CN116068903A - 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 PDF

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CN116068903A
CN116068903A CN202310355043.0A CN202310355043A CN116068903A CN 116068903 A CN116068903 A CN 116068903A CN 202310355043 A CN202310355043 A CN 202310355043A CN 116068903 A CN116068903 A CN 116068903A
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CN116068903B (en
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许雲淞
龙志强
窦峰山
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National University of Defense Technology
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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

Real-time optimization method, device and equipment for robustness performance of closed-loop system
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:
respectively for each target parameter through a formula
Figure SMS_1
Performing a first gradient calculation:
Figure SMS_2
；
Figure SMS_3
；
Figure SMS_4
；
Figure SMS_5
；
wherein ,
Figure SMS_17
in>
Figure SMS_7
State vector for each sampling instant +.>
Figure SMS_13
As a residual error, the residual error is determined,
Figure SMS_16
for the dynamic feedback subsystem +.>
Figure SMS_20
Time domain output of the individual sampling instants +.>
Figure SMS_21
、/>
Figure SMS_22
、/>
Figure SMS_15
All are the parameter matrix, and the parameter matrix is the parameter matrix,
Figure SMS_19
for the dynamic feedback subsystem +.>
Figure SMS_6
Frequency domain output of individual sampling instants, +.>
Figure SMS_11
、/>
Figure SMS_9
Is a known matrix>
Figure SMS_10
For sampling time +.>
Figure SMS_14
For matrix height parameter, +.>
Figure SMS_18
For the time window to be optimized, +.>
Figure SMS_8
Is->
Figure SMS_12
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:
Figure SMS_23
；/>
wherein ,
Figure SMS_24
，
Figure SMS_25
；/>
Figure SMS_26
constructing an obtained intermediate matrix;
calculating a lower triangular matrix according to the LQ decomposition result and the intermediate matrix through a formula:
Figure SMS_27
；
wherein ,
Figure SMS_28
、/>
Figure SMS_29
all are decomposition results, including->
Figure SMS_30
Representing the extraction of the lower triangular matrix elements of the input matrix with the remaining elements set to 0, < >>
Figure SMS_31
Diagonal elements of the extraction matrix are shown and the remaining elements are set to 0,>
Figure SMS_32
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.
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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:
Figure SMS_33
；
Figure SMS_34
；
wherein ,
Figure SMS_36
、/>
Figure SMS_38
、/>
Figure SMS_41
is determined by the structure and parameters of the controlled object, is known, such as magnetic levitation trains, servos, etc.)>
Figure SMS_37
Is a state vector +.>
Figure SMS_39
、/>
Figure SMS_42
Zero mean white noise>
Figure SMS_44
For control input +.>
Figure SMS_35
For measuring signal, < >>
Figure SMS_40
Refers to the sampling instant (i.e.)>
Figure SMS_43
The moment at which the sampling period starts).
The state observer is mathematically described as:
Figure SMS_45
;
Figure SMS_46
;/>
Figure SMS_47
;
wherein ,
Figure SMS_48
is a state vector +>
Figure SMS_49
Estimate of->
Figure SMS_50
As residual error->
Figure SMS_51
For observer gain, which is designed offline, +.>
Figure SMS_52
Is selected such that->
Figure SMS_53
Is located within the unit circle.
In FIG. 2
Figure SMS_54
Is a known reference signal->
Figure SMS_55
Is the output of the state feedback controllerThe mathematical description of the state feedback controller is:
Figure SMS_56
;
Figure SMS_57
gain for state feedback controller, which is designed offline, < ->
Figure SMS_58
Is selected such that->
Figure SMS_59
Is located within the unit circle. />
Figure SMS_60
For dynamic feedback subsystem->
Figure SMS_61
Output of->
Figure SMS_62
Has the following form:
Figure SMS_63
;
Figure SMS_64
;
wherein ,
Figure SMS_65
、/>
Figure SMS_66
、/>
Figure SMS_67
as the parameter matrix, the following form can be selected:
Figure SMS_68
;
Figure SMS_69
;
Figure SMS_70
;/>
Figure SMS_71
;
subscript of
Figure SMS_83
Refer to->
Figure SMS_75
Is determined by the controlled object, +.>
Figure SMS_79
Refer to->
Figure SMS_81
Is determined by the controlled object, +.>
Figure SMS_85
For the state vector of the dynamic feedback subsystem, the parameter matrix +.>
Figure SMS_86
Relates to->
Figure SMS_87
，…，/>
Figure SMS_80
;/>
Figure SMS_84
，…，/>
Figure SMS_72
，…，
Figure SMS_77
…，/>
Figure SMS_74
Co-ordination of->
Figure SMS_76
Number, off-line design, parameters selected to be satisfied by ∈>
Figure SMS_78
All the characteristic values of (2) are located in the unit circle. Parameter matrix->
Figure SMS_82
、/>
Figure SMS_73
For the parameter matrix needing real-time optimization, the included parameters to be optimized in real time are combined into the following parameter vectors:
Figure SMS_88
;
the above parameter vector is column vector, and is marked with superscript
Figure SMS_89
Representing the matrix transpose, the two parameter vectors comprising +.>
Figure SMS_90
The parameters to be designed on line are +.>
Figure SMS_91
Refer to->
Figure SMS_92
The%>
Figure SMS_93
The elements.
The robust performance index of the closed loop system is as follows:
Figure SMS_94
;
wherein ,
Figure SMS_95
;
Figure SMS_96
;
Figure SMS_97
;
Figure SMS_98
;
Figure SMS_99
、/>
Figure SMS_100
、/>
Figure SMS_101
、/>
Figure SMS_102
are all known to be->
Figure SMS_103
It requires real-time optimization determination for a dynamic feedback subsystem. Robust performance real-time optimization refers to dynamic feedback subsystem +.>
Figure SMS_104
So that->
Figure SMS_105
And decreasing until the optimization termination condition specified by the designer is met.
Due to dynamic feedback subsystem
Figure SMS_106
Middle->
Figure SMS_107
、/>
Figure SMS_108
To require a real-time optimized parameter matrix, therefore, real-time optimization only requires optimizing the parameter vector +.>
Figure SMS_109
。
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 subsystem
Figure SMS_110
Order of->
Figure SMS_111
Matrix height parameter->
Figure SMS_112
Time window to be optimized->
Figure SMS_113
，
Figure SMS_114
Is a positive integer>
Figure SMS_115
。
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 parameters
Figure SMS_116
And for each target parameter +.>
Figure SMS_117
Selecting learning rate->
Figure SMS_118
。
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
Figure SMS_119
，/>
Figure SMS_120
，
Figure SMS_121
The three are as follows:
Figure SMS_122
；
Figure SMS_123
；
Figure SMS_124
；
the time period should be at least
Figure SMS_125
Of sampling period, e.g.>
Figure SMS_126
，/>
Figure SMS_127
and />
Figure SMS_128
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:
Figure SMS_129
；
Figure SMS_130
；/>
Figure SMS_131
；
Figure SMS_132
；
Figure SMS_133
。
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:
Figure SMS_134
；
wherein ,
Figure SMS_135
，/>
Figure SMS_136
，/>
Figure SMS_137
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:
Figure SMS_138
dimension;
Figure SMS_139
dimension;
Figure SMS_140
dimension;
Figure SMS_141
dimension;
Figure SMS_142
dimension; />
Figure SMS_143
Dimension;
Figure SMS_144
dimension;
Figure SMS_145
dimension;
Figure SMS_146
dimension;
Figure SMS_147
dimension;
Figure SMS_148
dimension.
Definition:
Figure SMS_149
；
computing a multiplicative operator according to the LQ decomposition result:
Figure SMS_150
。
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 formula
Figure SMS_151
Singular value decomposition is performed:
Figure SMS_152
；
wherein ,
Figure SMS_154
for unitary matrix>
Figure SMS_156
For column vector, +.>
Figure SMS_158
，/>
Figure SMS_153
Is->
Figure SMS_157
Matrix of dimensions,/->
Figure SMS_159
Is->
Figure SMS_160
Rank, singular value->
Figure SMS_155
。
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 formula
Figure SMS_161
Performing a first gradient calculation:
Figure SMS_162
；
Figure SMS_163
；
Figure SMS_164
；/>
Figure SMS_165
；
wherein ,
Figure SMS_175
in the dynamic feedback subsystem +.>
Figure SMS_168
State vector for each sampling instant +.>
Figure SMS_171
As a residual error, the residual error is determined,
Figure SMS_176
for dynamic feedback subsystem->
Figure SMS_180
At each sampling timeTime domain output of>
Figure SMS_179
、/>
Figure SMS_182
、/>
Figure SMS_174
All are parameter matrixes>
Figure SMS_178
For dynamic feedback subsystem->
Figure SMS_166
Frequency domain output of individual sampling instants, +.>
Figure SMS_170
、/>
Figure SMS_169
Is a known matrix>
Figure SMS_173
For the moment of sampling,
Figure SMS_177
for matrix height parameter, +.>
Figure SMS_181
For the time window to be optimized, +.>
Figure SMS_167
Is->
Figure SMS_172
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 formula
Figure SMS_183
Performing a first gradient calculation:
Figure SMS_184
；
Figure SMS_185
；
Figure SMS_186
；
Figure SMS_187
；
wherein ,
Figure SMS_197
in the dynamic feedback subsystem +.>
Figure SMS_189
State vector for each sampling instant +.>
Figure SMS_195
As a residual error, the residual error is determined,
Figure SMS_191
for dynamic feedback subsystem->
Figure SMS_194
Time domain output of the individual sampling instants +.>
Figure SMS_198
、/>
Figure SMS_202
、/>
Figure SMS_196
All are parameter matrixes>
Figure SMS_200
For dynamic feedback subsystem->
Figure SMS_188
Frequency domain output of individual sampling instants, +.>
Figure SMS_192
、/>
Figure SMS_199
Is a known matrix>
Figure SMS_203
For the moment of sampling,
Figure SMS_201
for matrix height parameter, +.>
Figure SMS_204
For the time window to be optimized, +.>
Figure SMS_190
Is->
Figure SMS_193
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:
Figure SMS_205
；
wherein ,
Figure SMS_206
，
Figure SMS_207
，/>
Figure SMS_208
constructing an obtained intermediate matrix;
step two: calculating a lower triangular matrix according to the LQ decomposition result and the intermediate matrix through a formula:
Figure SMS_209
；
wherein ,
Figure SMS_210
、/>
Figure SMS_211
all are decomposition results, including->
Figure SMS_212
Representing the extraction of the lower triangular matrix elements of the input matrix with the remaining elements set to 0, < >>
Figure SMS_213
Represents the diagonal elements of the extraction matrix and the remaining elements are set to 0,>
Figure SMS_214
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:
Figure SMS_215
；
wherein
Figure SMS_216
，
Figure SMS_217
，/>
Figure SMS_218
To construct the resulting intermediate matrix.
Calculating a lower triangular matrix according to the LQ decomposition result and the intermediate matrix through a formula:
Figure SMS_219
；
wherein ,
Figure SMS_220
、/>
Figure SMS_221
all are decomposition results, including->
Figure SMS_222
Representing the extraction of the lower triangular matrix elements of the input matrix with the remaining elements set to 0, < >>
Figure SMS_223
Represents the diagonal elements of the extraction matrix and the remaining elements are set to 0,>
Figure SMS_224
is a lower triangular matrix with the dimension of
Figure SMS_225
。
For example, for a matrix
Figure SMS_226
，/>
Figure SMS_227
。
Figure SMS_228
The parts are expressed as: />
Figure SMS_229
；
Figure SMS_230
Dimension;
Figure SMS_231
dimension;
Figure SMS_232
dimension;
Figure SMS_233
dimension;
Figure SMS_234
dimension;
Figure SMS_235
dimension.
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.
Figure SMS_236
Extracting submatrix->
Figure SMS_237
and />
Figure SMS_238
。
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:
Figure SMS_239
。
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.
Figure SMS_240
；
wherein ,
Figure SMS_241
representing the number of iterative computations.
Updating the dynamic feedback subsystem with the parameter vector obtained by the current iteration, i.e. the parameter vector
Figure SMS_242
According to +.>
Figure SMS_243
，/>
Figure SMS_244
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:
Figure SMS_245
；
wherein ,
Figure SMS_246
represents->
Figure SMS_247
The element is at +.>
Figure SMS_248
Calculated after several iterations->
Figure SMS_249
，
Figure SMS_250
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 formula
Figure SMS_251
Performing a first gradient calculation:
Figure SMS_252
；
Figure SMS_253
；
Figure SMS_254
；
Figure SMS_255
；
wherein ,
Figure SMS_264
in the dynamic feedback subsystem +.>
Figure SMS_258
State vector for each sampling instant +.>
Figure SMS_260
As a residual error, the residual error is determined,
Figure SMS_259
for dynamic feedback subsystem->
Figure SMS_261
Time domain output of the individual sampling instants +.>
Figure SMS_265
、/>
Figure SMS_269
、/>
Figure SMS_267
All are parameter matrixes>
Figure SMS_271
For dynamic feedback subsystem->
Figure SMS_256
Frequency domain output of individual sampling instants, +.>
Figure SMS_263
、/>
Figure SMS_266
Is a known matrix>
Figure SMS_270
For the moment of sampling,
Figure SMS_268
for matrix height parameter, +.>
Figure SMS_272
For the time window to be optimized, +.>
Figure SMS_257
Is->
Figure SMS_262
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:
Figure SMS_273
；
wherein
Figure SMS_274
，
Figure SMS_275
，/>
Figure SMS_276
Constructing an obtained intermediate matrix;
a lower triangular matrix calculation unit for calculating a lower triangular matrix from the LQ decomposition result and the intermediate matrix by a formula:
Figure SMS_277
；
wherein ,
Figure SMS_278
、/>
Figure SMS_279
all are decomposition results, including->
Figure SMS_280
Representing the extraction of the lower triangular matrix elements of the input matrix with the remaining elements set to 0, < >>
Figure SMS_281
Represents the diagonal elements of the extraction matrix and the remaining elements are set to 0,>
Figure SMS_282
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 (10)

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;
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.
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 performing a first gradient calculation on each of the target parameters comprises:
respectively for each target parameter through a formula
Figure QLYQS_1
Performing a first gradient calculation:
Figure QLYQS_2
；
Figure QLYQS_3
；
Figure QLYQS_4
；
Figure QLYQS_5
；
wherein ,
Figure QLYQS_16
in>
Figure QLYQS_8
State vector for each sampling instant +.>
Figure QLYQS_12
As residual error->
Figure QLYQS_14
For the dynamic feedback subsystem +.>
Figure QLYQS_18
Time domain output of the individual sampling instants +.>
Figure QLYQS_20
、/>
Figure QLYQS_22
、/>
Figure QLYQS_15
All are the parameter matrix, and the parameter matrix is the parameter matrix,
Figure QLYQS_19
for the dynamic feedback subsystem +.>
Figure QLYQS_6
Frequency domain output of individual sampling instants, +.>
Figure QLYQS_11
、/>
Figure QLYQS_9
Is a known matrix>
Figure QLYQS_13
For sampling time +.>
Figure QLYQS_17
For matrix height parameter, +.>
Figure QLYQS_21
For the time window to be optimized, +.>
Figure QLYQS_7
Is->
Figure QLYQS_10
And calculating a first gradient corresponding to the target parameter.
5. The method of claim 4, wherein performing a second gradient calculation based on each of the first gradient calculation results and the singular value decomposition results, comprises:
constructing an intermediate matrix according to each first gradient calculation result:
Figure QLYQS_23
；
wherein ,
Figure QLYQS_24
，
Figure QLYQS_25
，/>
Figure QLYQS_26
constructing an obtained intermediate matrix;
calculating a lower triangular matrix according to the LQ decomposition result and the intermediate matrix through a formula:
Figure QLYQS_27
；/>
wherein ,
Figure QLYQS_28
、/>
Figure QLYQS_29
all are decomposition results, including->
Figure QLYQS_30
Representing the extraction of the lower triangular matrix elements of the input matrix with the remaining elements set to 0, < >>
Figure QLYQS_31
Represents the diagonal elements of the extraction matrix and the remaining elements are set to 0,>
Figure QLYQS_32
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.
6. The method of claim 5, 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.
7. 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.
8. 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 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.
9. 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 7 when executing said computer program.
10. 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 7.
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