Data-driven predictive control method for open-loop stable nonlinear system

Abstract

The invention relates to the technical field of industrial process control, and provides a data-driven predictive control method for an open-loop stable nonlinear system, which aims at the tracking control problem that a nonlinear system cannot be modeled widely in an industrial process, and comprises the following steps of: regressing a local model through an improved partial least square algorithm; an autoregression prediction model of the local model is obtained through a local weighted learning algorithm; and establishing a data-driven multi-step prediction model and a solving mode. The invention provides a data-driven prediction control method based on a local weighted learning framework. The data-driven prediction control method comprises the steps that regression is conducted on a local model through an improved partial least square algorithm, an autoregression prediction model is conducted on the local model through the local weighted learning algorithm, and a data-driven multi-step prediction model and a solving mode are established. Efficient tracking control of an open-loop stable nonlinear system under a local weighted learning framework is achieved, and the urgent demand of modern industrial production for high-precision and intelligent control is met.

Description

Technical Field

[0001] The present invention relates to the technical field of industrial process control, and in particular to a data-driven predictive control method for an open-loop stable nonlinear system. Background Art

[0002] With the rapid development of modern industry, production processes are becoming increasingly complex, and the scale of production continues to expand. In many actual production scenarios, it is increasingly difficult to establish accurate mathematical models for production equipment. For example, in the aerospace field, aircraft dynamics modeling and reaction process modeling in the biopharmaceutical process involve factors such as multi-physics field coupling, complex biochemical reactions, and time-varying characteristics, accurate modeling is almost impossible to achieve. Although most production equipment is in an open-loop stable state, unknown nonlinear characteristics are common. How to effectively track and control open-loop stable nonlinear systems in the absence of accurate models so that key performance indicators of the system, such as product quality parameters and production efficiency indicators, can be adjusted online in real time according to the expected indicators has become a major challenge facing the control field.

[0003] Currently, in the research of partial least squares regression algorithm and predictive control strategy under the partial least squares regression framework, many problems that need to be solved are exposed:

[0004] Traditional partial least squares algorithms suffer from incompleteness when processing data space decomposition, resulting in limited accuracy in the constructed regression models. Furthermore, their iterative computational approach prevents real-time model updates, making predictive control based on the partial least squares framework ineffective for nonlinear system control and unable to meet the stringent requirements of modern industry for real-time control and accuracy. Consequently, most existing nonlinear partial least squares algorithms lack online learning capabilities, making them difficult to adapt to the ever-changing operating conditions of the production process.

[0005] In predictive control within the nonlinear partial least squares framework, the linear constraints in the original data space are transformed into nonlinear constraints in the latent variable space, greatly increasing the difficulty of solving the control signal and limiting its application in practical engineering. When establishing a predictive model, the nonlinear regression model must be linearized, which reduces the original nonlinear regression model's prediction accuracy. Furthermore, the constraints imposed on the control signal can easily lead to slow convergence of the control signal, making it unable to respond to rapid changes in system state in a timely manner, seriously affecting control effectiveness and production efficiency.

[0006] Based on the problems in the prior art, the present invention provides a data-driven predictive control method for an open-loop stable nonlinear system. Summary of the Invention

[0007] The purpose of the present invention is to provide a data-driven predictive control method for an open-loop stable nonlinear system to solve the technical problems of low prediction accuracy and slow response speed of the predictive control model under the nonlinear partial least squares framework in the prior art.

[0008] The technical solution of the present invention is: a data-driven predictive control method for an open-loop stable nonlinear system, comprising: fitting a local model of a controlled object based on an improved partial least squares algorithm; fitting the autoregressive relationship of the local model based on a local weighted learning algorithm; updating the prediction model online, constructing a multi-step prediction model, and solving the optimal control sequence of the control signal online.

[0009] Preferably, the correlation model M is calculated online by using a block-by-block iterative PLS algorithm. k Perform regression;

[0010] Online update is used to fit the LWL model of unknown nonlinear transformation, and the correlation model M is updated through the LWL model. k The nonlinear autoregressive model M k+i Perform fitting to obtain M k+i The predicted value of

[0011] The optimal control sequence is solved by performing rolling optimization through the online cost function.

[0012] Preferably, the function representation of the unknown nonlinear transformation of the open-loop stable nonlinear system is simplified and equivalent to a finite step response model to obtain the correlation model M k ;

[0013] Correlation model M k Expressed as a nonlinear autoregressive model M k+i , and further expressed as a function representation f of the unknown nonlinear autoregressive model obeyed by the autocorrelation model at different moments M (·);

[0014] Based on the obtained nonlinear relationship, in the local weighted learning algorithm, the nonlinear relationship is fitted by multiple weighted local linear partial least squares models to obtain Indicated as M k+i The predicted value of

[0015] Based on the function representation of unknown nonlinear transformation and the unknown nonlinear autoregressive model obeyed by the autocorrelation model at different moments, the optimal control sequence is obtained through online rolling optimization of the cost function.

[0016] Preferably, at any time k, a fully stimulated initialization signal of length L is input to the system to construct a data matrix of input sampling points;

[0017] Based on the PLS algorithm, the correlation model M k Initialization is performed based on the nonlinear autoregressive model M k+i , for the initialized correlation model M k , perform k+n p Successive operations to obtain Multiple local models, used to initialize the LWL model;

[0018] Based on the LWPLS algorithm and introducing the cost function J, the parameters of each local receptive field in the initialized LWL model are updated, and then the receptive field weight of the r-th local receptive field is gradient updated: the online update of the LWL model for fitting unknown nonlinear transformations is realized;

[0019] Moreover, in the process of updating the LWL model, rolling optimization is performed through the online cost function to obtain the local model at time k. The predicted value of , obtains the single-step prediction model;

[0020] The single-step prediction model obtains N p A multi-step prediction model with a fixed prediction step length and a complete multi-step prediction model is constructed;

[0021] The multi-step prediction model performs online calculation of multi-step optimal control increments, and can calculate the optimal control quantity at time k+1, thereby obtaining the optimal control sequence.

[0022] Preferably, the correlation model M is calculated online by using a block-by-block iterative PLS algorithm. k The specific algorithm for regression includes:

[0023] The discrete-time unknown nonlinear process of the nonlinear autoregressive model is expressed as:

[0024] y(k)=f(y(k-1),...,y(kn y ),u(k),...,u(kn u +1);

[0025] Where u(k)∈R 1 and y(k)∈R m are the control input vector and output vector of the nonlinear process at time k, n u and n y are two unknown positive integers, representing the order of the nonlinear process, and f(·) represents an unknown nonlinear transformation;

[0026] Then the open-loop stable nonlinear system is simplified to an equivalent finite step response model, which is expressed as:

[0027]

[0028] Among them, U L (k) = [u(k-L+1) T ,...,u(k) T ] T is the generalized input vector of the FIR model, Represents the correlation model, L represents the order of the FIR model;

[0029] Correlation model M k With the characteristics of slow time variation, the nonlinear autoregressive model is expressed as:

[0030]

[0031] Among them, f M (·) represents the unknown nonlinear autoregressive model that the autocorrelation model at different moments obeys, n p Used to describe f M the number of M past values of the dynamic characteristic;

[0032] represents a matrix composed of the past values of M, and the residual dynamic information is regarded as part of the noise term.

[0033] Preferably, at any time k, a fully stimulated initialization signal of length L is input to the system, and the following data matrix is constructed:

[0034] U L (k) = [u(k-L+1) T ,...,u(k) T ] T ;

[0035] Φ pls (k)=[U L (kN w +1),...,U L (k)] T ;

[0036] Y pls (k) = [y(kN w +1),...,y(k)] T ;

[0037] Among them, N w is the data window size; U L (k) is the generalized input signal, Φ pls (k) is the generalized input expansion data matrix, Y pls (k) is the output signal expansion data matrix;

[0038] Based on the PLS algorithm, the correlation model Mk Initialize, the specific calculation formula is as follows:

[0039]

[0040] Where P is the unitary matrix of the generalized input expansion data matrix, P pc is the principal component vector of PLS, P res is the residual component vector of PLS. Λ is the diagonal matrix of importance coefficients, pc is the main component importance coefficient, Λ res is the residual importance coefficient and Λ res ≈0. M 0 (k) is the local correlation model of PLS including residual terms, and M 0 (k) is a vector matrix composed of the main component vector and the residual component vector, Λ M is the principal component importance coefficient, M k It is a completely decomposed local correlation model.

[0041] Preferably, based on In k+n p After the step, based on the nonlinear autoregressive model M k+i ,get A local model is used to initialize the LWL model. The initialization process is:

[0042] Initialize the model parameters as The diagonal matrix is used as the receptive field weight D0 of the first receptive field and the first receptive field parameter is randomly initialized

[0043] The receptive field can be updated by obtaining a new sample point Θ1.

[0044] Preferably, the parameters of each local receptive field are updated based on the LWPLS algorithm, and then the receptive field weight D of the rth local receptive field is updated. r To update the gradient, the calculation process is as follows:

[0045]

[0046] The cost function J is expressed as:

[0047]

[0048] Among them, w i For the i-th online sample, the receptive field weight D r The calculated weights, is the normalized model prediction error, ∑i,j d i,j is the weight of each element of the receptive field and serves as a penalty term to prevent the receptive field from collapsing during training, and Λ is the weight of the penalty term;

[0049] In each update process of the local receptive field parameters, if the projection direction of LWPLS is increased to reduce the rate of decrease of the mean square error, the projection direction is further increased, that is:

[0050] The default value is 0.3;

[0051] If the new sample point Θ i The weight of each receptive field is less than a certain threshold, that is:

[0052] w r <w th (The default value is 0.5), r=1,…,R;

[0053] Then Θ i Create new local models for local receptive field centers.

[0054] Preferably, at time k, based on the local model The predicted value of , the single-step prediction model is obtained as follows:

[0055]

[0056] Among them, N u represents the control step of predictive control; ΔU L (k+1) is the incremental generalized input matrix, ΔU p (k+1) is the backward (future) incremental input matrix, which is expressed as follows:

[0057] ΔU L (k+1)=U L (k+1)-U L (k);

[0058] ΔU p (k+1)=[Δu(k+1) T ,…,Δu(k+N u ) T ,0,…,0] T ;

[0059] And: R1 is the single-step prediction coefficient of the incremental generalized input matrix, R2 is the single-step prediction coefficient of the backward incremental input matrix, and B is the translation constant matrix, which are defined as follows:

[0060] B=[I|0],

[0061] Then we get Np The multi-step prediction model with the step prediction step length is as follows:

[0062]

[0063] Preferably, based on N p The multi-step prediction model with the step prediction step length can be constructed as follows:

[0064] Y p (K+1)=[I,I,…I] T y(k)+A1(k+1)ΔU L (k)+A2(k+1)ΔU p (k+1)

[0065] Among them, A1(k+1) is the multi-step prediction coefficient of the incremental generalized input matrix, and A2(k+1) is the multi-step prediction coefficient of the backward incremental input matrix, which are constructed as follows:

[0066]

[0067] Then the online calculation of multi-step optimal control increments is expressed as:

[0068]

[0069] Among them, E(k+1) is the backward tracking error, which is constructed as follows:

[0070] E(k+1)=Y sp (k+1)-[I,I,…I] T y(k)-A1(k+1)U L (k);

[0071] The optimal control quantity at time k+1 is calculated as:

[0072]

[0073] Compared with the prior art, the advantages of the present invention are:

[0074] (1) This invention designs a data-driven predictive control method under a local weighted learning framework, including regressing a local model using an improved partial least squares algorithm, applying an autoregressive predictive model to the local model using a local weighted learning algorithm, and establishing a data-driven multi-step prediction model and solution. This method achieves efficient tracking control of open-loop stable nonlinear systems under a local weighted learning framework, meeting the urgent need for high-precision, intelligent control in modern industrial production.

[0075] (2) The present invention is applicable to most open-loop stable industrial processes that cannot be modeled. By predicting the parameters of the local model, the nonlinear time series prediction model is transformed into a linear time-varying prediction model. This not only ensures the prediction and control accuracy of the nonlinear prediction model, but also ensures the solvability of the online rolling optimization problem of the predictive control.

[0076] (3) Compared with previous studies, such as traditional partial least squares-based predictive control methods, this method demonstrates higher prediction and tracking control accuracy in tracking control of nonlinear systems. In addition, due to the non-orthogonal decomposition of the data space by the traditional partial least squares algorithm, a large amount of valid data is classified as residuals, which reduces the prediction accuracy. The iterative calculation method of the traditional partial least squares method is too complex, which limits its ability to learn data online. These problems have been greatly improved in the present invention.

[0077] (4) Compared with the data-driven predictive control method of the nonlinear prediction model, the method of the present invention effectively avoids the problem of inevitable reduction in model accuracy in the traditional nonlinear predictive control framework (in order to ensure the solvability of the online rolling optimization problem). In addition, compared with the problem of additional constraints on rolling optimization variables such as control sequences in the traditional nonlinear predictive control framework, the method of the present invention effectively improves the convergence speed of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0079] Figure 1 A nonlinear system block diagram of the nonlinear system data-driven predictive control method based on local weighted learning according to the present invention;

[0080] Figure 2 This is a flowchart for implementing the data-driven predictive control method for nonlinear systems based on local weighted learning described in the present invention.

[0081] Figure 3 This is a graph showing how the prediction errors of PLS, LWPR, and the prediction control algorithm provided by the present invention vary with the prediction step size in the application embodiment of the present invention;

[0082] Figure 4 This is a schematic diagram of the convergence of the predictive control algorithm model under the PLS framework in the application embodiment of the present invention;

[0083] Figure 5 This is a schematic diagram of the convergence of the predictive control algorithm model provided by the present invention in the application embodiment of the present invention;

[0084] Figure 6 This is a schematic diagram of the tracking control effect of the predictive control algorithm under the PLS framework in the application embodiment of the present invention;

[0085] Figure 7 This is a schematic diagram of the tracking control effect of the predictive control algorithm provided by the present invention in the application embodiment of the present invention. DETAILED DESCRIPTION

[0086] The present invention will be described in further detail below with reference to specific embodiments:

[0087] The present invention relates to the field of automated control technology, and specifically to a method for realizing high-precision data-driven tracking control of open-loop stable nonlinear systems based on improved partial least squares and local weighted learning, and utilizing a predictive control algorithm. The method is particularly suitable for typical nonlinear process control fields, such as chemical production processes, power system control, and robot motion control, where high requirements are placed on system dynamic performance and control accuracy.

[0088] Aiming at the problems of insufficient regression model accuracy, complex regression process and difficulty in implementing predictive control under the partial least squares framework in traditional partial least squares methods, this paper proposes a data-driven predictive control method for open-loop stable nonlinear systems.

[0089] The basic idea of the data-driven predictive control algorithm for open-loop stable nonlinear systems is:

[0090] Nonlinear AutoRegressive eXogenous (NARX) models the unknown nonlinear process in discrete time:

[0091] y(k)=f(y(k-1),...,y(kn y ),u(k),...,u(kn u +1);

[0092] Where u(k)∈R 1 and y(k)∈R m are the control input vector and output vector of the nonlinear process at time k, n u and n y are two unknown positive integers representing the order of the nonlinear process, and f(·) is an unknown nonlinear transformation.

[0093] For open-loop stable nonlinear systems, the above nonlinear autoregressive model can be further simplified to an equivalent finite impulse response (FIR) model:

[0094]

[0095] Among them, U L (k) = [u(k-L+1) T,...,u(k) T ] T is the generalized input vector of the FIR model, represents the correlation model, and L represents the order of the FIR model. For nonlinear processes with unknown models, the selection of L usually depends on engineering experience.

[0096] For the open-loop stable nonlinear process, the correlation model M k It has the characteristics of slow time variation and can be approximately considered to satisfy the nonlinear autoregressive model in the statistical sense, that is:

[0097]

[0098] Among them, f M (·) represents the unknown nonlinear autoregressive model that the autocorrelation model at different moments obeys, n p Indicates the use to describe f M the number of M past values of the dynamic characteristic;

[0099] is a matrix composed of M past values, and the residual dynamic information ε k+i as part of the noise term.

[0100] The above nonlinear relationship is fitted by the Locally Weighted Learning (LWL) algorithm. Taking the Locally Weighted Projection Regression (LWPR) algorithm as an example, the nonlinear relationship is fitted by multiple weighted local linear partial least squares models in LWPR, namely:

[0101]

[0102] Weight

[0103] in, M k+i The predicted value, R is the number of linear models, c r is the center point of the rth local linear model, β r and is the parameter of the rth linear model, which can be regressed using algorithms such as partial least squares.

[0104] In obtaining the above f(·) and f M (·) based on the online form:

[0105]

[0106] The cost function is optimized online, and the optimal control sequence Δu can be solved * =argminJ. Where y sp is the desired output vector of the controlled object, Δu represents the optimal control vector increment to be solved, Λ is the weight factor to measure the relative importance of the two terms in the formula, N p and N u are the prediction step size and control step size of the cost function, and N p >N u , then there is an optimal control sequence.

[0107] In summary, the data-driven predictive control algorithm for open-loop stable nonlinear systems consists of three steps:

[0108] The correlation model M is trained online through block iterative PLS algorithm. k Perform regression;

[0109] (2) Online update is used to fit f M (·) LWL model, and Calculate the predicted value of

[0110] (3) Perform rolling optimization on the cost function J online and solve the optimal control sequence Δu * .

[0111] Refer to the attached Figure 1 As shown in the nonlinear system diagram and step method, the specific steps are as follows:

[0112] At any time k, the system is input with a fully stimulated initialization signal of length L, and the following data matrix is constructed

[0113] U L (k) = [u(k-L+1) T ,...,u(k) T ] T

[0114] Φ pls (k)=[U L (kN w +1),...,U L (k)] T

[0115] Y pls (k) = [y(kN w +1),...,y(k)] T

[0116] where N w is the data window size, usually 20 sampling points; U L (k) is the generalized input signal, Φpls (k) is the generalized input expansion data matrix, Y pls (k) is the output signal expansion data matrix.

[0117] Based on the improved partial least squares algorithm for the correlation model M k Initialize, the specific calculation formula is as follows:

[0118]

[0119] Where P is the unitary matrix of the generalized input expansion data matrix, P pc is the principal component vector of PLS, P res is the residual component vector of PLS. Λ is the diagonal matrix of importance coefficients, pc is the main component importance coefficient, Λ res is the residual importance coefficient and Λ res ≈0. M 0 (k) is the local correlation model of PLS including residual terms, and M 0 (k) is a vector matrix composed of the main component vector and the residual component vector, Λ M is the principal component importance coefficient, M k It is a completely decomposed local correlation model.

[0120] In k+n p After step 1, you get Local models are initialized, and then the LWL model (Locally Weighted Learning, LWL) is initialized. The model parameters are The diagonal matrix is used as the receptive field weight D0 of the first receptive field and the first receptive field parameter is randomly initialized

[0121]

[0122] Obtaining a new sample point Θ1 can update the receptive field;

[0123] The specific method of obtaining a new sample point Θ1 and updating the receptive field in the model is as follows:

[0124] First, the parameters of each local receptive field are updated based on the LWPLS algorithm (Locally Weighed Partial Least Square, LWPLS, local weighted partial least squares), and then the receptive field weight D of the rth local receptive field is updated. r Perform gradient update:

[0125]

[0126] The cost function J uses the following formula:

[0127]

[0128] Among them, w i For the i-th online sample, the receptive field weight D r The calculated weights, is the normalized model prediction error, ∑ i,j d i,j is the weight of each element of the receptive field and serves as a penalty term to avoid the collapse of the receptive field during training (overfitting caused by too dense receptive field generation), and Λ is the penalty term weight.

[0129] In the process of updating the local receptive field parameters each time, if increasing the projection direction of LWPLS will significantly reduce the rate of decrease of the mean square error, then further increase the projection direction, that is:

[0130] The default value is 0.3

[0131] If the new sample point Θ i The weight of each receptive field is less than a certain threshold, that is:

[0132] w r <w th (The default value is 0.5), r=1,…,R;

[0133] Then Θ i Create new local models for local receptive field centers.

[0134] The LWPLS algorithm is a local correlation model M k This approach models the nonlinear dynamics of the signal. Because it models a local linear model rather than the signal itself, it avoids the difficulties associated with online rolling optimization due to the complexity of model gradient calculations. Compared to data-driven predictive control approaches based on nonlinear predictive models, this approach effectively avoids the inevitable loss of model accuracy associated with traditional nonlinear predictive control frameworks, ensuring the solvability of the online rolling optimization problem and significantly improving the algorithm's convergence speed.

[0135] Based on the local model at time k The predicted value of , the single-step prediction model is as follows:

[0136]

[0137] Among them, N u represents the control step of predictive control; ΔU L(k+1) is the incremental generalized input matrix, ΔU p (k+1) is the backward (future) incremental input matrix, which is expressed as follows:

[0138] ΔU L (k+1)=U L (k+1)-U L (k);

[0139] ΔU p (k+1)=[Δu(k+1) T ,…,Δu(k+N u ) T ,0,…,0] T ;

[0140] R1 is the single-step prediction coefficient of the incremental generalized input matrix, R2 is the single-step prediction coefficient of the backward incremental input matrix, and B is the translation constant matrix, which are defined as follows:

[0141] B=[I|0];

[0142] Then we can get N p The multi-step prediction model with the step prediction step length is as follows:

[0143]

[0144] The complete multi-step forecasting model can be constructed as:

[0145] Y p (K+1)=[I,I,…I] T y(k)+A1(k+1)ΔU L (k)+A2(k+1)ΔU p (k+1)

[0146] Among them, A1(k+1) is the multi-step prediction coefficient of the incremental generalized input matrix, and A2(k+1) is the multi-step prediction coefficient of the backward incremental input matrix, which are constructed as follows:

[0147]

[0148] Then the multi-step optimal control increment can be calculated online as:

[0149]

[0150] Among them, E(k+1) is the backward tracking error, which is constructed as follows:

[0151] E(k+1)=Y sp (k+1)-[I,I,…I] Ty(k)-A1(k+1)U L (k);

[0152] The optimal control quantity at time k+1 can be calculated as:

[0153]

[0154] This invention regresses local linear models using an improved partial least squares algorithm and trains local receptive fields using a local weighted learning algorithm to accurately fit the autoregressive relationships of the local model of a nonlinear system, significantly improving the prediction accuracy of nonlinear systems. The resulting data-driven predictive control method within a local weighted learning framework achieves efficient tracking control of open-loop stable nonlinear systems within this framework, meeting the urgent need for high-precision, intelligent control in modern industrial production.

[0155] Furthermore, an application example of the present invention is provided, which is applied to a continuous stirred tank heater (CSTH) to adjust the heating input power of the heating tank online. This example is then compared and analyzed with predictive control based on LWPR and PLS.

[0156] The CSTH benchmark process can be regarded as a five-input and three-output system, where the input variables are the opening u1 of the cold water flow rate valve of tank 1, the opening u2 of the cold water flow rate valve of tank 2, the opening u3 of the circulation flow rate valve, the power input u4 of the electric heater of tank 1, and the power input u5 of the electric heater of tank 2.

[0157] The temperature T1 of tank 1 is taken as the key characteristic parameter of the continuous stirring heating tank CSTH system. The purpose of predictive control is to make the key characteristic parameter T1 track the expected output of the temperature of tank 1 online by adjusting the opening u4 and u5 of the heating input power of the two tanks online.

[0158] Compare the prediction errors of the predictive control algorithm based on PLS, LWPR and the present invention, and refer to the attached Figure 3 As shown, attached Figure 3 A curve diagram showing the change of prediction error with prediction step size for PLS, LWPR and the predictive control algorithm proposed in the present invention is provided.

[0159] In detail, Figure 4 A schematic diagram of the convergence of the prediction model of the predictive control algorithm under the PLS framework is provided. Figure 5 The present invention provides a schematic diagram of the convergence of the prediction model of the predictive control algorithm. Figure 4 , Attachment Figure 5 By comparing the astringency of the two, it can be seen that the astringency of the present invention is faster.

[0160] Attachment Figure 6 Provides a schematic diagram of the tracking control effect of the predictive control algorithm under the PLS framework, Figure 7 The following is a schematic diagram of the tracking control effect of the predictive control algorithm provided by the present invention in CSTH. Figure 6 , Attachment Figure 7 From the comparison of the effect diagrams in , it can be seen that the model fitting effect in this application is better and the prediction accuracy is higher.

[0161] By calculating the error, it is obtained that the root mean square value of the tracking error of the predictive control algorithm under the PLS framework is 0.0312, and the root mean square value of the tracking error of the predictive control algorithm provided by the present invention is 0.0112. It can be seen from the error results that the predictive control algorithm of the present application exhibits higher prediction and tracking control accuracy.

[0162] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable people familiar with this technology to understand the content of the present invention and implement it accordingly, and they are not intended to limit the scope of protection of the present invention. For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Therefore, no matter from which point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes that fall within the meaning and scope of the equivalent elements of the claims are included in the present invention.

Claims

1. A data-driven predictive control method for an open-loop stable nonlinear system, characterized in that: include: Fitting the local model of the controlled object based on the improved partial least squares algorithm; Fitting the autoregressive relationship of the local model based on the local weighted learning algorithm; Update the prediction model online, construct a multi-step prediction model, and solve the optimal control sequence of the control signal online.

2. The data-driven predictive control method for an open-loop stable nonlinear system according to claim 1, characterized in that: The correlation model M is trained online through block iterative PLS algorithm. k Perform regression; Online update is used to fit the LWL model of unknown nonlinear transformation, and the correlation model M is updated through the LWL model. k The nonlinear autoregressive model M k+i Perform fitting to obtain M k+i The predicted value of The optimal control sequence is solved by performing rolling optimization through the online cost function.

3. The data-driven predictive control method for an open-loop stable nonlinear system according to claim 2, characterized in that: Simplify the function representation of the unknown nonlinear transformation of the open-loop stable nonlinear system and make it equivalent to the finite step response model to obtain the correlation model M k ; Correlation model M k Expressed as a nonlinear autoregressive model M k+i , and further expressed as a function representation f of the unknown nonlinear autoregressive model obeyed by the autocorrelation model at different moments M (·); Based on the obtained nonlinear relationship, in the local weighted learning algorithm, the nonlinear relationship is fitted by multiple weighted local linear partial least squares models to obtain Indicated as M k+i The predicted value of Based on the function representation of unknown nonlinear transformation and the unknown nonlinear autoregressive model obeyed by the autocorrelation model at different moments, the optimal control sequence is obtained through online rolling optimization of the cost function.

4. The data-driven predictive control method for an open-loop stable nonlinear system according to claim 3, characterized in that: At any time k, the system is fed with a fully stimulated initialization signal of length L to construct a data matrix of input sampling points; Based on the PLS algorithm, the correlation model M k Initialization is performed based on the nonlinear autoregressive model M k+i , for the initialized correlation model M k , perform k+n p Calculate successively to obtain M k …M k+np Multiple local models, used to initialize the LWL model; Based on the LWPLS algorithm and introducing the cost function J, the parameters of each local receptive field in the initialized LWL model are updated, and then the receptive field weight of the r-th local receptive field is gradient updated: the online update of the LWL model for fitting unknown nonlinear transformations is realized; Moreover, in the process of updating the LWL model, rolling optimization is performed through the online cost function to obtain the local model at time k. The predicted value of , obtains the single-step prediction model; The single-step prediction model obtains N p A multi-step prediction model with a fixed prediction step length and a complete multi-step prediction model is constructed; The multi-step prediction model performs online calculation of multi-step optimal control increments, and can calculate the optimal control quantity at time k+1, thereby obtaining the optimal control sequence.

5. The data-driven predictive control method for an open-loop stable nonlinear system according to claim 3, characterized in that: The correlation model M is trained online through block iterative PLS algorithm. k The specific algorithm for regression includes: The discrete-time unknown nonlinear process of the nonlinear autoregressive model is expressed as: y(k)=f(y(k-1),...,y(k-n y ),u(k),...,u(k-n u +1)); Where u(k)∈R 1 and y(k)∈R m are the control input vector and output vector of the nonlinear process at time k, n u and n y are two unknown positive integers, representing the order of the nonlinear process, and f(·) represents an unknown nonlinear transformation; Then the open-loop stable nonlinear system is simplified to an equivalent finite step response model, which is expressed as: Among them, U L (k) = [u(k-L+1) T ,...,u(k) T ] T is the generalized input vector of the FIR model, Represents the correlation model, L represents the order of the FIR model; Correlation model M k With the characteristics of slow time variation, the nonlinear autoregressive model is expressed as: Among them, f M (·) represents the unknown nonlinear autoregressive model that the autocorrelation model at different moments obeys, n p Used to describe f M the number of M past values of the dynamic characteristic; represents a matrix composed of the past values of M, and the residual dynamic information is regarded as part of the noise term.

6. The data-driven predictive control method for an open-loop stable nonlinear system according to claim 4, characterized in that: At any time k, the system is input with a fully excited initialization signal of length L, and the following data matrix is constructed: IN L (k)=[u(k-L+1) T ,...,u(k) T ] T ; Φ pls (k)=[U L (kN w +1),...,U L (k)] T ; AND pls (k)=[y(kN w +1),...,y(k)] T ; Among them, N w is the data window size; U L (k) is the generalized input signal, Φ pls (k) is the generalized input expansion data matrix, Y pls (k) is the output signal expansion data matrix; Based on the PLS algorithm, the correlation model M k Initialize, the specific calculation formula is as follows: Where P is the unitary matrix of the generalized input expansion data matrix, P pc is the principal component vector of PLS, P res is the residual component vector of PLS. Λ is the diagonal matrix of importance coefficients, pc is the main component importance coefficient, Λ res is the residual importance coefficient and Λ res ≈0. M 0 (k) is the local correlation model of PLS including residual terms, and M 0 (k) is a vector matrix composed of the main component vector and the residual component vector, Λ M is the principal component importance coefficient, M k It is a completely decomposed local correlation model.

7. The data-driven predictive control method for an open-loop stable nonlinear system according to claim 6, characterized in that: based on In k+n p After the step, based on the nonlinear autoregressive model M k+i ,get A local model is used to initialize the LWL model. The initialization process is: Initialize the model parameters as The diagonal matrix is used as the receptive field weight D0 of the first receptive field and the first receptive field parameter β is randomly initialized r,0 , The receptive field can be updated by obtaining a new sample point Θ1.

8. The data-driven predictive control method for an open-loop stable nonlinear system according to claim 7, characterized in that: Based on the LWPLS algorithm, the parameters of each local receptive field are updated, and then the receptive field weight D of the rth local receptive field is updated. r To update the gradient, the calculation process is as follows: The cost function J is expressed as: Among them, w i For the i-th online sample, the receptive field weight D r The calculated weights, is the normalized model prediction error, ∑ i,j d i,j is the weight of each element of the receptive field and serves as a penalty term to prevent the receptive field from collapsing during training, and Λ is the weight of the penalty term; In each update process of the local receptive field parameters, if the projection direction of LWPLS is increased to reduce the rate of decrease of the mean square error, the projection direction is further increased, that is: The default value is 0.3; If the new sample point Θ i The weight of each receptive field is less than a certain threshold, that is: w r <w th (The default value is 0.5), r=1,…,R; Then Θ i Create new local models for local receptive field centers.

9. The data-driven predictive control method for an open-loop stable nonlinear system according to claim 8, characterized in that: Based on the local model at time k The predicted value of , the single-step prediction model is obtained as follows: Among them, N u represents the control step of predictive control; ΔU L (k+1) is the incremental generalized input matrix, ΔU p (k+1) is the backward (future) incremental input matrix, which is expressed as follows: ΔU L (k+1)=U L (k+1)-U L (k); ΔU p (k+1)=[Δu(k+1) T ,…,Δu(k+N u ) T ,0,…,0] T ; And: R1 is the single-step prediction coefficient of the incremental generalized input matrix, R2 is the single-step prediction coefficient of the backward incremental input matrix, and B is the translation constant matrix, which are defined as follows: Then we get N p The multi-step prediction model with the step prediction step length is as follows:

10. The data-driven predictive control method for an open-loop stable nonlinear system according to claim 9, characterized in that: Based on N p The multi-step prediction model with the step prediction step length can be constructed as follows: Y p (K+1)=[I,I,…I] T y(k)+A1(k+1)ΔU L (k)+A2(k+1)ΔU p (k+1); Where A1(k+1) is the multi-step prediction coefficient of the incremental generalized input matrix, and A2(k+1) is the multi-step prediction coefficient of the backward incremental input matrix, which are constructed as follows: Then the online calculation of multi-step optimal control increments is expressed as: Among them, E(k+1) is the backward tracking error, which is constructed as follows: E(k+1)=Y sp (k+1)-[I,I,…I] T y(k)-A1(k+1)U L (k); The optimal control quantity at time k+1 is calculated as:

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