furnace ironmaking process, which is of great significance to provide reliable operation means, stabilize the production process, and improve product quality and work efficiency.

[0003] The energy consumption of wind, electricity, fuel, etc. in the blast furnace ironmaking process accounts for about 50% of the total energy consumption of steel enterprises, of which fuel consumption accounts for 80% of the total energy consumption of the blast furnace ironmaking process. The study of blast furnace ironmaking fuel consumption has important practical significance. Fuel ratio is a key indicator of blast furnace ironmaking fuel consumption. By using the relationship between blast furnace operation variables and state variable data and fuel ratio, the blast furnace fuel ratio is monitored, and the key factors that cause abnormal fluctuations in fuel ratio are identified as early as possible and controlled, which is of great significance for blast furnace energy saving and consumption reduction. The ironmaking production process is an important part of the metallurgical industry. The entire process has many procedures and extremely complex process mechanisms. There are modeling and control difficulties such as multiple distributed parameters, large lags, high nonlinearity, strong coupling, and severe time variation. Therefore, the ironmaking production process operation control system is the central system of the entire ironmaking production process. The correctness of its control function and control strategy is directly related to the ironmaking production function and performance. It is also an important way to ensure the efficient operation of the production process, improve production efficiency, improve product quality, and reduce production operation costs. In order to achieve optimized control of ironmaking production, it is necessary to solve the optimized control of blast furnace ironmaking for molten iron quality such as Si content, P content, S content, so as to achieve the goal of "green smelting and clean production" with energy saving, consumption reduction and emission reduction.

[0004] Among the control-based modeling methods, subspace identification methods (SIMs) can directly construct state-space models that only rely on the measured data of process inputs and outputs. This form of state-space model, which is convenient for prediction, filtering, and control, has gradually attracted the attention of scholars. Zeng and Zhou et al. conducted a preliminary exploration of the state-space model basis of SIM-based molten iron quality. In order to characterize the nonlinear nature of BFIP, the IN-SIM method established a nonlinear state-space model by combining kernel technology and least squares support vector machine, and simplified the model by the lamellar cubic Hermite interpolation polynomial method. To the best of the authors' knowledge, kernel technology tends to describe only the nonlinear characteristics of shallow processes, but the complex nonlinearity of BFIP hinders the accuracy of the model. Summary of the invention

[0005] In order to overcome the shortcomings of the prior art, the present invention aims to provide a blast furnace ironmaking prediction and control method based on deep auxiliary typical variable analysis, which can realize key control variable selection, molten iron quality prediction and control tasks.

[0006] In the ironmaking process, hot metal quality indices such as phosphorus [P], sulfur [S], and silicon [Si] contents can accurately assess the current hot metal state and the internal operation of the blast furnace. Therefore, this paper proposes DLaCVA modeling and predictive control strategies to achieve the prediction and optimization of MIQ. First, partial least squares regression (PLSR) is used to identify influential controllable variables from a wide range of choices as model inputs. Faced with the nonlinear BFIP with extremely complex physical and chemical reactions, we propose a nonlinear state space model and use the DLaCVA method for state estimation. In addition, we theoretically analyze the path that deep learning methods should follow in assisting state space modeling. The corresponding optimization objectives and learning gradients are derived, which provide a basis for the subsequent exploration of deep learning system identification. Finally, a predictive control strategy based on quadratic performance index is designed to achieve the best hot metal quality control performance. Experiments on the actual blast furnace ironmaking process show that DLaCVA provides better prediction accuracy and excellent control effects compared with other methods.

[0007] A prediction and control method for blast furnace ironmaking based on deep auxiliary typical variable analysis, the steps of which include determining model input, state estimation, objective function establishment and prediction control strategy;

[0008] Among them, the model input is determined, and the influential controllable variables are determined as the model input using partial least squares regression (PLSR); a nonlinear state space model is proposed for nonlinear BFIP, and the state estimation is performed using the deep learning-assisted canonical variable analysis DLaCVA method; the deep learning method is used to model in the auxiliary state space, and the corresponding optimization objectives and learning gradients are obtained; a predictive control strategy based on the quadratic performance index is designed to achieve the best molten iron quality control performance.

[0009] The step of determining the model input comprises the following steps:

[0010] (1.1) In view of the large number of controllable variables in the blast furnace ironmaking process, the model inputs are first reduced and determined, with two factors as the main selection basis: the degree of divergence and the correlation with sulfur and phosphorus content; by considering the correlation, the input variables most relevant to MIQ are located; by combining the above factors, partial least squares regression is accepted as a multivariate regression method, which projects the input and output information into a latent space and extracts most of the variance of these original data while capturing the main correlations; considering that the input matrix U contains N observations and m process variables, and the output matrix Y contains l variables, it is defined as:

[0011]

[0012] (1.2) The following goal of PLSR aims to describe the correlation within the maximum variance that they all maintain: (w,c) = argmax w,c w T U Y T c(2)

[0013] st&||w||=1,||c||=1

[0014] where w and c are the direction vectors of U and Y respectively; the direction vector w is calculated by solving (2) using the Lagrange multiplier technique:

[0015] UU T YY T w=λ w W(3)

[0016] With the largest eigenvalue λ w and the corresponding feature vector w; then, the latent score vector t, loading vectors p and q containing the maximum variance information are given by:

[0017] t=U T w,

[0018] (1.3) In addition, the remaining parts of U and Y are estimated for the next modeling iteration:

[0019]

[0020] Then, the above calculation process is repeated until enough direction vectors are extracted; assuming that d direction vectors are extracted, the extracted direction matrix W = [w1, w2, ..., w d ]、Load matrix P=[p1,p2,…,p d ] and Q=[q1,q2,…,q d ]; Finally, the regression model between the potential score matrix of the main information in Y and the input matrix U is established through the regression matrix R, as shown below:

[0021]

[0022] in, is the regression error. Here, the variable corresponding to the significantly significant coefficient in the regression matrix R is the determined control input variable.

[0023] The state estimation comprises the following steps:

[0024] (2.1) In the nonlinear case, previous CVA-based methods use the kernel technique to achieve state estimation of nonlinear systems; by transforming the nonlinear mapping operator F(z t ; Θ) is integrated into the linear state space model and the following structure is proposed

[0025] x t+1 =Ax t +BF(z t ; Θ)+w t (7a)

[0026] y t =Cx t +DF(z t ; Θ)+v t (7b)

[0027] z t =[u t ,y t-1 ](7c)

[0028] In the formula, by taking the input u at sampling time t t and the output y at sampling time t-1 t Concatenating gives z t , F(.) is a nonlinear mapping operator specified by the parameter Θ of the deep learning model, and the combination of the delayed output and the current input obtains a nonlinear representation through the nonlinear mapping operator;

[0029] (2.2) First, assume that the time lag parameters p and f of the past and future are determined, and the future output Y fAnd the past combination Z p The Hankel matrix of is defined as follows:

[0030]

[0031] According to the generalized CVA optimization objective, DLaCVA intends to search for a pair of projections and so that they share the maximum correlation:

[0032]

[0033]

[0034] in and is the projection matrix, I is the identity matrix; Y f The sample covariance matrix of (Zp; Θ) is expressed as ∑ y and∑ z , and∑ yz is the cross-covariance matrix; the solution is provided by the singular value decomposition of the Hankel matrix K:

[0035]

[0036] The left singular matrix Γ, the right singular matrix Δ, Λ is a diagonal matrix containing singular values, Λ = diag(λ1,λ2,…,λ s ) represents the solution set of the maximum canonical correlation coefficient, s represents the rank of K; by using the most significant r canonical correlation coefficient, the projection matrix is ​​obtained Right now:

[0037]

[0038] (2.3) Then, as Z p The linear combination of the state sequence It is estimated by:

[0039]

[0040] The objective function establishment comprises the following steps:

[0041] (3.1) In order to converge to the best model accuracy, the objective function of the deep learning model in the proposed DLaCVA is constructed as follows to seek the optimal network parameters Θ, so

[0042]

[0043] where Σ ε =I-ΛΛ T ; In addition, Σ εThe corresponding gradient of is derived as:

[0044]

[0045] in

[0046]

[0047] (3.2) Given the momentum parameter γ and the learning rate η, the model parameters Θ will be updated in each iteration to approximate the optimal value in the following way:

[0048]

[0049] in, is the momentum vector, and k represents the number of model iterations; during the entire model learning process, the model parameters will be updated through continuous iterations until No longer decreases in the validation set.

[0050] The prediction control strategy establishment includes the following steps:

[0051] (4.1) Once the deep learning model is determined, the state sequence can be clearly given; the corresponding DLaCVA-based state space model and predictive control strategy will be formulated in turn; by using least squares regression, the system matrix Estimated to be:

[0052]

[0053] where ∑[.] is the sample covariance operator; So far, the state space model based on DLaCVA has been established;

[0054] (4.2) The predictive performance of the system output is defined as follows:

[0055]

[0056] Then, by introducing the input control quantity The state-space model transforms the following structure:

[0057]

[0058] in and The output and state variables of the system in the control situation;

[0059] (4.3) Multi-step prediction of future output for:

[0060]

[0061] The superscript is the generalized inverse operator, i is the size of the prediction step;

[0062] (4.4) To this end, by replacing t with t+i and extending to a multi-step prediction structure, the objective function of the predictive control is described as

[0063] Where N p is the prediction horizon, N c Indicates the control range, Contains the set point of the output; W y and W u are the weighted matrices of output and input, respectively, which are used to adjust the influence of the corresponding variables on the target; in addition, due to the particularity of the controlled object, the prediction of input and output and the control amount are bounded by their corresponding maximum and minimum values; considering better search performance and less resource computing consumption, random search is referred to determine the optimal control input value.

[0064] The present invention has the beneficial effects:

[0065] This paper proposes a modeling and predictive control architecture related to blast furnace hot metal quality, which includes DLaCVA. First, a PLSR-based regression coefficient matrix is ​​used to determine the input variables of the nonlinear state-space model. Next, the nonlinear state-space model is established through the DLaCVA model, which paves the way for the integration of deep learning models with CVA and theoretically proves its modeling efficiency. The corresponding DLaCVA-based predictive control strategy is also completed. In addition, our case study shows that the proposed DLaCVA has taken an important step in improving the modeling accuracy and control effect related to blast furnace hot metal quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 It is a schematic diagram of the route of the blast furnace ironmaking prediction and control method based on deep auxiliary typical variable analysis of the present invention. DETAILED DESCRIPTION

[0067] In order to more clearly describe the technical content of the present invention, the specific implementation method is further explained below in conjunction with the accompanying drawings.

[0068] like Figure 1 The figure is a schematic diagram of the blast furnace ironmaking prediction and control method based on deep learning-assisted typical variable analysis of the present invention. The method comprises the following steps:

[0069] (1) For offline modeling, it is necessary to install various sensors (flow sensor, temperature sensor, concentration sensor, etc.) at various locations in the blast furnace ironmaking process, and store the corresponding data through the database. In order to reduce the difficulty of modeling, it is necessary to first reduce and determine the model input. Here, we consider two factors as the main selection basis: the degree of divergence and the correlation with sulfur and phosphorus content. A smaller degree of input variable difference, such as a variance close to 0, indicates that the variable plays a smaller regulatory role and has less impact on BFIP. By considering the correlation, we can locate the input variables most relevant to MIQ. By combining the above factors, partial least squares regression (PLSR) is acceptable. As a multivariate regression method, PLSR can project the input and output information into a latent space and extract these raw data while capturing the main correlations.

[0070] Considering that the input matrix U contains N observations and m process variables, and the output matrix Y contains l variables, it can be defined as:

[0071]

[0072] The following goals of PLSR aim to describe correlations within the maximum variance they all preserve:

[0073] (w,c)=argmax w, w T U Y T c(2)

[0074] st&||w||=1,||c||=1

[0075] Where w and c are the direction vectors of U and Y respectively. The direction vector w can be calculated by solving (2) using the Lagrange multiplier technique:

[0076] UU T YY T w=λ w W(3)

[0077] With the largest eigenvalue λ w and the corresponding feature vector w. Subsequently, the latent score vector t, loading vectors p and q containing the maximum variance information are given by:

[0078] t=U T w,

[0079] Furthermore, the remaining parts of U and Y can be estimated for the next modeling iteration:

[0080]

[0081] Then, the above calculation process is repeated until enough direction vectors are extracted. Assuming that d direction vectors are extracted, the extracted direction matrix W = [w1, w2, ..., w d ]、Load matrix P=[p1,p2,…,p d ] and Q=[q1,q2,…,q d ]. Finally, the regression model between the potential score matrix of the main information in Y and the input matrix U is established through the regression matrix R, as shown below:

[0082]

[0083] in, is the regression error.

[0084] (2) In the nonlinear case, previous CVA-based methods use kernel techniques to achieve state estimation of nonlinear systems. Considering the extremely complex nonlinear characteristics of BFIP, we transform the nonlinear mapping operator F(z t ; Θ) is integrated into the linear state space model and the following structure is proposed:

[0085] x t+1 =Ax t +BF(z t ; Θ)+w t (7a)

[0086] y t =Cx t +DF(z t ; Θ)+v t (7b)

[0087] z t =[u t ,y t-1 ](7c)

[0088] In the formula, by taking the input u at sampling time t t and the output y at sampling time t-1 t Concatenating gives z t F(.) is a nonlinear mapping operator specified by the parameters θ of the deep learning model. The combination of the delayed output and the current input obtains a nonlinear representation through the nonlinear mapping operator.

[0089] (3) First, assume that the time lag parameters p and f of the past and future are determined, and the future output Y f And the past combination Z p The Hankel matrix of can be defined as follows:

[0090]

[0091] According to the generalized CVA optimization objective, DLaCVA intends to search for a pair of projections and so that they share the maximum correlation:

[0092]

[0093] in and Y is the projection matrix and I is the identity matrix. f The sample covariance matrix of (Zp; Θ) is expressed as ∑ y and∑ z , and Σ yz is the cross-covariance matrix. The solution to the above equation is provided by the singular value decomposition of the Hankel matrix K:

[0094]

[0095] The left singular matrix Γ, the right singular matrix Δ, Λ is a diagonal matrix containing singular values, Λ = diag(λ1,λ2,…,λ s ) represents the solution set of the maximum canonical correlation coefficient, and s represents the rank of K. By using the most significant r canonical correlation coefficient, the projection matrix can be obtained Right now:

[0096]

[0097]

[0098] Then, as Z p The linear combination of the state sequence It can be estimated by:

[0099]

[0100] (4) In order to converge to the best model accuracy, the objective function of the deep learning model in the proposed DLaCVA is constructed as follows to seek the optimal network parameter Θ, so

[0101]

[0102] where ∑ ε =I-ΛΛ T However, how to optimize deep learning model parameters has always been a challenge due to the difficulty in finding the optimal global solution and the complexity of model training. To deal with this situation, the stochastic gradient descent algorithm is used and demonstrates computational efficiency and global search capabilities. In addition, ∑ ε The corresponding gradient of can be derived as:

[0103]

[0104] in

[0105]

[0106] Here The specific iteration direction of the algorithm is given. Given the momentum parameter γ and the learning rate η, the model parameters Θ will be updated in each iteration to approximate the optimal value in the following way:

[0107]

[0108] in, is the momentum vector, and k is the number of model iterations. During the entire model learning process, the model parameters will be updated through continuous iterations until No longer decreases in the validation set.

[0109] (5) Once the deep learning model is determined, the state sequence can be clearly given. The corresponding DLaCVA-based state space model and predictive control strategy will be formulated in turn. By using least squares regression, the system matrix It can be estimated as:

[0110]

[0111] where is the sample covariance operator. So far, the state space model based on DLaCVA has been fully established.

[0112] Furthermore, the predictive performance of the system output can be defined in the following way:

[0113]

[0114] Then, by introducing the input control quantity The state-space model can transform the following structures:

[0115]

[0116] in and The output and state variables of the system under control.

[0117] Multi-step prediction of future output for:

[0118]

[0119] The superscript is the generalized inverse operator, and i is the size of the prediction step.

[0120] To this end, the objective function of predictive control can be easily extended to a multi-step prediction structure by replacing t with t+i.

[0121]

[0122] Where N p is the prediction horizon, N c Indicates the control range, Contains the set point for the output. W y and W u are the weighted matrices of output and input, respectively, which are used to adjust the influence of the corresponding variables on the target. In addition, due to the particularity of the controlled object, the prediction of input and output and the control amount should be bounded by their corresponding maximum and minimum values. Considering better search performance and less resource computing consumption, random search is referred to determine the optimal control input value.

[0123] This paper proposes a modeling and predictive control architecture related to blast furnace hot metal quality, which includes DLaCVA. First, a PLSR-based regression coefficient matrix is ​​used to determine the input variables of the nonlinear state-space model. Next, the nonlinear state-space model is established through the DLaCVA model, which paves the way for the integration of deep learning models with CVA and theoretically proves its modeling efficiency. The corresponding DLaCVA-based predictive control strategy is also completed. In addition, our case study shows that the proposed DLaCVA has taken an important step in improving the modeling accuracy and control effect related to blast furnace hot metal quality.

[0124] The above description is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

[0125] The above-mentioned embodiments only express several implementation modes of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the invention. It should be pointed out that, for a person of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the attached claims.

Claims

1. A blast furnace ironmaking prediction and control method based on deep auxiliary typical variable analysis, characterized in that: The steps include determining model input, state estimation, objective function establishment, and predictive control strategy; Among them, the model input is determined, and the influential controllable variables are determined as the model input using partial least squares regression (PLSR); a nonlinear state space model is proposed for nonlinear BFIP, and the state estimation is performed using the deep learning-assisted canonical variable analysis DLaCVA method; the deep learning method is used to model in the auxiliary state space, and the corresponding optimization objectives and learning gradients are obtained; a predictive control strategy based on the quadratic performance index is designed to achieve the best molten iron quality control performance; The step of determining the model input comprises the following steps: (1.1) In view of the large number of controllable variables in the blast furnace ironmaking process, the model inputs are first reduced and determined, with two factors as the main selection basis: the degree of divergence and the correlation with sulfur and phosphorus content; by considering the correlation, the input variables most relevant to MIQ are located; by combining the above factors, partial least squares regression is accepted as a multivariate regression method, which projects the input and output information into a latent space and extracts most of the variance of these original data while capturing the main correlations; considering that the input matrix U contains N observations and m process variables, and the output matrix Y contains l variables, it is defined as: (1.2) The following goal of PLSR aims to describe the correlation within the maximum variance that they all maintain: (w,c) = argmax w, c w T U Y T c(2) st&||w||=1,||c||=1 where w and c are the direction vectors of U and Y respectively; the direction vector w is calculated by solving (2) using the Lagrange multiplier technique: UU T YY T in=λ w In(3) With the largest eigenvalue λ w and the corresponding feature vector w; then, the latent score vector t, loading vectors p and q containing the maximum variance information are given by: (1.3) In addition, the remaining parts of U and Y are estimated for the next modeling iteration: U T :=U T -tp T (5a) Y T :=Y T -tq T (5b) Then, the above calculation process is repeated until enough direction vectors are extracted; assuming that d direction vectors are extracted, the extracted direction matrix W = [w1, w2, ..., w d ]、Load matrix P=[p1,p2,…,p d ] and Q=[q1,q2,…,q d ]; Finally, the regression model between the potential score matrix of the main information in Y and the input matrix U is established through the regression matrix R, as shown below: in, is the regression error, where the variable corresponding to the significant coefficient in the regression matrix R is the determined control input variable; The state estimation comprises the following steps: (2.1) In the nonlinear case, previous CVA-based methods use the kernel technique to achieve state estimation of nonlinear systems; by transforming the nonlinear mapping operator F(z t ; Θ) is integrated into the linear state space model and the following structure is proposed x t+1 =Ax t +BF(z t (Θ)+w t (7a) y t =Cx t +DF(z t (Θ)+v t (7b) z t =[u t ,y t-1 ](7c) In the formula, by taking the input u at sampling time t t and the output y at sampling time t-1 t Concatenating gives z t , F(.) is a nonlinear mapping operator specified by the parameter Θ of the deep learning model, and the combination of the delayed output and the current input obtains a nonlinear representation through the nonlinear mapping operator; (2.2) First, assume that the time lag parameters p and f of the past and future are determined, and the future output Y f And the past combination Z p The Hankel matrix of is defined as follows: According to the generalized CVA optimization objective, DLaCVA intends to search for a pair of projections and so that they share the maximum correlation: in and is the projection matrix, I is the identity matrix; Y f The sample covariance matrix of (Zp; Θ) is denoted as Σ y and Σ z , and Σ yz is the cross-covariance matrix; the solution is provided by the singular value decomposition of the Hankel matrix K: The left singular matrix Γ, the right singular matrix Δ, Λ is a diagonal matrix containing singular values, Λ = diag(λ1,λ2,…,λ s ) represents the solution set of the maximum canonical correlation coefficient, s represents the rank of K; by using the most significant r canonical correlation coefficient, the projection matrix is ​​obtained Right now: (2.3) Then, as Z p The linear combination of the state sequence It is estimated by: The objective function establishment comprises the following steps: (3.1) In order to converge to the best model accuracy, the objective function of the deep learning model in the proposed DLaCVA is constructed as follows to seek the optimal network parameters Θ, so where ∑ ε =I-ΛΛ T ; In addition, ∑ ε The corresponding gradient of is derived as: in (3.2) Given the momentum parameter γ and the learning rate η, the model parameters Θ will be updated in each iteration to approximate the optimal value in the following way: in, is the momentum vector, and k represents the number of model iterations; during the entire model learning process, the model parameters will be updated through continuous iterations until No longer decreases in the validation set; The prediction control strategy establishment includes the following steps: (4.1) Once the deep learning model is determined, the state sequence can be clearly given; the corresponding DLaCVA-based state space model and predictive control strategy will be formulated in turn; by using least squares regression, the system matrix Estimated to be: where ∑[.] is the sample covariance operator; So far, the state space model based on DLaCVA has been established; (4.2) The predictive performance of the system output is defined as follows: Then, by introducing the input control quantity The state-space model transforms the following structure: in and The output and state variables of the system in the control situation; (4.3) Multi-step prediction of future output for: The superscript is the generalized inverse operator, i is the size of the prediction step; (4.4) To this end, by replacing t with t+i and extending to a multi-step prediction structure, the objective function of the predictive control is described as Where N p is the prediction horizon, N c Indicates the control range, Contains the set point of the output; W y and W u are the weighted matrices of output and input, respectively, which are used to adjust the influence of the corresponding variables on the target; in addition, due to the particularity of the controlled object, the prediction of input and output and the control amount are bounded by their corresponding maximum and minimum values; considering better search performance and less resource computing consumption, random search is referenced to determine the optimal control input value.

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