CN114462241A - Fully-symmetrical multi-cell centralized member state estimation method for multi-rate system - Google Patents

Fully-symmetrical multi-cell centralized member state estimation method for multi-rate system Download PDF

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CN114462241A
CN114462241A CN202210111985.XA CN202210111985A CN114462241A CN 114462241 A CN114462241 A CN 114462241A CN 202210111985 A CN202210111985 A CN 202210111985A CN 114462241 A CN114462241 A CN 114462241A
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李琦
郅玉福
谭海龙
盛伟国
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Hangzhou Normal University
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Abstract

The invention discloses a method for estimating a fully-symmetrical multi-cell centralized member state of a multi-rate system. The method comprises the following steps: establishing a discrete time-varying linear multi-rate system model; converting the discrete time-varying linear multi-rate system model into a corresponding discrete time-varying linear single-rate system model by applying a lifting technology; aiming at the converted discrete time-varying linear single-rate system, a dynamic event triggering mechanism is introduced to save limited communication resources; designing a fully-symmetrical multi-cell shape set member state estimator based on a dynamic event trigger mechanism to obtain a parameterized fully-symmetrical multi-cell shape estimation set containing a system real state; and optimizing parameters to obtain a fully-symmetrical multi-cell estimation set with the minimum F norm meaning. The method can simultaneously process the problem of sparse data transmission caused by a multi-rate mechanism and a dynamic event triggering mechanism, can solve the problem of state estimation of a multi-rate system, and saves limited network communication resources.

Description

Fully-symmetrical multi-cell centralized member state estimation method for multi-rate system
Technical Field
The invention belongs to the technical field of information, particularly relates to the field of state estimation, and particularly relates to a fully-symmetrical multi-cell collector state estimation method of a multi-rate system based on a dynamic event trigger mechanism.
Background
In the field of state estimation, commonly used state estimation methods include a Kalman state estimation method, H∞The method comprises a state estimation method, an ellipsoid-based member state estimation method, a fully-symmetrical multi-cell-shaped member state estimation method and the like. The Kalman state estimation method needs to be advancedAccurate statistical characteristics of system disturbance and measurement noise are obtained, however, the accurate statistical characteristics are difficult to achieve in engineering practice, and therefore, in many practical applications, the Kalman state estimation method has certain limitations. H∞The state estimation method is suitable for the situation that the system disturbance and the measurement noise energy are bounded, and can provide an estimation error limit of the system under the worst condition. While the H-infinity state estimation method does not need to be based on statistical properties of system perturbation and measurement noise, H is when the system perturbation and measurement noise are unknown but bounded∞The state method appears somewhat deficient. In addition, Kalman State estimation method and H∞The state estimation methods can only perform point estimation on the state, but cannot estimate the range to which the state belongs. The ellipsoid-based ensemble state estimation method may be applicable to situations where system perturbation and measurement noise are unknown but bounded and again without the need to acquire statistical properties of the system perturbation and measurement noise. However, the ellipsoid-based membership state estimation method cannot well realize the balance between the calculation accuracy and the calculation complexity. In many practical applications, it is difficult to sample system devices and sensors at a consistent rate, and therefore, multi-rate mechanisms should be considered adequate in the state estimation problem. Under the dynamic event trigger mechanism, the measurement output is transmitted to the estimator when meeting a certain trigger condition, thereby avoiding unnecessary data transmission and saving limited communication resources. However, under the dynamic event triggering mechanism, there is no fully-symmetric multi-manifold state estimation method for the multi-rate system.
Disclosure of Invention
The invention aims to provide a fully-symmetrical multi-cell centralized member state estimation method of a multi-rate system based on a dynamic event trigger mechanism.
The method comprises the following steps:
establishing a discrete time-varying linear multi-rate system model;
converting a discrete time-varying linear multi-rate system model into a corresponding discrete time-varying linear single-rate system model by applying a lifting technology;
step (3) aiming at the converted discrete time-varying linear single-rate system, a dynamic event triggering mechanism is introduced to save limited communication resources;
designing a fully-symmetrical multi-cell shape set member state estimator based on a dynamic event trigger mechanism to obtain a parameterized fully-symmetrical multi-cell shape estimation set containing the real state of the system;
and (5) optimizing parameters to obtain a fully-symmetrical multi-cell estimation set with the minimum F norm meaning.
Further, the discrete time-varying linear multi-rate system model established in the step (1) is as follows:
Figure BDA0003494155720000021
wherein s is a time sequence number, tsAnd ksSampling time at two rates;
Figure BDA0003494155720000022
is tsThe state of the system at the time of day,
Figure BDA0003494155720000023
represents nxThe Euclidean space of the dimension is maintained,
Figure BDA0003494155720000024
is tsThe system disturbance at the moment of time,
Figure BDA0003494155720000025
represents nwA Euclidean space of dimensions;
Figure BDA0003494155720000026
is ksThe measured output of the time of day is,
Figure BDA0003494155720000027
represents nyThe Euclidean space of the dimension is maintained,
Figure BDA0003494155720000028
is ksThe noise of the measurement at the time of day,
Figure BDA0003494155720000029
represents nvA Euclidean space of dimensions;
Figure BDA00034941557200000210
and
Figure BDA00034941557200000211
is a known real time-varying matrix.
Sampling period T ═ T of systems+1-tsAnd t is00; the sampling period K' K of the measurements+1-ksAnd k is00; ratio of cycles
Figure BDA00034941557200000212
Is a positive integer greater than or equal to 2.
Setting alpha system initial states
Figure BDA00034941557200000213
System disturbance
Figure BDA00034941557200000214
And measuring noise
Figure BDA00034941557200000215
Included in the following holosymmetric polytypes:
Figure BDA00034941557200000216
wherein the content of the first and second substances,
Figure BDA00034941557200000217
and
Figure BDA00034941557200000218
are known as a vector and a matrix and,
Figure BDA00034941557200000219
and
Figure BDA00034941557200000220
respectively of order nwAnd nvThe identity matrix of (2).
The step (2) is specifically as follows:
iteratively applying a discrete time-varying linear multi-rate system model to obtain
Figure BDA00034941557200000221
Wherein the intermediate parameter
Figure BDA0003494155720000031
System disturbance of converted single rate system
Figure BDA0003494155720000032
Is composed of
Figure BDA0003494155720000033
The transposing of (1).
Intermediate parameter
Figure BDA0003494155720000034
Intermediate parameter
Figure BDA0003494155720000035
Figure BDA0003494155720000036
Time-varying real matrix for converted single rate systems
Figure BDA0003494155720000037
And
Figure BDA0003494155720000038
comprises the following steps:
Figure BDA0003494155720000039
intermediate parameter
Figure BDA00034941557200000310
g∈{1,2,…,α}；
Figure BDA00034941557200000311
System state of single rate system after conversion
Figure BDA00034941557200000312
Is composed of
Figure BDA00034941557200000313
The transposing of (1).
Obtaining a discrete time-varying linear single-rate system model after the following conversion:
Figure BDA00034941557200000314
initial state of transformed discrete time-varying linear single-rate system model
Figure BDA00034941557200000315
And system disturbances
Figure BDA00034941557200000316
The following conditions are satisfied:
Figure BDA00034941557200000317
initial state of discrete time-varying linear single-rate system model after conversion
Figure BDA00034941557200000318
Belongs to the holosymmetric polycythemia
Figure BDA00034941557200000319
Wherein the center of the holosymmetric polycycle
Figure BDA00034941557200000320
Fully symmetric multi-cell generator matrix
Figure BDA00034941557200000321
Step (3) introduces the following dynamic event triggering mechanism for the converted discrete time-varying linear single-rate system:
the sequence of trigger times is 0 ═ iota0＜ι1＜…＜ιm＜…，ιmM is a trigger time, m is a trigger time sequence number, m is 0,1, …, and the following conditions are satisfied:
Figure BDA00034941557200000322
wherein k issMeasured output of time of day
Figure BDA00034941557200000323
With the last transmitted measurement output
Figure BDA00034941557200000324
Difference of (2)
Figure BDA00034941557200000325
To represent
Figure BDA00034941557200000326
Euclidean norm of; auxiliary dynamic variables
Figure BDA00034941557200000327
Satisfies the following conditions:
Figure BDA00034941557200000328
σ, λ and θ are given positive scalars, given initial values of the auxiliary dynamic variables
Figure BDA00034941557200000329
If λ θ is not less than 1, then for any ksIs greater than or equal to 0, has
Figure BDA00034941557200000330
After introducing the dynamic event trigger mechanism, the input actually received by the collector estimator
Figure BDA0003494155720000041
Is shown as：
Figure BDA0003494155720000042
ks∈[ιm,ιm+1)。
The step (4) is specifically as follows:
parameterized fully-symmetric multi-cell estimation set containing system real state obtained by order reduction technology
Figure BDA0003494155720000043
Has the following structure:
Figure BDA0003494155720000044
wherein the content of the first and second substances,
Figure BDA0003494155720000045
a technique for reducing the order of a full-symmetric multi-cell shape before reduction is disclosed
Figure BDA0003494155720000046
Of order of (i) i.e
Figure BDA0003494155720000047
Generating matrix of
Figure BDA0003494155720000048
Is not greater than the set value r.
Holohedral symmetry polytope before order reduction
Figure BDA0003494155720000049
Selecting the center of a holosymmetric polytope
Figure BDA00034941557200000410
As a fully-symmetrical multi-cell collector state estimator based on a dynamic event trigger mechanism, thereby realizing the pair
Figure BDA00034941557200000411
Point estimation of (1), intermediate parameters
Figure BDA00034941557200000412
Fully-symmetric multi-cell generating matrix before order reduction
Figure BDA00034941557200000413
Intermediate parameter
Figure BDA00034941557200000414
Reduced-order fully-symmetric multi-cell generator matrix
Figure BDA00034941557200000415
Is a parameter matrix of the fully symmetric polytope estimation set, namely the parameters to be optimized.
Dynamic event trigger mechanism related parameters
Figure BDA00034941557200000416
Comprises the following steps:
Figure BDA00034941557200000417
wherein the content of the first and second substances,
Figure BDA00034941557200000418
and
Figure BDA00034941557200000419
is a given positive scalar quantity. Order to
Figure BDA00034941557200000420
And is
Figure BDA00034941557200000421
Then
Figure BDA00034941557200000422
Is composed of
Figure BDA00034941557200000423
To the upper bound, i.e.
Figure BDA00034941557200000424
To pair
Figure BDA00034941557200000425
Performing range estimation to obtain
Figure BDA00034941557200000426
Upper bound of (2)
Figure BDA00034941557200000427
And lower bound
Figure BDA00034941557200000428
The following were used:
Figure BDA00034941557200000429
wherein the content of the first and second substances,
Figure BDA00034941557200000430
row and matrix of
Figure BDA00034941557200000431
Intermediate parameter
Figure BDA00034941557200000432
Is that
Figure BDA00034941557200000433
The element of the ith row of (1) and the qth column,
Figure BDA00034941557200000434
is a matrix
Figure BDA00034941557200000435
The number of columns.
The step (5) is specifically as follows:
optimized parameters
Figure BDA0003494155720000051
Intermediate parameter
Figure BDA0003494155720000052
Intermediate parameter
Figure BDA0003494155720000053
When the fully symmetric multi-cell estimation set
Figure BDA0003494155720000054
Parameter (d) of
Figure BDA0003494155720000055
Has the advantages of
Figure BDA0003494155720000056
Formally, a fully symmetric polytope estimate set
Figure BDA0003494155720000057
Is the full-symmetric multi-cell estimation set containing the system true state
Figure BDA0003494155720000058
Is the smallest.
The invention designs a fully-symmetrical multi-cell centralized member state estimation method of a multi-rate system based on a dynamic event trigger mechanism, which can simultaneously process the problem of sparse data transmission caused by the multi-rate mechanism and the dynamic event trigger mechanism, thereby solving the problem of state estimation of the multi-rate system and saving limited network communication resources. The method provided by the invention assumes that the system disturbance and the measurement noise are unknown and bounded, and the statistical characteristics of the system disturbance and the measurement noise which are difficult to obtain do not need to be determined, so that the method has more universality compared with the traditional estimation method based on the statistical characteristics of the system disturbance and the measurement noise; the center of the minimum fully-symmetrical multi-cell estimation set containing the real state of the system is used as the point estimation of the state, and the method is simple and easy to implement; and the value intervals of each state in the multi-rate system can be obtained, so that the range estimation of the states is facilitated.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a diagram of system state variables in an embodiment
Figure BDA0003494155720000059
System state variable
Figure BDA00034941557200000510
Is estimated by
Figure BDA00034941557200000511
System state variable
Figure BDA00034941557200000512
Results of upper and lower bounds of (1);
FIG. 3 is a diagram of system state variables in an embodiment
Figure BDA00034941557200000513
System state variable
Figure BDA00034941557200000514
Is estimated by
Figure BDA00034941557200000515
System state variable
Figure BDA00034941557200000516
Results of upper and lower bounds of (1);
FIG. 4 is a diagram of state variables of the system in the embodiment
Figure BDA00034941557200000517
Estimation error of estimation
Figure BDA00034941557200000518
For system state variable
Figure BDA00034941557200000519
Estimation error of estimation
Figure BDA00034941557200000520
Schematic diagram of the results of (1);
FIG. 5 is a diagram illustrating transmission timings of system measurement outputs under a dynamic event trigger mechanism according to an embodiment;
fig. 6 is a schematic diagram showing a comparison of the estimated mean square error when the sampling period of the sensor measurement in the embodiment is 2 and 4, respectively.
Detailed Description
The following detailed description of the embodiments of the invention is provided in connection with the accompanying drawings.
For the convenience of the following description, the following definitions and quotations are given:
definition of the holosymmetric polytope: an m-order holohedral symmetry polycycle
Figure BDA0003494155720000061
Is to hypercube Hm＝[-1,+1]mThe following affine transformations are performed:
Figure BDA0003494155720000062
wherein p ∈ RnCalled the center of the holosymmetric polytope X, n being the dimension; j is an element of Rn×mA generator matrix called a fully symmetric polytope X. For convenience of presentation, let X ═<p,J>。
Leading: given a fully symmetric polytope
Figure BDA0003494155720000063
And an integer order-reducing parameter r (n < r < m), if there is an order-reducing operator of the form:
Figure BDA0003494155720000064
wherein the content of the first and second substances,
Figure BDA0003494155720000065
and is
Figure BDA0003494155720000066
Figure BDA0003494155720000067
Is that
Figure BDA0003494155720000068
The ith row and the qth column of (1), then
Figure BDA0003494155720000069
As shown in fig. 1, a method for estimating a fully symmetric multi-cell membership state of a multi-rate system based on a dynamic event trigger mechanism specifically includes the following steps:
step (1) establishing a discrete time-varying linear multi-rate system model.
Further, the discrete time-varying linear multi-rate system model established in the step (1) is as follows:
Figure BDA00034941557200000610
wherein s is a time sequence number, tsAnd ksSampling time at two rates;
Figure BDA00034941557200000611
is tsThe state of the system at the time of day,
Figure BDA00034941557200000612
represents nxThe Euclidean space of the dimension is maintained,
Figure BDA00034941557200000613
is tsThe system disturbance at the moment of time,
Figure BDA00034941557200000614
represents nwA Euclidean space of dimensions;
Figure BDA00034941557200000615
is ksThe measured output of the time of day is,
Figure BDA00034941557200000616
represents nyThe Euclidean space of the dimension is maintained,
Figure BDA00034941557200000617
is ksThe noise of the measurement at the time of day,
Figure BDA00034941557200000618
represents nvA Euclidean space of dimensions;
Figure BDA00034941557200000619
and
Figure BDA00034941557200000620
is a known real time-varying matrix.
Sampling period T ═ T of systems+1-tsAnd t is00; the sampling period K' K of the measurements+1-ksAnd k is00; ratio of cycles
Figure BDA00034941557200000621
Is a positive integer greater than or equal to 2.
Setting alpha system initial states
Figure BDA00034941557200000622
System disturbance
Figure BDA00034941557200000623
And measuring noise
Figure BDA00034941557200000624
Included in the following holosymmetric polytypes:
Figure BDA0003494155720000071
wherein the content of the first and second substances,
Figure BDA0003494155720000072
and
Figure BDA0003494155720000073
are known as a vector and a matrix and,
Figure BDA0003494155720000074
and
Figure BDA0003494155720000075
respectively of order nwAnd nvThe identity matrix of (2).
And (2) converting the discrete time-varying linear multi-rate system model into a corresponding discrete time-varying linear single-rate system model by applying a lifting technology. The method comprises the following steps:
iteratively applying a discrete time-varying linear multi-rate system model to obtain
Figure BDA0003494155720000076
Wherein the intermediate parameter
Figure BDA0003494155720000077
System disturbance of converted single rate system
Figure BDA0003494155720000078
Is composed of
Figure BDA0003494155720000079
The transposing of (1).
Intermediate parameter
Figure BDA00034941557200000710
Intermediate parameter
Figure BDA00034941557200000711
Figure BDA00034941557200000712
Time-varying real matrix for converted single rate systems
Figure BDA00034941557200000713
And
Figure BDA00034941557200000714
comprises the following steps:
Figure BDA00034941557200000715
intermediate parameter
Figure BDA00034941557200000716
g∈{1,2,…,α}；
Figure BDA00034941557200000717
System state of single rate system after conversion
Figure BDA00034941557200000718
Is composed of
Figure BDA00034941557200000719
The transposing of (1).
Obtaining a discrete time-varying linear single-rate system model after the following conversion:
Figure BDA00034941557200000720
initial state of transformed discrete time-varying linear single-rate system model
Figure BDA00034941557200000721
And system disturbances
Figure BDA00034941557200000722
The following conditions are satisfied:
Figure BDA00034941557200000723
initial state of discrete time-varying linear single-rate system model after conversion
Figure BDA00034941557200000724
Belongs to the holosymmetric polycythemia
Figure BDA0003494155720000081
Wherein the center of the holosymmetric polycell shape
Figure BDA0003494155720000082
Fully symmetric multi-cell generator matrix
Figure BDA0003494155720000083
And (3) aiming at the converted discrete time-varying linear single-rate system, introducing a dynamic event triggering mechanism to save limited communication resources.
Aiming at the converted discrete time-varying linear single-rate system, the following dynamic event triggering mechanism is introduced:
the sequence of trigger times is 0 ═ iota0＜ι1＜…＜ιm＜…，ιmM is a trigger time, m is a trigger time sequence number, m is 0,1, …, and the following conditions are satisfied:
Figure BDA0003494155720000084
wherein k issMeasured output of time of day
Figure BDA0003494155720000085
With the last transmitted measurement output
Figure BDA0003494155720000086
Difference of (2)
Figure BDA0003494155720000087
To represent
Figure BDA0003494155720000088
Euclidean norm of; auxiliary dynamic variables
Figure BDA0003494155720000089
Satisfies the following conditions:
Figure BDA00034941557200000810
σ, λ and θ are given positive scalars, given initial values of the auxiliary dynamic variables
Figure BDA00034941557200000811
If λ θ is not less than 1, then for any ksIs greater than or equal to 0, has
Figure BDA00034941557200000812
After introducing the dynamic event trigger mechanism, the input actually received by the collector estimator
Figure BDA00034941557200000813
Expressed as:
Figure BDA00034941557200000814
ks∈[ιm,ιm+1)。
it can be seen that only
Figure BDA00034941557200000815
Satisfies the trigger condition
Figure BDA00034941557200000816
The sensor transmits the current measurement information to the estimator, otherwise the estimator continues to use the last transmitted measurement output
Figure BDA00034941557200000817
Limited communication resources may be saved.
And (4) designing a fully-symmetrical multi-cell shape set member state estimator based on a dynamic event trigger mechanism to obtain a parameterized fully-symmetrical multi-cell shape estimation set containing the real state of the system. The method comprises the following steps:
parameterized fully-symmetric multi-cell estimation set containing system real state obtained by order reduction technology
Figure BDA00034941557200000818
Has the following structure:
Figure BDA00034941557200000819
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00034941557200000820
a technique for reducing the order of a full-symmetric multi-cell shape before reduction is disclosed
Figure BDA00034941557200000821
Of order of (i) i.e
Figure BDA00034941557200000822
Generating matrix of
Figure BDA00034941557200000823
Is not greater than the set value r.
Holohedral symmetry polytope before order reduction
Figure BDA00034941557200000824
Selecting the center of a holosymmetric polytope
Figure BDA00034941557200000825
As a fully-symmetrical multi-cell collector state estimator based on a dynamic event trigger mechanism, thereby realizing the pair
Figure BDA0003494155720000091
Point estimation of (1), intermediate parameters
Figure BDA0003494155720000092
Fully-symmetric multi-cell generating matrix before order reduction
Figure BDA0003494155720000093
Intermediate parameter
Figure BDA0003494155720000094
Reduced-order fully-symmetric multi-cell generator matrix
Figure BDA0003494155720000095
Is a parameter matrix of the fully symmetric polytope estimation set, i.e. the parameters that need to be optimized.
Dynamic event trigger mechanism related parameters
Figure BDA0003494155720000096
Comprises the following steps:
Figure BDA0003494155720000097
wherein the content of the first and second substances,
Figure BDA0003494155720000098
and
Figure BDA0003494155720000099
is a given positive scalar quantity. Order to
Figure BDA00034941557200000910
And is
Figure BDA00034941557200000911
Then
Figure BDA00034941557200000912
Is composed of
Figure BDA00034941557200000913
To the upper bound, i.e.
Figure BDA00034941557200000914
To pair
Figure BDA00034941557200000915
Performing range estimation to obtain
Figure BDA00034941557200000916
Upper bound of (2)
Figure BDA00034941557200000917
And lower bound
Figure BDA00034941557200000918
The following were used:
Figure BDA00034941557200000919
wherein the content of the first and second substances,
Figure BDA00034941557200000920
row and matrix of
Figure BDA00034941557200000921
Intermediate parameter
Figure BDA00034941557200000922
Is that
Figure BDA00034941557200000923
The element of the ith row of (1) and the qth column,
Figure BDA00034941557200000924
is a matrix
Figure BDA00034941557200000925
The number of columns.
And (5) optimizing parameters to obtain a fully-symmetrical multi-cell estimation set with the minimum F norm meaning. The method comprises the following steps:
optimized parameters
Figure BDA00034941557200000926
Intermediate parameter
Figure BDA00034941557200000927
Intermediate parameter
Figure BDA00034941557200000928
When the fully symmetric multi-cell estimation set
Figure BDA00034941557200000929
Parameter (d) of
Figure BDA00034941557200000930
Has the advantages of
Figure BDA00034941557200000931
Formally, a fully symmetric polytope estimate set
Figure BDA00034941557200000932
F norm (i.e. of
Figure BDA00034941557200000933
Generating matrix of
Figure BDA00034941557200000934
F norm of (d) minimum, i.e., a fully-symmetric polytope estimate set containing the system true state
Figure BDA00034941557200000935
Is the smallest.
The method of the invention is adopted for simulation verification.
System parameters:
Figure BDA0003494155720000101
Figure BDA0003494155720000102
system disturbance
Figure BDA0003494155720000103
Measuring noise
Figure BDA0003494155720000104
The sampling period T 'of the system is 1, and the sampling period K' of the measurement is 2. Given a positive scalar σ of 0.3, λ of 0.15, and θ of 20. Initial value of given auxiliary dynamic variable
Figure BDA0003494155720000105
The reduced order parameter r in the quote is 20.
The initial values of the states are set to:
Figure BDA0003494155720000106
setting alpha system initial states
Figure BDA0003494155720000107
n is equal to {0,1, …, alpha-1 }. Initial state
Figure BDA0003494155720000108
Contained in a fully symmetrical multicellular body
Figure BDA0003494155720000109
In which
Figure BDA00034941557200001010
I2Is a second order identity matrix.
The simulation results are shown in fig. 2-6: FIG. 2 shows system state variables
Figure BDA00034941557200001011
System state variable
Figure BDA00034941557200001012
Is estimated by
Figure BDA00034941557200001013
System state variable
Figure BDA00034941557200001014
The upper and lower bounds of (1); FIG. 3 shows system state variables
Figure BDA00034941557200001015
System state variable
Figure BDA00034941557200001016
Is estimated by
Figure BDA00034941557200001017
System state variable
Figure BDA00034941557200001018
The upper and lower bounds of (1); FIG. 4 shows the method of the present invention applied to system state variables
Figure BDA00034941557200001019
And
Figure BDA00034941557200001020
error due to estimation
Figure BDA00034941557200001021
And
Figure BDA00034941557200001022
FIG. 5 shows the transmission time of the system measurement output under the dynamic event trigger mechanism; figure 6 compares the estimated mean square error for measurement sample periods of 2 and 4 respectively. The simulation result shows that the estimation error is bounded and in a reasonable range, so that the effectiveness of the fully-symmetrical multi-cell centralized state estimation method of the multi-rate system based on the dynamic event trigger mechanism can be demonstrated.
In summary, the invention provides a fully-symmetric multi-cell membership state estimation method based on a dynamic event trigger mechanism for a discrete time-varying multi-rate system under unknown but bounded noise constraints. The method can simultaneously process the problem of sparse data transmission caused by a multi-rate mechanism and a dynamic event trigger mechanism, not only solves the problem of state estimation of the multi-rate system, but also saves limited communication resources. The method can obtain a parameterized fully-symmetrical multi-cell estimation set containing a real state; then, a fully-symmetrical multi-cell estimation set with the minimum F norm meaning can be obtained through parameter optimization, so that excellent estimation precision is ensured. The state estimation can be achieved by selecting the center of the smallest fully symmetric polytope estimate set as the point estimate of the state.

Claims (6)

1. A method for estimating the state of a fully symmetric polytope member of a multirate system, the method comprising:
establishing a discrete time-varying linear multi-rate system model;
converting a discrete time-varying linear multi-rate system model into a corresponding discrete time-varying linear single-rate system model by applying a lifting technology;
step (3) aiming at the converted discrete time-varying linear single-rate system, a dynamic event triggering mechanism is introduced to save limited communication resources;
designing a fully-symmetrical multi-cell shape set member state estimator based on a dynamic event trigger mechanism to obtain a parameterized fully-symmetrical multi-cell shape estimation set containing the real state of the system;
and (5) optimizing parameters to obtain a fully-symmetrical multi-cell estimation set with the minimum F norm meaning.
2. The fully symmetric multi-manifold membership state estimation method for multi-rate system according to claim 1, wherein the discrete time-varying linear multi-rate system model established in step (1) is as follows:
Figure FDA0003494155710000011
wherein s is a time sequence number, tsAnd ksSampling time at two rates;
Figure FDA0003494155710000012
is tsThe state of the system at the time of day,
Figure FDA0003494155710000013
represents nxThe Euclidean space of the dimension is maintained,
Figure FDA0003494155710000014
is tsThe system disturbance at the moment of time,
Figure FDA0003494155710000015
represents nwA Euclidean space of dimensions;
Figure FDA0003494155710000016
is ksThe measured output of the time of day is,
Figure FDA0003494155710000017
represents nyThe Euclidean space of the dimension is maintained,
Figure FDA0003494155710000018
is ksThe noise of the measurement at the time of day,
Figure FDA0003494155710000019
represents nvA Euclidean space of dimensions;
Figure FDA00034941557100000110
and
Figure FDA00034941557100000111
is a known real time-varying matrix;
sampling period T ═ T of systems+1-tsAnd t is00; the sampling period K' K of the measurements+1-ksAnd k is00; ratio of periods
Figure FDA00034941557100000112
Is a positive integer greater than or equal to 2;
setting alpha system initial states
Figure FDA00034941557100000113
System disturbance
Figure FDA00034941557100000114
And measuring noise
Figure FDA00034941557100000115
Included in the following holosymmetric polytypes:
Figure FDA00034941557100000116
wherein the content of the first and second substances,
Figure FDA00034941557100000117
and
Figure FDA00034941557100000118
are known as a vector and a matrix and,
Figure FDA00034941557100000119
and
Figure FDA00034941557100000120
respectively of order nwAnd nvThe identity matrix of (2).
3. The fully symmetric multi-cell membership state estimation method for multi-rate systems according to claim 2, wherein the step (2) is specifically:
iteratively applying a discrete time-varying linear multi-rate system model to obtain
Figure FDA0003494155710000021
Wherein the intermediate parameter
Figure FDA0003494155710000022
System disturbance of converted single rate system
Figure FDA0003494155710000023
Figure FDA0003494155710000024
Is composed of
Figure FDA0003494155710000025
Transposing;
intermediate parameter
Figure FDA0003494155710000026
Intermediate parameter
Figure FDA0003494155710000027
p,f∈{1,2,...,α}；
Time-varying real matrix for converted single rate systems
Figure FDA0003494155710000028
And
Figure FDA0003494155710000029
comprises the following steps:
Figure FDA00034941557100000210
intermediate parameter
Figure FDA00034941557100000211
System state of single rate system after conversion
Figure FDA00034941557100000212
Figure FDA00034941557100000213
Is composed of
Figure FDA00034941557100000222
Transposing;
obtaining a discrete time-varying linear single-rate system model after the following conversion:
Figure FDA00034941557100000214
initial state of transformed discrete time-varying linear single-rate system model
Figure FDA00034941557100000215
And system disturbances
Figure FDA00034941557100000216
The following conditions are satisfied:
Figure FDA00034941557100000217
initial state of discrete time-varying linear single-rate system model after conversion
Figure FDA00034941557100000218
Belongs to the holosymmetric polycythemia
Figure FDA00034941557100000219
Wherein the center of the holosymmetric polycell shape
Figure FDA00034941557100000220
Fully symmetric multi-cell generator matrix
Figure FDA00034941557100000221
4. The fully symmetric multi-manifold membership state estimation method for multi-rate system according to claim 3, wherein step (3) introduces the following dynamic event triggering mechanism for the transformed discrete time-varying linear single rate system:
the sequence of trigger times is 0 ═ iota0＜ι1＜...＜ιm＜...，ιmM is a trigger time, m is a trigger time sequence number, m is 0,1, …, and the following conditions are satisfied:
Figure FDA0003494155710000031
wherein k issMeasured output of time of day
Figure FDA00034941557100000327
With the last transmitted measurement output
Figure FDA0003494155710000032
Difference of (2)
Figure FDA0003494155710000033
Figure FDA0003494155710000034
To represent
Figure FDA0003494155710000035
Euclidean norm of; auxiliary dynamic variables
Figure FDA0003494155710000036
Satisfies the following conditions:
Figure FDA0003494155710000037
σ, λ and θ are given positive scalars, given initial values of the auxiliary dynamic variables
Figure FDA0003494155710000038
If λ θ is not less than 1, then for any ksIs more than or equal to 0, has
Figure FDA0003494155710000039
After introducing the dynamic event trigger mechanism, the input actually received by the collector estimator
Figure FDA00034941557100000310
Expressed as:
Figure FDA00034941557100000311
ks∈[ιm,ιm+1)。
5. the fully symmetric multi-cell membership state estimation method for multi-rate system according to claim 4, wherein the step (4) is specifically:
parameterized fully-symmetric multi-cell estimation set containing system real state obtained by order reduction technology
Figure FDA00034941557100000312
Has the following structure:
Figure FDA00034941557100000313
wherein the content of the first and second substances,
Figure FDA00034941557100000314
a technique for reducing the order of a full-symmetric multi-cell shape before reduction is disclosed
Figure FDA00034941557100000315
Of order of (i) i.e
Figure FDA00034941557100000316
Generating matrix of
Figure FDA00034941557100000317
The number of columns of (d) is not more than a set value r;
holohedral symmetry polytope before order reduction
Figure FDA00034941557100000318
Selecting the center of a holosymmetric polytope
Figure FDA00034941557100000319
As a fully-symmetrical multi-cell collector state estimator based on a dynamic event trigger mechanism, thereby realizing the pair
Figure FDA00034941557100000320
Point estimation of (1), intermediate parameters
Figure FDA00034941557100000321
Fully-symmetric multi-cell generating matrix before order reduction
Figure FDA00034941557100000322
Intermediate parameter
Figure FDA00034941557100000323
Reduced-order fully-symmetric multi-cell generator matrix
Figure FDA00034941557100000324
Is a parameter matrix of a fully-symmetrical multi-cell estimation set, namely parameters needing to be optimized;
dynamic event trigger mechanism related parameters
Figure FDA00034941557100000325
Comprises the following steps:
Figure FDA00034941557100000326
wherein the content of the first and second substances,
Figure FDA0003494155710000041
and
Figure FDA0003494155710000042
is a given positive scalar quantity; order to
Figure FDA0003494155710000043
And is
Figure FDA0003494155710000044
Then
Figure FDA0003494155710000045
Is composed of
Figure FDA0003494155710000046
To the upper bound, i.e.
Figure FDA0003494155710000047
To pair
Figure FDA0003494155710000048
Performing range estimation to obtain
Figure FDA0003494155710000049
Upper bound of (2)
Figure FDA00034941557100000410
And lower bound
Figure FDA00034941557100000411
The following were used:
Figure FDA00034941557100000412
wherein the content of the first and second substances,
Figure FDA00034941557100000413
row and matrix of
Figure FDA00034941557100000414
Intermediate parameter
Figure FDA00034941557100000415
Figure FDA00034941557100000416
Is that
Figure FDA00034941557100000417
The element of the ith row of (1) and the qth column,
Figure FDA00034941557100000418
is a matrix
Figure FDA00034941557100000419
The number of columns.
6. The fully symmetric multi-cell membership state estimation method for multi-rate systems according to claim 5, wherein step (5) is specifically:
optimized parameters
Figure FDA00034941557100000420
Intermediate parameter
Figure FDA00034941557100000421
Intermediate parameter
Figure FDA00034941557100000422
When the fully symmetric multi-cell estimation set
Figure FDA00034941557100000423
Parameter (d) of
Figure FDA00034941557100000424
Has the advantages of
Figure FDA00034941557100000425
Formally, a fully symmetric polytope estimate set
Figure FDA00034941557100000426
Is the full-symmetric multi-cell estimation set containing the system true state
Figure FDA00034941557100000427
Is the smallest.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114859731A (en) * 2022-05-18 2022-08-05 杭州师范大学 Interval two-type fuzzy time-lag system controller design method based on line integral method
CN117828864A (en) * 2023-12-29 2024-04-05 江南大学 System state estimation method based on multi-cell spatial filtering and P norm

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114859731A (en) * 2022-05-18 2022-08-05 杭州师范大学 Interval two-type fuzzy time-lag system controller design method based on line integral method
CN117828864A (en) * 2023-12-29 2024-04-05 江南大学 System state estimation method based on multi-cell spatial filtering and P norm

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