CN112989275B - Multidirectional method for network large-scale control system - Google Patents

Multidirectional method for network large-scale control system Download PDF

Info

Publication number
CN112989275B
CN112989275B CN202110260092.7A CN202110260092A CN112989275B CN 112989275 B CN112989275 B CN 112989275B CN 202110260092 A CN202110260092 A CN 202110260092A CN 112989275 B CN112989275 B CN 112989275B
Authority
CN
China
Prior art keywords
matrix
vector
orthogonal directions
control system
parameter
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202110260092.7A
Other languages
Chinese (zh)
Other versions
CN112989275A (en
Inventor
陈晶
浦琰
胡满峰
毛亚文
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Jiangnan University
Original Assignee
Jiangnan University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Jiangnan University filed Critical Jiangnan University
Priority to CN202110260092.7A priority Critical patent/CN112989275B/en
Publication of CN112989275A publication Critical patent/CN112989275A/en
Application granted granted Critical
Publication of CN112989275B publication Critical patent/CN112989275B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16Y—INFORMATION AND COMMUNICATION TECHNOLOGY SPECIALLY ADAPTED FOR THE INTERNET OF THINGS [IoT]
    • G16Y20/00—Information sensed or collected by the things
    • G16Y20/10—Information sensed or collected by the things relating to the environment, e.g. temperature; relating to location
    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16Y—INFORMATION AND COMMUNICATION TECHNOLOGY SPECIALLY ADAPTED FOR THE INTERNET OF THINGS [IoT]
    • G16Y40/00—IoT characterised by the purpose of the information processing
    • G16Y40/30—Control

Abstract

The invention discloses a multidirectional method for a network large-scale control system, which comprises the steps of collecting system control data to construct a source direction vector; obtaining a plurality of orthogonal directions by using a Schmitt orthogonalization method according to the source direction vector; calculating corresponding step lengths using the plurality of orthogonal directions; updating system parameters in conjunction with the plurality of orthogonal directions and step sizes. The method can avoid solving the solution of the derivative function equation; converting the high-order matrix inversion into the low-order matrix inversion, thereby reducing the resource consumption of the whole identification process; the speed can be adjusted in a self-adaptive mode, the speed is faster when the number of directions is more, the gradient algorithm is equivalent to when the number of directions is 1, and the least square algorithm is equivalent to when the number of directions and the number of parameter dimensions are equal.

Description

Multidirectional method for network large-scale control system
Technical Field
The invention relates to the technical field of parameter identification, in particular to a multidirectional method for a network large-scale control system.
Background
With the high-speed development of the internet of things technology, signals are collected by sensors among industrial control systems, the signals are transmitted through a network, mutual connection and mutual communication are achieved, the control systems are larger and larger in scale, and a high-order system is required to describe the dynamic process of the control systems. The traditional identification algorithm such as Least Square (LS) method and Gradient algorithm (GI) method aims at parameter identification of large-scale system, wherein when the Least square algorithm is applied to parameter identification of large-scale system, the inverse of a high-order matrix needs to be calculated, which results in large calculation amount and influences identification efficiency; when the least square algorithm updates system parameters, analytical solutions of derivative function equations of cost functions need to be assumed, and the application range of the least square algorithm is limited by the strong assumption condition; the gradient algorithm only uses one direction each time the parameters are updated, and two connected directions are orthogonal, so the convergence speed is very slow.
Disclosure of Invention
This section is for the purpose of summarizing some aspects of embodiments of the invention and to briefly introduce some preferred embodiments. In this section, as well as in the abstract and the title of the invention of this application, simplifications or omissions may be made to avoid obscuring the purpose of the section, the abstract and the title, and such simplifications or omissions are not intended to limit the scope of the invention.
The present invention has been made in view of the above-mentioned problems with the conventional update system parameters.
Therefore, the technical problem solved by the invention is as follows: when the traditional least square algorithm is applied to parameter identification of a large-scale system, the inverse of a high-order matrix needs to be calculated, so that the calculated amount is large, the identification efficiency is influenced, and when the least square algorithm updates system parameters, the analytic solution of a derivative function equation of a cost function needs to be assumed, and the application range of the least square algorithm is limited by the strong assumption condition; on the other hand, the gradient algorithm only uses one direction each time the parameters are updated, and two connected directions are orthogonal, so that the convergence speed is very slow.
In order to solve the technical problems, the invention provides the following technical scheme: collecting system control data to construct a source direction vector; obtaining a plurality of orthogonal directions by using a Schmitt orthogonalization method according to the source direction vector; calculating corresponding step lengths using the plurality of orthogonal directions; updating system parameters in conjunction with the plurality of orthogonal directions and step sizes.
As a preferable solution of the multidirectional method for the network large-scale control system of the present invention, wherein: the constructing of the source direction vector includes that the collected system control data are L groups, and an initial error constructing source direction vector is constructed by using an information vector matrix and a data vector matrix, and is specifically represented as follows:
Figure BDA0002969579140000021
this can be normalized to give:
Figure BDA0002969579140000022
wherein:
Figure BDA0002969579140000023
is the initial raw vector of the m-th iteration, vm(1) Is composed of
Figure BDA0002969579140000024
The unit vector of (a) is,
Figure BDA0002969579140000025
is the m-th parameter estimation, Y (L) is the output of L sets of system, and phi (L) is the information vector matrix.
As a preferable solution of the multidirectional method for the network large-scale control system of the present invention, wherein: the information vector matrix comprises setting an information vector to be phi (t), and constructing the vector into L groups of data
Figure BDA0002969579140000026
The vector matrix of the information vector phi (t) is then:
Figure BDA0002969579140000027
wherein: t is the rank of the matrix.
As a preferable solution of the multidirectional method for the network large-scale control system of the present invention, wherein: the data vector matrix comprises that in L groups of data, the input and output of system control are respectively: u (1), …, u (L) and y (1), …, y (L), given a positive integer k, satisfy 1 ≦ k<n, and an initial parameter vector
Figure BDA0002969579140000028
The constructed data vector is as follows:
Y(L)＝[y(1)，…,y(L)]T
as a preferable solution of the multidirectional method for the network large-scale control system of the present invention, wherein: the acquiring the plurality of orthogonal directions by using the schmitt orthogonalization method includes setting the acquired plurality of orthogonal directions to be k, and then, a calculation formula is expressed as follows:
Figure BDA0002969579140000029
wherein: n is a symmetric positive definite matrix.
As a preferable solution of the multidirectional method for the network large-scale control system of the present invention, wherein: the step length corresponding to the calculation comprises the steps of constructing a transfer matrix by utilizing the orthogonal direction, and calculating the step length updated by the parameters of the transfer matrix, wherein the calculation formula is as follows:
Figure BDA0002969579140000031
wherein:
Figure BDA0002969579140000032
and i is 1, …, k, j is 1, …, k, k is the number of orthogonal directions.
As a preferable solution of the multidirectional method for the network large-scale control system of the present invention, wherein: the transfer matrix comprises that the construction of the subspace by using the orthogonal direction is as follows:
Figure BDA0002969579140000033
wherein: n is the dimension of the unknown parameter, k is the direction number, a transfer matrix is constructed according to the subspace, and the transfer matrix is expressed by the following formula:
Figure BDA0002969579140000034
as a preferable solution of the multidirectional method for the network large-scale control system of the present invention, wherein: updating the system parameters by combining the plurality of orthogonal directions and the step length comprises combining the plurality of orthogonal directions and the corresponding step length to obtain a new parameter vector
Figure BDA0002969579140000035
The concrete expression is as follows:
Figure BDA0002969579140000036
wherein:
Figure BDA0002969579140000037
is an estimate of the parameter after the m-th iteration, wherein:
Figure BDA0002969579140000038
for the estimated values of the parameters after the m-th iteration, comparison is made
Figure BDA0002969579140000039
And
Figure BDA00029695791400000310
if it is
Figure BDA00029695791400000311
The loop is terminated to obtain the parameter estimate
Figure BDA00029695791400000312
If not, increasing m by 1, and recalculating the source direction, wherein delta is a preset threshold value and is a normal number.
As a preferable solution of the multidirectional method for the network large-scale control system of the present invention, wherein: the updating of the system parameters also comprises that as k is less than n, the updating of the system parameters can reduce the calculated amount by reducing the value of k, and the parameter identification precision is improved by iteration times.
The invention has the beneficial effects that: the method can avoid solving the solution of the derivative function equation; converting the high-order matrix inversion into the low-order matrix inversion, thereby reducing the resource consumption of the whole identification process; the speed can be adjusted in a self-adaptive mode, the speed is faster when the number of directions is more, the gradient algorithm is equivalent to when the number of directions is 1, and the least square algorithm is equivalent to when the number of directions and the number of parameter dimensions are equal.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise. Wherein:
FIG. 1 is a flow chart of a multidirectional method for a network large-scale control system according to a first embodiment of the present invention;
FIG. 2 is a schematic diagram of a three-tank system for a multidirectional method of a networked large-scale control system according to a second embodiment of the present invention;
FIG. 3 is a diagram illustrating the parameter identification effect of a multidirectional method for a network large-scale control system according to a second embodiment of the present invention;
FIG. 4 is a diagram illustrating the mean and variance of parameter estimates calculated by each method of the multidirectional method for the networked large-scale control system according to the second embodiment of the present invention;
FIG. 5 is a diagram illustrating the time consuming algorithms of the multi-directional method for the networked large-scale control system according to the second embodiment of the present invention.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, specific embodiments accompanied with figures are described in detail below, and it is apparent that the described embodiments are a part of the embodiments of the present invention, not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making creative efforts based on the embodiments of the present invention, shall fall within the protection scope of the present invention.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described and will be readily apparent to those of ordinary skill in the art without departing from the spirit of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.
Furthermore, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one implementation of the invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.
The present invention will be described in detail with reference to the drawings, wherein the cross-sectional views illustrating the structure of the device are not enlarged partially in general scale for convenience of illustration, and the drawings are only exemplary and should not be construed as limiting the scope of the present invention. In addition, the three-dimensional dimensions of length, width and depth should be included in the actual fabrication.
Meanwhile, in the description of the present invention, it should be noted that the terms "upper, lower, inner and outer" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of describing the present invention and simplifying the description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation and operate, and thus, cannot be construed as limiting the present invention. Furthermore, the terms first, second, or third are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
The terms "mounted, connected and connected" in the present invention are to be understood broadly, unless otherwise explicitly specified or limited, for example: can be fixedly connected, detachably connected or integrally connected; they may be mechanically, electrically, or directly connected, or indirectly connected through intervening media, or may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
Example 1
Referring to fig. 1, a first embodiment of the present invention provides a multidirectional method for a network large-scale control system, including:
s1: the acquisition system controls the data to construct a source direction vector. In which it is to be noted that,
for the following network large scale control system:
Figure BDA0002969579140000051
wherein: y (t) is the output of the system, v (t) is the noise of the system, and follows a Gaussian distribution with mean zero and variance σ, φi(t), i ═ 1, …, n is a scalar consisting of inputs u (1), …, u (t) and outputs y (1), …, y (t-1), a1,…,anT is the rank of the matrix for the parameter to be identified by the system.
L sets of input-output and noise data are collected and define:
Y(L)＝[y(1),y(2),…,y(L)]T∈RL
Φ(L)＝[φT(1),φT(2),…,φT(L)]T∈RL×2n
Figure BDA0002969579140000052
V(L)＝[v(1),v(2),…,v(L)]T∈RL
wherein
Figure BDA0002969579140000061
Is an information vector, phii(t), i is 1, …, n is the formed information matrix, v (L) is the formed noise vector v (t), t is 1, …, L.
It is possible to obtain:
Y(L)＝Φ(L)θ+V(L)
θ＝[a1，…，an]T∈Rn
using a conventional least squares algorithm, one can find:
Figure BDA0002969579140000062
i.e., each time one matrix inverse (n × n) needs to be solved, it is difficult or infeasible to solve the inverse when the matrix dimensions are large or when the matrix is sparse.
In order to construct a source direction vector, an initial error construction source direction vector is constructed by using an information vector matrix and a data vector matrix, and the method is specifically represented as follows:
Figure BDA0002969579140000063
this can be normalized to give:
Figure BDA0002969579140000064
wherein:
Figure BDA0002969579140000065
is the initial raw vector of the m-th iteration, vm(1) Is composed of
Figure BDA0002969579140000066
The unit vector of (a) is,
Figure BDA0002969579140000067
is the m-th parameter estimation, Y (L) is the output of L sets of system, and phi (L) is the information vector matrix.
S2: and acquiring a plurality of orthogonal directions by using a Schmitt orthogonalization method according to the source direction vector. In which it is to be noted that,
acquiring the plurality of orthogonal directions by using the schmitt orthogonalization method includes setting the acquired plurality of orthogonal directions to be k, and then, a calculation formula is expressed as follows:
Figure BDA0002969579140000068
wherein: n is a symmetric positive definite matrix.
S3: the corresponding step size is calculated using a plurality of orthogonal directions. In which it is to be noted that,
constructing the subspace using orthogonal directions is:
Figure BDA0002969579140000069
wherein: n is the dimension of the unknown parameter, k is the direction number, a transfer matrix is constructed according to the subspace, and the transfer matrix is expressed by the following formula:
Figure BDA0002969579140000071
and calculating the step length of parameter updating by using the transition matrix, wherein the calculation formula is as follows:
Figure BDA0002969579140000072
wherein:
Figure BDA0002969579140000073
and i is 1, …, k, j is 1, …, k, k is the number of orthogonal directions.
S4: the system parameters are updated in conjunction with a plurality of orthogonal directions and step sizes. In which it is to be noted that,
combining the calculated multiple orthogonal directions and corresponding step lengths to obtain a new parameter vector
Figure BDA0002969579140000074
The concrete expression is as follows:
Figure BDA0002969579140000075
wherein:
Figure BDA0002969579140000076
is an estimate of the parameter after the m-th iteration, wherein:
Figure BDA0002969579140000077
for the estimated values of the parameters after the m-th iteration, comparison is made
Figure BDA0002969579140000078
And
Figure BDA0002969579140000079
if it is
Figure BDA00029695791400000710
The loop is terminated to obtain the parameter estimate
Figure BDA00029695791400000711
If not, increasing m by 1, and recalculating the source direction, wherein δ is a threshold value set in advance, and is generally selected adaptively according to the estimated value, if the estimated value of the parameter is large, a relatively large normal number can be selected, and if the estimated value of the parameter is small, a small normal number is selected.
Further, updating the system parameters further comprises that since k is less than n, the calculation amount can be reduced by reducing the value of k for updating the system parameters, and the parameter identification precision is improved by iteration times.
When the traditional least square iteration method is used for a network large-scale control system, the inverse of a high-dimensional matrix needs to be solved, an analytic solution exists in a derivative function equation, because the inversion of the high-dimensional matrix needs a large amount of calculation, the algorithm speed becomes slow, and the derivative function equation is supposed to have a strong condition that the analytical solution is a strong condition, the application range of the least square iterative algorithm is limited, the invention provides a multidirectional method aiming at the identification of the network large-scale control system, k orthogonal vectors are obtained by using a Schmidt orthogonalization method to form a vector space of n multiplied by k, the dimension reduction of the system is realized, the inversion of the high-dimensional matrix is converted into the inversion of the low-dimensional matrix, the calculated amount is far less than the calculated amount of the least square algorithm, meanwhile, the solution of solving the derivative function equation is avoided, and then, the system parameters are identified by using the traditional algorithm, and the speed is far faster than that of the traditional gradient algorithm.
Example 2
Referring to fig. 2 to 5, a second embodiment of the present invention is different from the first embodiment in that, in order to better verify and explain the technical effects adopted in the method of the present invention, the actual effects of the method are verified by means of scientific demonstration.
Referring to fig. 2, the present embodiment models a three-tank model having ten parameters, i.e., θ ═ a1,a2,a3,a4,a5]T＝[0.8,0.9,0.4,0.27,0.12]TWhere q denotes the drip speed, i.e. the input to the three-tank system, H1Is the liquid level of the first tank body of the three-tank water tank, C1Is the flow rate of the first tank as input to the second tank, H2Is the level of the second tank, C2Is the flow rate of the second tank, which is the input of the third tank, H3Is the level of the third tank, which is the output of the entire three-tank, C3Is the flow of the third tankThe speed is a fixed value, and the dripping speed q controls the liquid level of the third water tank to be H3Oscillating up and down according to the dropping speed q (input u) and the real liquid level value H of the third water tank3And (y) is output, and then the relation between the three water tanks is found out through a corresponding algorithm, so that the establishment of a mathematical model of the three water tanks is realized.
In the model, the input u (t) is the water inlet (q) of the upper water tank and is based on the liquid level (H) of the third water tank3) The water inflow is adjusted to be large when the liquid level is lower than an ideal value, and the water inflow is reduced when the liquid level is higher than the ideal value; and the output y (t) is the measured value of the liquid level of the third water tank, a pressure sensor is arranged at the bottom of the third water tank, the liquid level of the real water tank collected by the sensor is transmitted to a control center through a network, and the measurement error is represented by v (t), namely the measured value y (t) is formed by the real liquid level value and the noise v (t).
In the experimental process, when the liquid level of the third (lowest) water tank is stabilized near an ideal value, the three-water-tank model can be considered to reach a stable state, input data u (1), …, u (L) are collected at the moment, corresponding output display values collected by a sensor and transmitted to a control center are y (1), …, y (L), and corresponding measurement errors v (1), …, v (L), the three-water-tank model is modeled by using a traditional gradient algorithm (GI) and a least square algorithm (LS) and the method, the effectiveness of the three-water-tank model is verified from two aspects of algorithm speed and parameter estimation accuracy, and the experimental result refers to fig. 3-5.
It can be seen that fig. 3 is a parameter identification effect diagram of the multi-direction algorithm, the traditional gradient algorithm (GI) and the least square algorithm (LS) provided by the present invention, the multi-direction method provided by the present invention can quickly identify the parameters of the double-volume water tank, only 12 iterations are needed, the error is lower than 2% as compared with the traditional LS algorithm, and the error of the traditional GI method exceeds 40% when 12 iterations are performed, the GI algorithm is slowest in convergence speed, the LS is fastest, but it has a high-order matrix inversion operation, the speed of the method of the present invention is between the two, but it avoids the high-order matrix inversion, so it is simpler and more convenient; FIG. 4 is a graph of the mean and variance of parameter identification in different directions, where the upper bound of each column represents the final estimated value (the closer to the true value, the more accurate), and the vertical bars on the columns represent the distribution of the parameter identification (the shorter the vertical bars, the smaller the identification oscillation, the better the effect), so that it can be seen that as the number of directions is greater, the higher the parameter estimation accuracy is, the smaller the parameter estimation variance is, and the convergence speed of the multi-directional method proposed by the present invention increases and accelerates along with the number of directions; fig. 5 is a diagram of three different algorithms used for a three-tank water tank: the time consumed by the GI, LS and the multi-direction algorithm (one of the situations is selected, three directions are selected) identification model of the invention can be seen, the time consumed by the method of the invention is only 0.95874 seconds when 3 directions are selected each time, and the time consumed by the method of the invention is far lower than that of the traditional GI and LS algorithms under the same precision, so that the real-time performance is optimal.
It should be noted that the above-mentioned embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, which should be covered by the claims of the present invention.

Claims (7)

1. A multidirectional method for a networked large-scale control system, characterized by: comprises the steps of (a) preparing a mixture of a plurality of raw materials,
collecting system control data to construct a source direction vector;
obtaining a plurality of orthogonal directions by using a Schmitt orthogonalization method according to the source direction vector;
calculating a corresponding step size using the plurality of orthogonal directions,
said calculating the corresponding step size comprises calculating a corresponding step size,
constructing a transfer matrix by utilizing the orthogonal direction, and calculating the step length of parameter updating through the transfer matrix, wherein the calculation formula is as follows:
Figure FDA0003481917600000011
wherein:
Figure FDA0003481917600000012
and i is 1, …, k, j is 1, …, k, k is the number of orthogonal directions;
updating system parameters in conjunction with the plurality of orthogonal directions and step sizes,
combining the calculated multiple orthogonal directions and corresponding step lengths to obtain a new parameter vector
Figure FDA0003481917600000013
The concrete expression is as follows:
Figure FDA0003481917600000014
wherein:
Figure FDA0003481917600000015
for the estimated values of the parameters after the m-th iteration, comparison is made
Figure FDA0003481917600000016
And
Figure FDA0003481917600000017
if it is
Figure FDA0003481917600000018
Figure FDA0003481917600000019
The loop is terminated to obtain the parameter estimate
Figure FDA00034819176000000110
If not, increasing m by 1, and recalculating the source direction, wherein delta is a preset threshold value and is a normal number.
2. The multidirectional method for a networked large-scale control system of claim 1, wherein: the constructing of the source direction vector comprises,
the acquired system control data are in L groups, and an initial error construction source direction vector is constructed by using an information vector matrix and a data vector matrix, and is specifically represented as follows:
Figure FDA00034819176000000111
this can be normalized to give:
Figure FDA00034819176000000112
wherein:
Figure FDA00034819176000000113
is the initial raw vector of the m-th iteration, vm(1) Is composed of
Figure FDA00034819176000000114
The unit vector of (a) is,
Figure FDA00034819176000000115
for the m-th parameter estimation, Y (L) is the output of L sets of systems, and phi (L) is the information vector matrix.
3. The multidirectional method for a networked large-scale control system of claim 2, wherein: the matrix of information vectors comprises a matrix of,
setting the information vector as phi (t), and constructing the vector as L groups of data
Figure FDA0003481917600000021
The vector matrix of the information vector phi (t) is then:
Figure FDA0003481917600000022
wherein: t is the rank of the matrix.
4. The multidirectional method for the network large-scale control system according to claim 2 or 3, wherein: the matrix of data vectors comprises a matrix of,
in the group of L data, the input and output of the system control are respectively: u (1), …, u (L) and y (1), …, y (L), given a positive integer k, satisfy 1 ≦ k<n, and an initial parameter vector
Figure FDA0003481917600000023
The constructed data vector is as follows:
Y(L)＝[y(1),…,y(L)]T。
5. the multidirectional method for a networked large-scale control system of claim 4, wherein: the obtaining a plurality of orthogonal directions using a stewart orthogonalization method includes,
setting the acquired orthogonal directions to be k, and then expressing a calculation formula as follows:
Figure FDA0003481917600000024
wherein: n is a symmetric positive definite matrix.
6. The multidirectional method for a networked large-scale control system of claim 5, wherein: the transition matrix includes a plurality of transition matrices,
constructing a subspace using the orthogonal directions is:
Figure FDA0003481917600000025
wherein: n is the dimension of the unknown parameter, k is the direction number, a transfer matrix is constructed according to the subspace, and the transfer matrix is expressed by the following formula:
Figure FDA0003481917600000026
7. the multidirectional method for a networked large-scale control system of claim 6, wherein: the updating of the system parameters may further include,
since k is less than n, the updating of the system parameters can reduce the calculated amount by reducing the value of k, and the parameter identification precision is improved by the iteration times.
CN202110260092.7A 2021-03-10 2021-03-10 Multidirectional method for network large-scale control system Active CN112989275B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110260092.7A CN112989275B (en) 2021-03-10 2021-03-10 Multidirectional method for network large-scale control system

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110260092.7A CN112989275B (en) 2021-03-10 2021-03-10 Multidirectional method for network large-scale control system

Publications (2)

Publication Number Publication Date
CN112989275A CN112989275A (en) 2021-06-18
CN112989275B true CN112989275B (en) 2022-03-25

Family

ID=76334872

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110260092.7A Active CN112989275B (en) 2021-03-10 2021-03-10 Multidirectional method for network large-scale control system

Country Status (1)

Country Link
CN (1) CN112989275B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113569195B (en) * 2021-07-19 2023-12-01 江南大学 Preconditioning method for distributed network system

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2003044830A (en) * 2001-07-30 2003-02-14 Ricoh Co Ltd Neural network, neural network system, program and recording medium
CN106354015A (en) * 2016-10-27 2017-01-25 福州大学 Remote monitoring and online debugging method of diagonal recurrent neural network control system
CN110398942A (en) * 2019-07-02 2019-11-01 江南大学 A kind of parameter identification method for industrial processes control
CN110611599A (en) * 2019-11-01 2019-12-24 浙江诺诺网络科技有限公司 Network control system and control method thereof
CN111025898A (en) * 2019-11-07 2020-04-17 江南大学 Dimension reduction identification method for large-scale process control of process industry
CN112417683A (en) * 2020-11-20 2021-02-26 中国人民解放军63921部队 Data processing method and device for antenna on-orbit pointing calibration, electronic equipment and storage medium

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8296069B2 (en) * 2008-10-06 2012-10-23 Bp Corporation North America Inc. Pseudo-analytical method for the solution of wave equations

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2003044830A (en) * 2001-07-30 2003-02-14 Ricoh Co Ltd Neural network, neural network system, program and recording medium
CN106354015A (en) * 2016-10-27 2017-01-25 福州大学 Remote monitoring and online debugging method of diagonal recurrent neural network control system
CN110398942A (en) * 2019-07-02 2019-11-01 江南大学 A kind of parameter identification method for industrial processes control
CN110611599A (en) * 2019-11-01 2019-12-24 浙江诺诺网络科技有限公司 Network control system and control method thereof
CN111025898A (en) * 2019-11-07 2020-04-17 江南大学 Dimension reduction identification method for large-scale process control of process industry
CN112417683A (en) * 2020-11-20 2021-02-26 中国人民解放军63921部队 Data processing method and device for antenna on-orbit pointing calibration, electronic equipment and storage medium

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
"Modified orthogonal matching pursuit for multiple measurement vector with joint sparsity in super-resolution compressed sensing";Vinh Nguyen Xuan等;《2017 51st Asilomar Conference on Signals, Systems, and Computers》;20171101;第840-844页 *
"基于正交子空间投影的电力系统同调机群辨识";姜涛等;《电工技术学报》;20171128;2077-2087 *
"多元方程误差系统的递阶迭代辨识方法";葛政炜等;《中国优秀硕士学位论文全文数据库 (基础科学辑)》;20201115;A003-4 *

Also Published As

Publication number Publication date
CN112989275A (en) 2021-06-18

Similar Documents

Publication Publication Date Title
Natarajan et al. Convergence and accuracy of displacement based finite element formulations over arbitrary polygons: Laplace interpolants, strain smoothing and scaled boundary polygon formulation
Bernardini et al. Aerodynamic shape optimization of civil structures: A CFD-enabled Kriging-based approach
Farhat et al. Mixed explicit/implicit time integration of coupled aeroelastic problems: three‐field formulation, geometric conservation and distributed solution
Rüberg et al. A fixed‐grid b‐spline finite element technique for fluid–structure interaction
CN111859530B (en) Iterative propulsion disturbance domain updating method for aircraft dynamic aerodynamic characteristic simulation
CN108121856B (en) Dynamic stability analysis method for full-flight-domain aircraft
CN112989275B (en) Multidirectional method for network large-scale control system
CN113434921A (en) Structure equal-geometry topological optimization method considering mesoscale effect
Keshavarzzadeh et al. Shape optimization under uncertainty for rotor blades of horizontal axis wind turbines
CN111159636A (en) Flexible multi-body system dynamics semi-analytic sensitivity analysis method based on absolute node coordinate description
CN116451584B (en) Thermal stress prediction method and system based on neural network
KR102578263B1 (en) Multi-agent system consistency distributed control method for agriculture based on sampling data
Li et al. Analysis of the accuracy and pressure oscillation of the lattice Boltzmann method for fluid–solid interactions
Kedward et al. Towards generic modal design variables for aerodynamic shape optimisation
Qiao et al. A fast finite difference/RBF meshless approach for time fractional convection-diffusion equation with non-smooth solution
CN103942377B (en) A kind of reverse shape designing method manufactured towards elastomeric objects
CN108242808A (en) Time-lag power system stability method of discrimination based on IGD-LMS
CN108462180A (en) A method of probability optimal load flow is determined based on vine copula functions
CN116013443A (en) Method, device, equipment and readable storage medium for predicting heat transfer characteristic
CN113569195B (en) Preconditioning method for distributed network system
Kedward et al. Generic modal design variables for aerodynamic shape optimisation
CN107122569B (en) Power consumption prediction method for difference parallel HCMAC neural network bilateral variable flow ground source heat pump system
Fidkowski Analysis of Iterative Solvers for Hybridized Discontinuous Galerkin Methods
CN112632800B (en) High-precision temperature control method, system and equipment for 3D cover plate glass mold
CN115995277B (en) Method, device, equipment and medium for evaluating material dynamic characteristics

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant