CN116068903B - Real-time optimization method, device and equipment for robustness performance of closed-loop system - Google Patents
Real-time optimization method, device and equipment for robustness performance of closed-loop system Download PDFInfo
- Publication number
- CN116068903B CN116068903B CN202310355043.0A CN202310355043A CN116068903B CN 116068903 B CN116068903 B CN 116068903B CN 202310355043 A CN202310355043 A CN 202310355043A CN 116068903 B CN116068903 B CN 116068903B
- Authority
- CN
- China
- Prior art keywords
- matrix
- parameter
- gradient calculation
- target
- preset
- 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
Links
- 238000005457 optimization Methods 0.000 title claims abstract description 73
- 238000000034 method Methods 0.000 title claims abstract description 59
- 239000011159 matrix material Substances 0.000 claims abstract description 150
- 238000004364 calculation method Methods 0.000 claims abstract description 133
- 238000000354 decomposition reaction Methods 0.000 claims abstract description 104
- 239000013598 vector Substances 0.000 claims abstract description 64
- 238000005070 sampling Methods 0.000 claims description 27
- 238000000605 extraction Methods 0.000 claims description 16
- 238000004590 computer program Methods 0.000 claims description 10
- 238000010276 construction Methods 0.000 claims description 6
- 230000000694 effects Effects 0.000 abstract description 2
- 238000010586 diagram Methods 0.000 description 8
- 241000612182 Rexea solandri Species 0.000 description 3
- 230000006978 adaptation Effects 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000003247 decreasing effect Effects 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000005339 levitation Methods 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 230000002085 persistent effect Effects 0.000 description 1
- 230000000750 progressive effect Effects 0.000 description 1
- 230000001052 transient effect Effects 0.000 description 1
- 230000017105 transposition Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T10/00—Road transport of goods or passengers
- Y02T10/10—Internal combustion engine [ICE] based vehicles
- Y02T10/40—Engine management systems
Landscapes
- Engineering & Computer Science (AREA)
- Health & Medical Sciences (AREA)
- Artificial Intelligence (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Evolutionary Computation (AREA)
- Medical Informatics (AREA)
- Software Systems (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The invention discloses a real-time optimization method for the robustness of a closed-loop system, which comprises the steps of initializing optimization related parameters of each dynamic feedback subsystem; collecting system operation data of each preset type in preset time length in the operation process of the closed-loop system, and constructing a Hank matrix by utilizing the system operation data of each preset type; performing LQ decomposition on the Hanker matrix, and calculating a multiplicative operator according to the LQ decomposition result; singular value decomposition is carried out on the multiplicative operator; respectively carrying out first gradient calculation on each target parameter, and carrying out second gradient calculation according to each first gradient calculation result and a singular value decomposition result; and calculating the variation value of each parameter according to the second gradient calculation result and the learning rate corresponding to each target parameter, and updating the dynamic feedback subsystem by using the parameter vector obtained by the current iteration. The invention realizes the real-time online optimization of the robust performance when the closed-loop system operates. The invention also discloses a device, equipment and a storage medium, which have corresponding technical effects.
Description
Technical Field
The present invention relates to the field of control system design technologies, and in particular, to a real-time optimization method, apparatus, device, and computer readable storage medium for robust performance of a closed loop system.
Background
In control system design, optimization of robust performance is an important class of problems often faced by designing a well-controlled system. The existing design method aiming at the robust performance mostly adopts a model-based design method to carry out offline design aiming at the robust performance index according to a control system model; however, how to optimize the robust performance in real time while the system is running still lacks discussion, which has important application value in the control engineering practice.
In summary, how to solve the contradiction that the real-time optimization method lacks and has important application value in engineering practice is a problem that needs to be solved by those skilled in the art at present.
Disclosure of Invention
The invention aims to provide a real-time optimization method for the robustness of a closed-loop system, which realizes real-time online optimization of the robustness of the system when the closed-loop system is running, and realizes real-time optimization of the robustness of the closed-loop system, so that the system service can normally run in the optimization process; it is another object of the present invention to provide a real-time optimization apparatus, device and computer readable storage medium for robust performance of closed loop systems.
In order to solve the technical problems, the invention provides the following technical scheme:
a real-time optimization method for the robustness of a closed-loop system comprises the following steps:
initializing optimization related parameters of each dynamic feedback subsystem; wherein, each dynamic feedback subsystem optimizes the relevant parameter and includes each goal parameter to be optimized in real time;
collecting system operation data of each preset type in preset time length in the operation process of a closed-loop system, and constructing a Hank matrix by utilizing the system operation data of each preset type;
performing LQ decomposition on the Hanker matrix, and calculating a multiplicative operator according to an LQ decomposition result;
singular value decomposition is carried out on the multiplicative operator, and a singular value decomposition result is obtained;
respectively carrying out first gradient calculation on each target parameter, and carrying out second gradient calculation according to each first gradient calculation result and the singular value decomposition result to obtain each second gradient calculation result;
when the fact that the preset iteration termination condition is not met is determined according to the second gradient calculation results, calculating parameter change values according to learning rates respectively corresponding to the second gradient calculation results and the target parameters, calculating parameter vectors obtained by current iteration according to the parameter change values, and updating the dynamic feedback subsystem by utilizing the parameter vectors obtained by the current iteration; the learning rate corresponding to each target parameter is obtained through pre-selection; the parameter vector obtained by the current iteration is composed of various changed target parameters;
And stopping updating when the preset iteration termination condition is determined to be met according to each second gradient calculation result.
In a specific embodiment of the present invention, initializing optimization-related parameters of each dynamic feedback subsystem includes:
selecting the order, matrix height parameters and time window to be optimized of the dynamic feedback subsystem;
initializing a parameter vector formed by the target parameters, and selecting a learning rate for each target parameter.
In one embodiment of the present invention, constructing a hank matrix using each of the predetermined types of system operation data includes:
and constructing a Hanker matrix by utilizing the system operation data of each preset type according to the matrix height parameter and the preset time length.
In a specific embodiment of the present invention, the first gradient calculation is performed on each target parameter, including:
wherein ,in>At each sampling timeState vector of>As a residual error, the residual error is determined,for the dynamic feedback subsystem +.>Time domain output of the individual sampling instants +.>、/>、/>All are the parameter matrix, and the parameter matrix is the parameter matrix, For the dynamic feedback subsystem +.>Frequency domain output of individual sampling instants, +.>、/>Is a known matrix>For sampling time +.>For matrix height parameter, +.>For the time window to be optimized, +.>Is->And calculating a first gradient corresponding to the target parameter.
In a specific embodiment of the present invention, performing a second gradient calculation according to each first gradient calculation result and the singular value decomposition result includes:
constructing an intermediate matrix according to each first gradient calculation result:
calculating a lower triangular matrix according to the LQ decomposition result and the intermediate matrix through a formula:
wherein ,、/>all are decomposition results, including->Representing the extraction of the lower triangular matrix elements of the input matrix with the remaining elements set to 0, < >>Diagonal elements of the extraction matrix are shown and the remaining elements are set to 0,>is a lower triangular matrix;
extracting each target submatrix from the lower triangular matrix;
and performing second gradient calculation according to the LQ decomposition result, each target submatrix, the multiplicative operator and the singular value decomposition result.
In one embodiment of the present invention, extracting each target submatrix from the lower triangular matrix includes:
And extracting each target submatrix according to the dimension of each submatrix in the lower triangular matrix.
In a specific embodiment of the present invention, when it is determined that the preset iteration termination condition is satisfied according to each of the second gradient calculation results, stopping updating includes:
calculating whether the average value of F norms of the parameter vector change values of the continuous preset iteration times is smaller than a preset value;
if yes, stopping updating;
if not, repeating the step of collecting the system operation data of each preset type in the preset time period in the operation process of the closed-loop system.
A real-time optimization apparatus for robust performance of a closed loop system, comprising:
the initialization module is used for initializing optimization related parameters of each dynamic feedback subsystem; wherein, each dynamic feedback subsystem optimizes the relevant parameter and includes each goal parameter to be optimized in real time;
the matrix construction module is used for collecting system operation data of each preset type in a preset time period in the operation process of the closed-loop system and constructing a Hank matrix by utilizing the system operation data of each preset type;
the multiplicative operator calculation module is used for carrying out LQ decomposition on the Hank matrix and calculating a multiplicative operator according to an LQ decomposition result;
The singular value decomposition module is used for carrying out singular value decomposition on the multiplicative operator to obtain a singular value decomposition result;
the gradient calculation module is used for respectively carrying out first gradient calculation on each target parameter, and carrying out second gradient calculation according to each first gradient calculation result and the singular value decomposition result to obtain each second gradient calculation result;
the system updating module is used for calculating each parameter change value according to the learning rate corresponding to each second gradient calculation result and each target parameter respectively when the preset iteration termination condition is not met according to each second gradient calculation result, calculating a parameter vector obtained by the current iteration according to each parameter change value, and updating the dynamic feedback subsystem by utilizing the parameter vector obtained by the current iteration; the learning rate corresponding to each target parameter is obtained through pre-selection; the parameter vector obtained by the current iteration is composed of various changed target parameters;
and the updating stopping module is used for stopping updating when the preset iteration termination condition is determined to be met according to each second gradient calculation result.
A real-time optimization apparatus for closed loop system robustness performance, comprising:
A memory for storing a computer program;
a processor for implementing the steps of the real-time optimization method of the robustness of the closed-loop system as described above when executing said computer program.
A computer readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of a method of real-time optimization of the robustness of a closed loop system as described above.
The real-time optimization method for the robustness of the closed-loop system provided by the invention initializes optimization related parameters of each dynamic feedback subsystem; wherein, each dynamic feedback subsystem optimizes the relevant parameter and includes each goal parameter to be optimized in real time; collecting system operation data of each preset type in preset time length in the operation process of the closed-loop system, and constructing a Hank matrix by utilizing the system operation data of each preset type; performing LQ decomposition on the Hanker matrix, and calculating a multiplicative operator according to the LQ decomposition result; singular value decomposition is carried out on the multiplicative operator, and a singular value decomposition result is obtained; respectively carrying out first gradient calculation on each target parameter, and carrying out second gradient calculation according to each first gradient calculation result and a singular value decomposition result to obtain each second gradient calculation result; when the preset iteration termination condition is not met according to the second gradient calculation results, calculating each parameter change value according to the second gradient calculation results and the learning rate corresponding to each target parameter respectively, calculating a parameter vector obtained by the current iteration according to each parameter change value, and updating the dynamic feedback subsystem by using the parameter vector obtained by the current iteration; the learning rate corresponding to each target parameter is obtained through pre-selection; the parameter vector obtained by the current iteration is composed of various changed target parameters; and stopping updating when the preset iteration termination condition is determined to be met according to each second gradient calculation result.
According to the technical scheme, through a real-time solving method, system operation data are collected when the system is operated, LQ decomposition is conducted on a Hanker matrix constructed by utilizing system operation data of each preset type, a multiplicative operator is calculated according to an LQ decomposition result, singular value decomposition is conducted on the multiplicative operator, a singular value decomposition result is obtained, first gradient calculation is conducted on each target parameter respectively, second gradient calculation is conducted according to each first gradient calculation result and a singular value decomposition result, each parameter change value is calculated according to each second gradient calculation result and a learning rate corresponding to each target parameter respectively, and a parameter vector obtained through current iteration is used for updating the dynamic feedback subsystem. Therefore, the real-time online optimization of the robustness of the system is realized when the closed-loop system is operated, and the system service can be normally operated in the optimization process.
Correspondingly, the invention also provides a real-time optimization device, equipment and a computer readable storage medium of the robustness of the closed-loop system corresponding to the real-time optimization method of the robustness of the closed-loop system, which have the technical effects and are not repeated herein.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of an implementation of a method for real-time optimization of the robustness of a closed-loop system in accordance with an embodiment of the present invention;
FIG. 2 is a block diagram of a closed loop system according to an embodiment of the present invention;
FIG. 3 is a flowchart of another implementation of a method for real-time optimization of the robustness of a closed-loop system according to an embodiment of the present invention;
FIG. 4 is a block diagram of a real-time optimization device for robust performance of a closed loop system according to an embodiment of the present invention;
FIG. 5 is a block diagram of a real-time optimization device for robust performance of a closed loop system according to an embodiment of the present invention;
fig. 6 is a schematic diagram of a specific structure of a real-time optimization device for robust performance of a closed-loop system according to the present embodiment.
Detailed Description
In order to better understand the aspects of the present invention, the present invention will be described in further detail with reference to the accompanying drawings and detailed description. It will be apparent that the described embodiments are only some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1, fig. 1 is a flowchart showing an implementation of a method for real-time optimization of robustness of a closed loop system according to an embodiment of the present invention, where the method may include the following steps:
S101: initializing optimization related parameters of each dynamic feedback subsystem; wherein, each dynamic feedback subsystem optimizes the relevant parameter and includes each target parameter to be optimized in real time.
Referring to fig. 2, fig. 2 is a block diagram illustrating a closed loop system according to an embodiment of the present invention. The mathematical description of the controlled object is as follows:
wherein ,、/>、/>is determined by the structure and parameters of the controlled object, is known, such as magnetic levitation trains, servos, etc.)>Is a state vector +.>、/>Zero mean white noise>For control input +.>In order to measure the signal,refers to the sampling instant (i.e.)>The moment at which the sampling period starts).
The state observer is mathematically described as:
wherein ,is a state vector +>Estimate of->As residual error->For observer gain, which is designed offline, +.>Is selected such that->Is located within the unit circle.
In FIG. 2Is a known reference signal->For the output of the state feedback controller, the mathematical description of the state feedback controller is:
gain for state feedback controller, which is designed offline, < ->Is selected from (a)Should be made +.>Is located within the unit circle. />For dynamic feedback subsystem->Output of->Has the following form:
Subscript ofRefer to->Is determined by the controlled object, +.>Refer to->Is determined by the controlled object, +.>For the state vector of the dynamic feedback subsystem, the parameter matrix +.>Relates to->,…,/>;/>,…,/>,…,…,/>Co-ordination of->Number, off-line design, parameters selected to be satisfied by ∈>All the characteristic values of (2) are located in the unit circle. Parameter matrix->、/>For the parameter matrix needing real-time optimization, the included parameters to be optimized in real time are combined into the following parameter vectors:
the above parameter vector is column vector, and is marked with superscriptRepresenting matrix transposition, two parameter vectors together comprisingThe parameters to be designed on line are +.>Refer to->The%>The elements.
The robust performance index of the closed loop system is as follows:
wherein ,
、/>、/>、/>are all known to be->It requires real-time optimization determination for a dynamic feedback subsystem. Robust performance real-time optimization refers to dynamic feedback subsystem +.>So that->And decreasing until the optimization termination condition specified by the designer is met.
Due to dynamic feedback subsystemMiddle->、/>To require a real-time optimized parameter matrix, therefore, real-time optimization only requires optimizing the parameter vector +.>。
And pre-determining optimization related parameters of each dynamic feedback subsystem used for optimizing the dynamic feedback subsystem, initializing the optimization related parameters of each dynamic feedback subsystem, wherein each optimization related parameter of each dynamic feedback subsystem comprises each target parameter to be optimized in real time.
S102: and collecting system operation data of each preset type in preset time length in the operation process of the closed-loop system, and constructing a Hank matrix by utilizing the system operation data of each preset type.
And collecting system operation data of each preset type in preset time length in the operation process of the closed-loop system, and constructing a Hankel Matrix by utilizing the system operation data of each preset type.
The hank matrix refers to a matrix with equal elements on each pair diagonal, and has wide application in the fields of digital signal processing, numerical calculation, system control and the like.
S103: and performing LQ decomposition on the Hanker matrix, and calculating a multiplicative operator according to the LQ decomposition result.
After the Hank matrix is constructed, LQ decomposition is carried out on the Hank matrix, and a multiplicative operator is calculated according to the LQ decomposition result. The hanker matrix, such as matrix a, originally constructed by LQ decomposition can be decomposed into a form of a=lq, where L is the lower triangular matrix and Q is the unitary (orthogonal) matrix.
S104: singular value decomposition is carried out on the multiplicative operator, and a singular value decomposition result is obtained.
After the multiplicative operator is obtained through calculation, singular value decomposition is carried out on the multiplicative operator, and a singular value decomposition result is obtained.
S105: and respectively carrying out first gradient calculation on each target parameter, and carrying out second gradient calculation according to each first gradient calculation result and the singular value decomposition result to obtain each second gradient calculation result.
After the singular value decomposition result is obtained, performing first gradient calculation on each target parameter, and performing second gradient calculation according to each first gradient calculation result and the singular value decomposition result to obtain each second gradient calculation result.
S106: when the preset iteration termination condition is not met according to the second gradient calculation results, calculating each parameter change value according to the second gradient calculation results and the learning rate corresponding to each target parameter, calculating a parameter vector obtained by the current iteration according to each parameter change value, and updating the dynamic feedback subsystem by using the parameter vector obtained by the current iteration.
The learning rate corresponding to each target parameter is obtained through pre-selection; the parameter vector obtained by the current iteration is composed of various target parameters after the change.
And after each second gradient calculation result is obtained, when the preset iteration termination condition is not met according to each second gradient calculation result, calculating each parameter change value according to each second gradient calculation result and each learning rate corresponding to each target parameter, calculating a parameter vector which is obtained by current iteration and is formed by each changed target parameter according to each parameter change value, and updating the dynamic feedback subsystem by utilizing the parameter vector obtained by current iteration. Therefore, the real-time online optimization of the system robustness performance is realized when the closed-loop system is operated, the real-time optimization of the closed-loop system robustness performance is realized, and the system service can be normally operated in the optimization process.
S107: and stopping updating when the preset iteration termination condition is determined to be met according to each second gradient calculation result.
And stopping updating when the preset iteration termination condition is determined to be met according to each second gradient calculation result.
According to the technical scheme, through a real-time solving method, system operation data are collected when the system is operated, LQ decomposition is conducted on a Hanker matrix constructed by utilizing system operation data of each preset type, a multiplicative operator is calculated according to an LQ decomposition result, singular value decomposition is conducted on the multiplicative operator, a singular value decomposition result is obtained, first gradient calculation is conducted on each target parameter respectively, second gradient calculation is conducted according to each first gradient calculation result and a singular value decomposition result, each parameter change value is calculated according to each second gradient calculation result and a learning rate corresponding to each target parameter respectively, and a parameter vector obtained through current iteration is used for updating the dynamic feedback subsystem. Therefore, the real-time online optimization of the robustness of the system is realized when the closed-loop system is operated, and the system service can be normally operated in the optimization process.
It should be noted that, based on the above embodiments, the embodiments of the present invention further provide corresponding improvements. The following embodiments relate to the same steps as those in the above embodiments or the steps corresponding to the steps may be referred to each other, and the corresponding beneficial effects may also be referred to each other, which will not be described in detail in the following modified embodiments.
Referring to fig. 3, fig. 3 is a flowchart showing another implementation of a method for real-time optimization of robustness of a closed loop system according to an embodiment of the present invention, where the method may include the following steps:
s301: and selecting the order, the matrix height parameter and the time window to be optimized of the dynamic feedback subsystem.
Selecting dynamic feedback subsystemOrder of->Matrix height parameter->Time window to be optimized->,/>Is a positive integer>。
S302: initializing a parameter vector formed by target parameters, and selecting a learning rate for each target parameter.
Initializing a parameter vector made up of target parametersAnd for each target parameter +.>Selection learningRate->。
S303: and collecting system operation data of each preset type in a preset time period in the operation process of the closed-loop system, and constructing a Hank matrix by utilizing the system operation data of each preset type according to the matrix height parameter and the preset time period.
Collecting system operation data of each preset type in preset time length in the operation process of closed-loop system,/>,The three are as follows:
the time period should be at leastOf sampling period, e.g.>, and />Zero mean white noise data is selected for the noise added by the designer.
And constructing a Hank matrix by utilizing system operation data of each preset type according to the matrix height parameters:
S304: and performing LQ decomposition on the Hanker matrix, and calculating a multiplicative operator according to the LQ decomposition result.
After the construction of the hake matrix, LQ decomposition is performed on the hake matrix by the following formula:
wherein ,,/>,/>for values resulting from LQ decomposition, the present embodiments do not focus on values.
The dimensions of each part in the matrix are as follows:
s305: singular value decomposition is carried out on the multiplicative operator, and a singular value decomposition result is obtained.
After the multiplicative operator is obtained according to the LQ decomposition result, singular value decomposition is carried out on the multiplicative operator, and a singular value decomposition result is obtained.
Accepting step S304, the multiplicative operator can be prepared by the following formulaSingular value decomposition is performed:
wherein ,for unitary matrix>For column vector, +.>,/>Is->Matrix of dimensions,/->Is->Rank, singular value of (a)。
S306: and respectively carrying out first gradient calculation on each target parameter, and carrying out second gradient calculation according to each first gradient calculation result and the singular value decomposition result to obtain each second gradient calculation result.
In a specific embodiment of the present invention, the first gradient calculation is performed on each target parameter, which may include the following steps:
Respectively aiming at each target parameter through a formulaPerforming a first gradient calculation:
wherein ,in the dynamic feedback subsystem +.>State vector for each sampling instant +.>As a residual error, the residual error is determined,for dynamic feedback subsystem->Time domain output of the individual sampling instants +.>、/>、/>All are parameter matrixes>For dynamic feedback subsystem->Frequency domain output of individual sampling instants, +.>、/>Is a known matrix>For the moment of sampling,for matrix height parameter, +.>For the time window to be optimized, +.>Is->And calculating a first gradient corresponding to the target parameter.
After initializing the parameter vector composed of the target parameters, the target parameters are respectively calculated by the formulaPerforming a first gradient calculation:
wherein ,in the dynamic feedback subsystem +.>State vector for each sampling instant +.>As a residual error, the residual error is determined,for dynamic feedback subsystem->Time domain output of the individual sampling instants +.>、/>、/>All are parameter matrixes>For dynamic feedback subsystem->Frequency domain output of individual sampling instants, +.>、/>Is a known matrix>For the moment of sampling,for matrix height parameter, +.>For the time window to be optimized, +.>Is->And calculating a first gradient corresponding to the target parameter.
In a specific embodiment of the present invention, performing the second gradient calculation according to each of the first gradient calculation result and the singular value decomposition result may include the steps of:
Step one: constructing an intermediate matrix according to each first gradient calculation result:
step two: calculating a lower triangular matrix according to the LQ decomposition result and the intermediate matrix through a formula:
wherein ,、/>all are decomposition results, including->Representing the extraction of the lower triangular matrix elements of the input matrix with the remaining elements set to 0, < >>Represents the diagonal elements of the extraction matrix and the remaining elements are set to 0,>is a lower triangular matrix;
step three: extracting each target submatrix from the lower triangular matrix;
step four: and performing second gradient calculation according to the LQ decomposition result, each target submatrix, multiplicative operator and singular value decomposition result.
For convenience of description, the above four steps may be combined for explanation.
After first gradient calculation is carried out on each target parameter respectively to obtain each first gradient calculation result, an intermediate matrix is constructed according to each first gradient calculation result:
Calculating a lower triangular matrix according to the LQ decomposition result and the intermediate matrix through a formula:
wherein ,、/>all are decomposition results, including->Representing the extraction of the lower triangular matrix elements of the input matrix with the remaining elements set to 0, < >>Represents the diagonal elements of the extraction matrix and the remaining elements are set to 0, >Is a lower triangular matrix with the dimension of。
In one embodiment of the present invention, extracting each target submatrix from the lower triangular matrix may include the steps of:
and extracting each target submatrix according to the dimension of each submatrix in the lower triangular matrix.
After the lower triangular matrix is calculated according to the LQ decomposition result and the intermediate matrix, each target sub-matrix is extracted according to the dimension of each sub-matrix in the lower triangular matrix.
S307: when the preset iteration termination condition is not met according to the second gradient calculation results, calculating each parameter change value according to the second gradient calculation results and the learning rate corresponding to each target parameter, calculating a parameter vector obtained by the current iteration according to each parameter change value, and updating the dynamic feedback subsystem by using the parameter vector obtained by the current iteration.
The second gradient calculation may be performed according to the following formula, to obtain a second gradient calculation result:
and when the preset iteration termination condition is not met according to the second gradient calculation results, calculating the parameter change values according to the second gradient calculation results and the learning rates corresponding to the target parameters.
Updating the dynamic feedback subsystem with the parameter vector obtained by the current iteration, i.e. the parameter vectorAccording to +.>,/>The corresponding position is filled in by the structural form of the dynamic feedback subsystem, thereby completing the updating of the dynamic feedback subsystem.
S308: and stopping updating when the preset iteration termination condition is determined to be met according to each second gradient calculation result.
In one embodiment of the present invention, step S308 may include the steps of:
step one: and calculating whether the average value of F norms of the continuous preset iteration times parameter vector change values is smaller than a preset value, if so, executing the second step, and if not, returning to execute the step S303.
Step two: the update is stopped.
For convenience of description, the above two steps may be combined for explanation.
Calculating whether the average value of F norms of the parameter vector change values of the continuous preset iteration times is smaller than a preset value or not through the following formula:
wherein ,represents->The element is at +.>Calculated after several iterations->,Is a normal value, and is preset.
And stopping updating when the average value of F norms of the parameter vector change values for calculating the continuous preset iteration times is smaller than a preset value.
Corresponding to the above method embodiment, the present invention further provides a real-time optimization device for robustness of the closed-loop system, where the real-time optimization device for robustness of the closed-loop system described below and the real-time optimization method for robustness of the closed-loop system described above can be referred to correspondingly.
Referring to fig. 4, fig. 4 is a block diagram of a real-time optimization apparatus for robustness of a closed-loop system according to an embodiment of the present invention, where the apparatus may include:
an initialization module 41, configured to initialize optimization-related parameters of each dynamic feedback subsystem; wherein, each dynamic feedback subsystem optimizes the relevant parameter and includes each goal parameter to be optimized in real time;
the matrix construction module 42 is configured to collect system operation data of each preset type within a preset duration in a closed-loop system operation process, and construct a hank matrix by using the system operation data of each preset type;
the multiplicative operator calculating module 43 is configured to perform LQ decomposition on the hake matrix, and calculate a multiplicative operator according to the LQ decomposition result;
a singular value decomposition module 44, configured to perform singular value decomposition on the multiplicative operator to obtain a singular value decomposition result;
the gradient calculation module 45 is configured to perform first gradient calculation on each target parameter, and perform second gradient calculation according to each first gradient calculation result and the singular value decomposition result, so as to obtain each second gradient calculation result;
The system updating module 46 is configured to calculate, when it is determined that the preset iteration termination condition is not met according to each second gradient calculation result, each parameter change value according to each second gradient calculation result and a learning rate corresponding to each target parameter, calculate a parameter vector obtained by a current iteration according to each parameter change value, and update the dynamic feedback subsystem by using the parameter vector obtained by the current iteration; the learning rate corresponding to each target parameter is obtained through pre-selection; the parameter vector obtained by the current iteration is composed of various changed target parameters;
an update stopping module 47, configured to stop updating when it is determined that the preset iteration termination condition is satisfied according to each second gradient calculation result.
According to the technical scheme, through a real-time solving method, system operation data are collected when the system is operated, LQ decomposition is conducted on a Hanker matrix constructed by utilizing system operation data of each preset type, a multiplicative operator is calculated according to an LQ decomposition result, singular value decomposition is conducted on the multiplicative operator, a singular value decomposition result is obtained, first gradient calculation is conducted on each target parameter respectively, second gradient calculation is conducted according to each first gradient calculation result and a singular value decomposition result, each parameter change value is calculated according to each second gradient calculation result and a learning rate corresponding to each target parameter respectively, and a parameter vector obtained through current iteration is used for updating the dynamic feedback subsystem. Therefore, the real-time online optimization of the robustness of the system is realized when the closed-loop system is operated, and the system service can be normally operated in the optimization process.
In one embodiment of the present invention, the initialization module 41 includes:
the parameter selection sub-module is used for selecting the order number, the matrix height parameter and the time window to be optimized of the dynamic feedback sub-system;
and the parameter vector initialization sub-module is used for initializing a parameter vector formed by each target parameter and selecting a learning rate for each target parameter.
In one embodiment of the present invention, the matrix construction module 42 is specifically a module for constructing a hank matrix according to the matrix height parameter and the preset duration by using each preset type of system operation data.
In one embodiment of the present invention, the gradient calculation module 45 includes a first gradient calculation sub-module, which is specifically configured to calculate each target parameter separately by a formulaPerforming a first gradient calculation:
wherein ,in the dynamic feedback subsystem +.>State vector for each sampling instant +.>As a residual error, the residual error is determined,for dynamic feedback subsystem->Time domain output of the individual sampling instants +.>、/>、/>All are parameter matrixes>For dynamic feedback subsystem->Frequency domain output of individual sampling instants, +.>、/>Is a known matrix>For the moment of sampling,for matrix height parameter, +. >For the time window to be optimized, +.>Is->And calculating a first gradient corresponding to the target parameter.
In one embodiment of the present invention, the gradient computation module 45 includes a second gradient computation submodule including:
an intermediate matrix constructing unit for constructing an intermediate matrix from each of the first gradient calculation results:
a lower triangular matrix calculation unit for calculating a lower triangular matrix from the LQ decomposition result and the intermediate matrix by a formula:
wherein ,、/>all are decomposition results, including->Representing the extraction of the lower triangular matrix elements of the input matrix with the remaining elements set to 0, < >>Represents the diagonal elements of the extraction matrix and the remaining elements are set to 0,>is a lower triangular matrix;
a sub-matrix extraction unit for extracting each target sub-matrix from the lower triangular matrix;
and the second gradient calculation unit is used for carrying out second gradient calculation according to the LQ decomposition result, each target submatrix, the multiplicative operator and the singular value decomposition result.
In a specific embodiment of the present invention, the submatrix extraction unit is specifically a unit for extracting each target submatrix according to the dimensions of each submatrix in the lower triangular matrix.
In one embodiment of the present invention, the update stop module 47 includes:
The average value calculation sub-module is used for calculating whether the average value of F norms of the continuous preset iteration frequency parameter vector change values is smaller than a preset value or not;
the updating stopping sub-module is used for stopping updating when the average value of F norms of the calculated continuous preset iteration times parameter vector change values is smaller than a preset value;
and the repeated execution sub-module is used for repeatedly executing the step of collecting the system operation data of each preset type in the preset duration in the operation process of the closed-loop system when the average value of F norms of the continuous preset iteration frequency parameter vector change values is larger than or equal to a preset value.
Corresponding to the above method embodiment, referring to fig. 5, fig. 5 is a schematic diagram of a real-time optimization apparatus for robust performance of a closed loop system according to the present invention, where the apparatus may include:
a memory 332 for storing a computer program;
a processor 322 for implementing the steps of the real-time optimization method of the closed-loop system robustness performance of the method embodiment described above when executing a computer program.
Specifically, referring to fig. 5, fig. 5 is a schematic diagram of a specific structure of a real-time optimization apparatus for robust performance of a closed loop system according to the present embodiment, where the real-time optimization apparatus for robust performance of a closed loop system may have relatively large differences due to different configurations or performances, and may include a processor (central processing units, CPU) 322 (e.g., one or more processors) and a memory 332, where the memory 332 stores one or more computer programs 342 or data 344. Wherein the memory 332 may be transient storage or persistent storage. The program stored in memory 332 may include one or more modules (not shown), each of which may include a series of instruction operations in the data processing apparatus. Still further, the processor 322 may be configured to communicate with the memory 332 to execute a series of instruction operations in the memory 332 on the real-time optimization device 301 for closed-loop system robustness.
The real-time optimization device 301 for closed loop system robust performance may also include one or more power supplies 326, one or more wired or wireless network interfaces 350, one or more input/output interfaces 358, and/or one or more operating systems 341.
The steps in the real-time optimization method for the robustness of the closed-loop system described above may be implemented by the structure of the real-time optimization device for the robustness of the closed-loop system.
Corresponding to the above method embodiments, the present invention also provides a computer readable storage medium having a computer program stored thereon, which when executed by a processor, performs the steps of:
initializing optimization related parameters of each dynamic feedback subsystem; wherein, each dynamic feedback subsystem optimizes the relevant parameter and includes each goal parameter to be optimized in real time; collecting system operation data of each preset type in preset time length in the operation process of the closed-loop system, and constructing a Hank matrix by utilizing the system operation data of each preset type; performing LQ decomposition on the Hanker matrix, and calculating a multiplicative operator according to the LQ decomposition result; singular value decomposition is carried out on the multiplicative operator, and a singular value decomposition result is obtained; respectively carrying out first gradient calculation on each target parameter, and carrying out second gradient calculation according to each first gradient calculation result and a singular value decomposition result to obtain each second gradient calculation result; when the preset iteration termination condition is not met according to the second gradient calculation results, calculating each parameter change value according to the second gradient calculation results and the learning rate corresponding to each target parameter respectively, calculating a parameter vector obtained by the current iteration according to each parameter change value, and updating the dynamic feedback subsystem by using the parameter vector obtained by the current iteration; the learning rate corresponding to each target parameter is obtained through pre-selection; the parameter vector obtained by the current iteration is composed of various changed target parameters; and stopping updating when the preset iteration termination condition is determined to be met according to each second gradient calculation result.
The computer readable storage medium may include: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
For the description of the computer-readable storage medium provided by the present invention, refer to the above method embodiments, and the disclosure is not repeated here.
In this specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, so that the same or similar parts between the embodiments are referred to each other. The apparatus, device and computer readable storage medium of the embodiments are described more simply because they correspond to the methods of the embodiments, and the description thereof will be given with reference to the method section.
The principles and embodiments of the present invention have been described herein with reference to specific examples, but the description of the examples above is only for aiding in understanding the technical solution of the present invention and its core ideas. It should be noted that it will be apparent to those skilled in the art that various modifications and adaptations of the invention can be made without departing from the principles of the invention and these modifications and adaptations are intended to be within the scope of the invention as defined in the following claims.
Claims (8)
1. A real-time optimization method for robustness of a closed-loop system, comprising:
initializing optimization related parameters of each dynamic feedback subsystem; wherein, each dynamic feedback subsystem optimizes the relevant parameter and includes each goal parameter to be optimized in real time;
collecting system operation data of each preset type in preset time length in the operation process of a closed-loop system, and constructing a Hank matrix by utilizing the system operation data of each preset type;
performing LQ decomposition on the Hanker matrix, and calculating a multiplicative operator according to an LQ decomposition result;
singular value decomposition is carried out on the multiplicative operator, and a singular value decomposition result is obtained;
wherein ,target parameters to be optimized in real time +.>Number of (A)>In>State vector for each sampling instant +.>As residual error->For the dynamic feedback subsystem +.>Time domain output of the individual sampling instants +.>、/>、/>All are parameter matrixes>For the dynamic feedback subsystem +.>Frequency domain output of individual sampling instants, +.>、Is a known matrix>For sampling time +.>For matrix height parameter, +.>For the time window to be optimized, +. >Is->A first gradient calculation result corresponding to the target parameter;
constructing an intermediate matrix according to each first gradient calculation result:
calculating a lower triangular matrix according to the LQ decomposition result and the intermediate matrix through a formula:
wherein ,、/>all are decomposition results, including->Representing the extraction of the lower triangular matrix elements of the input matrix and the rest of the elements set to 0,represents the diagonal elements of the extraction matrix and the remaining elements are set to 0,>is a lower triangular matrix;
extracting each target submatrix from the lower triangular matrix;
performing second gradient calculation according to the LQ decomposition result, each target submatrix, the multiplicative operator and the singular value decomposition result to obtain each second gradient calculation result;
when the fact that the preset iteration termination condition is not met is determined according to the second gradient calculation results, calculating parameter change values according to learning rates respectively corresponding to the second gradient calculation results and the target parameters, calculating parameter vectors obtained by current iteration according to the parameter change values, and updating the dynamic feedback subsystem by utilizing the parameter vectors obtained by the current iteration; the learning rate corresponding to each target parameter is obtained through pre-selection; the parameter vector obtained by the current iteration is composed of various changed target parameters;
And stopping updating when the preset iteration termination condition is determined to be met according to each second gradient calculation result.
2. The method for optimizing the robustness of a closed loop system according to claim 1, wherein initializing each dynamic feedback subsystem optimization-related parameter comprises:
selecting the order, matrix height parameters and time window to be optimized of the dynamic feedback subsystem;
initializing a parameter vector formed by the target parameters, and selecting a learning rate for each target parameter.
3. The method of claim 2, wherein constructing a hank matrix using each of the predetermined types of system operation data comprises:
and constructing a Hanker matrix by utilizing the system operation data of each preset type according to the matrix height parameter and the preset time length.
4. The method of claim 1, wherein extracting each target submatrix from the lower triangular matrix comprises:
and extracting each target submatrix according to the dimension of each submatrix in the lower triangular matrix.
5. The real-time optimization method of closed loop system robustness according to claim 2, wherein when it is determined that the preset iteration termination condition is satisfied according to each of the second gradient calculation results, stopping updating comprises:
Calculating whether the average value of F norms of the parameter vector change values of the continuous preset iteration times is smaller than a preset value;
if yes, stopping updating;
if not, repeating the step of collecting the system operation data of each preset type in the preset time period in the operation process of the closed-loop system.
6. A real-time optimization device for robustness of a closed-loop system, comprising:
the initialization module is used for initializing optimization related parameters of each dynamic feedback subsystem; wherein, each dynamic feedback subsystem optimizes the relevant parameter and includes each goal parameter to be optimized in real time;
the matrix construction module is used for collecting system operation data of each preset type in a preset time period in the operation process of the closed-loop system and constructing a Hank matrix by utilizing the system operation data of each preset type;
the multiplicative operator calculation module is used for carrying out LQ decomposition on the Hank matrix and calculating a multiplicative operator according to an LQ decomposition result;
the singular value decomposition module is used for carrying out singular value decomposition on the multiplicative operator to obtain a singular value decomposition result;
the gradient calculation module comprises a first gradient calculation sub-module and a second gradient calculation sub-module, wherein the first gradient calculation sub-module is specifically used for respectively calculating each target parameter through a formula Performing a first gradient calculation:
wherein ,target parameters to be optimized in real time +.>Number of (A)>In>State vector for each sampling instant +.>As residual error->For the dynamic feedback subsystem +.>Time domain output of the individual sampling instants +.>、/>、/>All are parameter matrixes>For the dynamic feedback subsystem +.>Frequency domain output of individual sampling instants, +.>、Is a known matrix>For sampling time +.>For matrix height parameter, +.>For the time window to be optimized, +.>Is->A first gradient calculation result corresponding to the target parameter;
the second gradient calculation submodule comprises an intermediate matrix construction unit, a lower triangular matrix calculation unit, a submatrix extraction unit and a second gradient calculation unit, and is used for constructing an intermediate matrix according to each first gradient calculation result:
the lower triangular matrix calculating unit is configured to calculate a lower triangular matrix according to the LQ decomposition result and the intermediate matrix by using a formula:
wherein ,、/>all are decomposition results, including->Representing the extraction of the lower triangular matrix elements of the input matrix and the rest of the elements set to 0,represents the diagonal elements of the extraction matrix and the remaining elements are set to 0, >Is a lower triangular matrix;
the submatrix extraction unit is used for extracting each target submatrix from the lower triangular matrix;
the second gradient calculation unit is used for performing second gradient calculation according to the LQ decomposition result, each target submatrix, the multiplicative operator and the singular value decomposition result to obtain each second gradient calculation result;
the system updating module is used for calculating each parameter change value according to the learning rate corresponding to each second gradient calculation result and each target parameter respectively when the preset iteration termination condition is not met according to each second gradient calculation result, calculating a parameter vector obtained by the current iteration according to each parameter change value, and updating the dynamic feedback subsystem by utilizing the parameter vector obtained by the current iteration; the learning rate corresponding to each target parameter is obtained through pre-selection; the parameter vector obtained by the current iteration is composed of various changed target parameters;
and the updating stopping module is used for stopping updating when the preset iteration termination condition is determined to be met according to each second gradient calculation result.
7. A real-time optimization device for robust performance of a closed loop system, comprising:
A memory for storing a computer program;
a processor for implementing the steps of the real-time optimization method of closed loop system robustness according to any one of claims 1 to 5 when executing said computer program.
8. A computer readable storage medium, characterized in that the computer readable storage medium has stored thereon a computer program which, when executed by a processor, implements the steps of the real-time optimization method of the robustness of a closed loop system according to any of the claims 1 to 5.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202310355043.0A CN116068903B (en) | 2023-04-06 | 2023-04-06 | Real-time optimization method, device and equipment for robustness performance of closed-loop system |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202310355043.0A CN116068903B (en) | 2023-04-06 | 2023-04-06 | Real-time optimization method, device and equipment for robustness performance of closed-loop system |
Publications (2)
Publication Number | Publication Date |
---|---|
CN116068903A CN116068903A (en) | 2023-05-05 |
CN116068903B true CN116068903B (en) | 2023-06-20 |
Family
ID=86182261
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN202310355043.0A Active CN116068903B (en) | 2023-04-06 | 2023-04-06 | Real-time optimization method, device and equipment for robustness performance of closed-loop system |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN116068903B (en) |
Family Cites Families (13)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN108762072B (en) * | 2018-05-21 | 2021-07-27 | 南京邮电大学 | Prediction control method based on nuclear norm subspace method and augmentation vector method |
CN108875276B (en) * | 2018-07-19 | 2019-09-13 | 哈尔滨工业大学 | A kind of closed-loop system stability monitoring method of data-driven |
CN108646573B (en) * | 2018-07-19 | 2019-09-13 | 哈尔滨工业大学 | A kind of closed-loop system stability margin of data-driven determines method |
CN109697691B (en) * | 2018-12-27 | 2022-11-25 | 重庆大学 | Dual-regularization-term-optimized finite-angle projection reconstruction method based on L0 norm and singular value threshold decomposition |
CN110070028B (en) * | 2019-04-17 | 2023-03-07 | 深圳大学 | Method, system and storage medium for representing and identifying non-negative features of face image based on conjugate gradient method |
CN111310794B (en) * | 2020-01-19 | 2021-04-20 | 北京字节跳动网络技术有限公司 | Target object classification method and device and electronic equipment |
CN112254798B (en) * | 2020-10-12 | 2022-07-12 | 中国人民解放军国防科技大学 | Method, system and medium for forecasting ocean vector sound field |
CN112488183B (en) * | 2020-11-27 | 2024-05-10 | 平安科技(深圳)有限公司 | Model optimization method, device, computer equipment and storage medium |
CN113516754B (en) * | 2021-03-16 | 2024-05-03 | 哈尔滨工业大学(深圳) | Three-dimensional visual imaging method based on magnetic abnormal modulus data |
CN113987742A (en) * | 2021-09-14 | 2022-01-28 | 东华大学 | Modeling method for optimizing gradient descent process based on SVD algorithm |
CN113945967A (en) * | 2021-10-14 | 2022-01-18 | 中国矿业大学(北京) | Diffraction wave separation method and device |
CN114545767A (en) * | 2022-02-28 | 2022-05-27 | 中国人民解放军国防科技大学 | Suspension control performance real-time optimization method and device based on PID controller |
CN115657140A (en) * | 2022-10-21 | 2023-01-31 | 中国地质大学(武汉) | Magnetic anomaly detection method and system based on structured Hankel total variation regularization |
-
2023
- 2023-04-06 CN CN202310355043.0A patent/CN116068903B/en active Active
Non-Patent Citations (2)
Title |
---|
数据驱动过程监测系统设计及其在线优化方法研究;宋雪;《中国优秀硕士学位论文全文数据库信息科技辑》;2020年(第1期);I140-933 * |
高速磁浮列车悬浮系统性能优化问题研究;翟明达;《中国博士学位论文全文数据库工程科技Ⅱ辑》;2022年(第1期);C033-24 * |
Also Published As
Publication number | Publication date |
---|---|
CN116068903A (en) | 2023-05-05 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
Salhi et al. | A recursive parametric estimation algorithm of multivariable nonlinear systems described by Hammerstein mathematical models | |
SE543674C2 (en) | Evaluation and/or adaptation of industrial and/or technical process models | |
Hajare et al. | Decentralized PID controller for TITO systems using characteristic ratio assignment with an experimental application | |
CN111913803A (en) | Service load fine granularity prediction method based on AKX hybrid model | |
CN107102634A (en) | A kind of parameter Estimation and tracking and controlling method based on table servo system | |
Bigdeli | The design of a non-minimal state space fractional-order predictive functional controller for fractional systems of arbitrary order | |
Betti et al. | Realization issues, tuning, and testing of a distributed predictive control algorithm | |
He | Energy-to-peak filtering for T–S fuzzy systems with Markovian jumping: The finite-time case | |
Liu et al. | New results on H∞ filtering for Markov jump systems with uncertain transition rates | |
CN116068903B (en) | Real-time optimization method, device and equipment for robustness performance of closed-loop system | |
Gu et al. | Parameter estimation for a multivariable state space system with d-step state-delay | |
CN112564557B (en) | Control method, device and equipment of permanent magnet synchronous motor and storage medium | |
CN113537614A (en) | Construction method, system, equipment and medium of power grid engineering cost prediction model | |
CN104794101A (en) | Fractional order nonlinear system state estimating method | |
Tanemura et al. | Closed-loop data-driven estimation on passivity property | |
CN112287605A (en) | Flow check method based on graph convolution network acceleration | |
CN107505834A (en) | A kind of design method of fractional order pi controller | |
Tacx et al. | Accurate $\mathcal {H} _ {\infty} $-Norm Estimation via Finite-Frequency Norms of Local Parametric Models | |
CN107276561A (en) | Based on the Hammerstein system identifying methods for quantifying core least mean-square error | |
Zhang et al. | Distributed static output feedback robust model predictive control for process networks | |
Hu et al. | Further results on H∞ filtering for a class of discrete-time singular systems with interval time-varying delay | |
CN114077195A (en) | Subspace model identification prediction control method based on data driving | |
CN114355781A (en) | Method for solving time-varying complex value linear matrix equation based on zero-valued neurodynamic model | |
Sun et al. | Improving industrial MPC performance with data-driven disturbance modeling | |
CN116757095B (en) | Electric power system operation method, device and medium based on cloud edge end cooperation |
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 |