CN114609913A - Nonlinear predictive control modeling method for Support Vector Machine (SVM) - Google Patents
Nonlinear predictive control modeling method for Support Vector Machine (SVM) Download PDFInfo
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Abstract
The invention discloses a nonlinear predictive control modeling method of a Support Vector Machine (SVM), which comprises the following specific steps: s1, carrying out generalized predictive control on the nonlinear system; s2, introducing a Support Vector Machine (SVM) model; s3, inputting reference track parameters; s4, Support Vector Machine (SVM) model prediction; s5, measuring input data and output data of the controlled object as a sample of the training SVM; s6, performing off-line training on the SVM to obtain an SVM prediction model; s7, generating the output of a nonlinear system through the obtained SVM prediction model, calculating an error, and performing feedback correction; and S8, obtaining the global optimal control quantity through feedback correction, obtaining the optimal control strategy under the generalized predictive model, and realizing the generalized predictive control. According to the invention, the support vector machine model is introduced to calculate the global optimal control quantity of the system, so that an optimal control strategy is provided for the nonlinear control prediction system, and the efficiency of the automatic control system is further improved.
Description
Technical Field
The invention relates to the field of modeling control, in particular to a nonlinear predictive control modeling method of a Support Vector Machine (SVM).
Background
In real life, linear model prediction is suitable for a control system with a system parameter change rule, and many system parameters have large and irregular change amplitude, so that nonlinear model prediction, namely a generalized prediction control model, appears, and is nonlinear model prediction. The basis of the generalized predictive control model is adaptive control, and the predictive model, rolling optimization and feedback correction become three main parameters for evaluating the generalized predictive control. Linear models can control weak nonlinear objects, but strong nonlinear systems cannot be controlled by linear models, and therefore, the linear models become a hot topic of research in the control field.
Therefore, a non-linear predictive control modeling method for a Support Vector Machine (SVM) is needed to solve the defects in the prior art.
Disclosure of Invention
The purpose of the invention is as follows: in view of the above problems and deficiencies in the prior art, it is an object of the present invention to provide a modeling method for nonlinear predictive control of a support vector machine SVM. By introducing a support vector machine model, the global optimal control quantity of the system is calculated, an optimal control strategy is provided for the nonlinear control prediction system, and the efficiency of the automatic control system is further improved.
The technical scheme is as follows: in order to achieve the above purpose, the nonlinear predictive control modeling method of the support vector machine SVM according to the present invention comprises the following steps:
s1, carrying out generalized predictive control on the nonlinear system;
s2, introducing a Support Vector Machine (SVM) model;
s3, inputting reference track parameters;
s4, Support Vector Machine (SVM) model prediction;
s5, measuring input data and output data of the controlled object as a sample of the training SVM;
s6, performing off-line training on the SVM to obtain an SVM prediction model;
s7, generating the output of a nonlinear system through the obtained SVM prediction model, calculating the error, and performing feedback correction;
and S8, obtaining the global optimal control quantity through feedback correction, obtaining the optimal control strategy under the generalized predictive model, and realizing the generalized predictive control.
Further, in step S1, the controlled autoregressive integrated moving average cari model is used to describe the randomly disturbed object, and the description of the object is given by a transfer function z, where the transfer function z from the input u to the output is:
further, in step S2, the support vector machine SVM model is predicted in a non-recursive prediction manner, and multi-step prediction is performed using input/output data of a plurality of parallel SVM prediction models.
Further, in step S6, the off-line training method of the SVM prediction model is as follows:
(1) establishing an optimal hyperplane of the SVM according to the risk minimization principle;
(2) converting the nonlinear classification problem into a quadratic optimization problem;
(3) and establishing an SVM decision function.
Further, the SVM optimal hyperplane is represented as:
wherein w is a hyperplane normal vector, and b is a hyperplane offset vector;
further, the nonlinear classification problem is transformed into a formula adopted by quadratic optimization as follows:
the corresponding constraint conditions are:
yi(wgΦ(xi)+b)≥1-ξi
ξ≥0,i＝1,2L,n
where xi is (═ xi)i,...,ξl)TAnd c is a penalty parameter.
Further, the formula of the SVM decision function is as follows:
where sign is a sign function, αiAre Lagrange multipliers.
According to the technical scheme, the invention has the beneficial effects that:
(1) the invention relates to a nonlinear generalized predictive control modeling method for obtaining a global optimal control variable by using a support vector machine model.
(2) The problem that a nonlinear prediction control model is difficult to construct can be solved based on SVM modeling.
Drawings
FIG. 1 is a model of predictive control for a support vector machine predictive control algorithm of the present invention;
FIG. 2 is a non-recursive multi-step prediction process of the SVM model of the present invention.
Detailed Description
The present invention is further illustrated by the following figures and specific examples, which are to be understood as illustrative only and not as limiting the scope of the invention, which is to be given the full breadth of the appended claims and any and all equivalent modifications thereof which may occur to those skilled in the art upon reading the present specification.
1-2, the modeling method for the nonlinear predictive control of the SVM comprises the nonlinear system generalized predictive control; constructing an SVM model and carrying out global optimal control quantity; the method comprises the following specific steps:
s1, in the generalized predictive control, a controlled autoregressive integrated moving average (CARIMA) model is adopted to describe a random interference object, a transfer function z is used to describe the object, and the transfer function z from an input u to an output is as follows:
s2, introducing a Support Vector Machine (SVM) model;
s3, inputting reference track parameters;
s4, Support Vector Machine (SVM) model prediction;
s5, measuring input data and output data of the controlled object as a sample of the training SVM;
s6, performing off-line training on the SVM to obtain an SVM prediction model, wherein the specific process is as follows:
1) according to the principle of risk minimization, the SVM optimal hyperplane is represented as:
wherein w is a hyperplane normal vector and b is a hyperplane offset vector.
2) The nonlinear classification problem is converted into a quadratic optimization problem, namely:
the corresponding constraint conditions are:
yi(yi(wgΦ(xi)+b)≥1-ξi
ξ≥0，i＝1，2L，n
where xi is (═ xi)i，...，ξl)TAnd c is a penalty parameter.
3) Establishing SVM decision function
Where sign is a sign function, αiIs Lagrange multiplier.
And S7, generating the output of the nonlinear system through the obtained SVM prediction model, calculating the error, and performing feedback correction.
And S8, obtaining the global optimal control quantity through feedback correction, obtaining the optimal control strategy under the generalized predictive model, and realizing the generalized predictive control.
The examples are given solely for the purpose of illustration and are not to be construed as limitations of the present invention, as various equivalents will occur to those skilled in the art upon reading the present invention and are intended to be within the scope of the invention as defined in the claims appended hereto.
Claims (7)
1. A nonlinear predictive control modeling method of a Support Vector Machine (SVM) is characterized in that: the method comprises the following specific steps:
s1, carrying out generalized predictive control on the nonlinear system;
s2, introducing a Support Vector Machine (SVM) model;
s3, inputting reference track parameters;
s4, Support Vector Machine (SVM) model prediction;
s5, measuring input data and output data of the controlled object as a sample of the training SVM;
s6, performing off-line training on the SVM to obtain an SVM prediction model;
s7, generating the output of a nonlinear system through the obtained SVM prediction model, calculating an error, and performing feedback correction;
and S8, obtaining the global optimal control quantity through feedback correction, obtaining the optimal control strategy under the generalized predictive model, and realizing the generalized predictive control.
2. The modeling method for nonlinear predictive control of a Support Vector Machine (SVM) according to claim 1, wherein: in step S1, a controlled autoregressive integrated moving average CARIMA model is used to describe the randomly disturbed object, and a transfer function z is used to describe the object, where the transfer function z from input u to output is:
3. the modeling method for nonlinear predictive control of a Support Vector Machine (SVM) according to claim 1, wherein: in step S2, the support vector machine SVM model is predicted in a non-recursive prediction manner, and multi-step prediction is performed using input and output data of a plurality of parallel SVM prediction models.
4. The modeling method for nonlinear predictive control of the support vector machine SVM as claimed in claim 1, wherein: in step S6, the off-line training method of the SVM prediction model is as follows:
(1) establishing an optimal hyperplane of the SVM according to the risk minimization principle;
(2) converting the nonlinear classification problem into a quadratic optimization problem;
(3) and establishing an SVM decision function.
5. The modeling method for nonlinear predictive control of the support vector machine SVM of claim 4, wherein: the SVM optimal hyperplane is represented as:
wherein w is a hyperplane normal vector, and b is a hyperplane offset vector;
6. the modeling method for nonlinear predictive control of the support vector machine SVM as claimed in claim 5, wherein: the nonlinear classification problem is converted into a formula for quadratic optimization, and the formula is as follows:
the corresponding constraint conditions are:
yi(wgΦ(xi)+b)≥1-ξi
ξ≥0,i＝1,2L,n
where xi is (═ xi)i,...,ξl)TAnd c is a penalty parameter.
7. The modeling method for nonlinear predictive control of the support vector machine SVM as claimed in claim 6, wherein: the formula of the SVM decision function is as follows:
where sign is a sign function, αiAre Lagrange multipliers.
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| US20210049515A1 (en) * | 2019-08-16 | 2021-02-18 | China Institute Of Water Resources And Hydropower Research | Prediction method and system of high slope deformation |
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Patent Citations (4)
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| CN102662324A (en) * | 2012-04-28 | 2012-09-12 | 江南大学 | Non-linear model predication control method of tank reactor based on on-line support vector machine |
| CN104318090A (en) * | 2014-10-13 | 2015-01-28 | 江苏大学 | Least square method support vector machine-based generalized prediction method in lysozyme fermentation process |
| CN108196450A (en) * | 2017-12-29 | 2018-06-22 | 吉林大学 | Engine idling control system design method based on support vector machines |
| US20210049515A1 (en) * | 2019-08-16 | 2021-02-18 | China Institute Of Water Resources And Hydropower Research | Prediction method and system of high slope deformation |
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