CN112260867B - State estimation method of event-triggered transmission complex network based on collective member estimation - Google Patents

State estimation method of event-triggered transmission complex network based on collective member estimation Download PDF

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CN112260867B
CN112260867B CN202011127988.XA CN202011127988A CN112260867B CN 112260867 B CN112260867 B CN 112260867B CN 202011127988 A CN202011127988 A CN 202011127988A CN 112260867 B CN112260867 B CN 112260867B
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CN112260867A (en
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赵忠义
王子栋
邹磊
白星振
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Shandong University of Science and Technology
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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Abstract

The invention discloses a state estimation method of an event-triggered transmission complex network based on collective member estimation, which specifically comprises the following steps: establishing a state space model of each node of the complex network; establishing a transmission model for transmitting data to the centralized estimator by each node of the complex network under the scheduling of an event trigger mechanism; calculating an estimated parameter of the ensemble estimator; and constructing an ensemble estimator and calculating a fully-symmetrical multi-cell estimation set containing the real state of the complex network. The method considers the influence of high-order terms of nonlinear function Taylor expansion in a complex network dynamic equation, and the calculated fully-symmetrical multi-cell shape estimation set necessarily comprises a true value of a system state; moreover, by using the set member estimator parameters, the obtained full-symmetry multi-cell estimation set can be ensured to have the minimum F radius, so that the estimation precision is ensured; in addition, the method is given in a recursion mode, so that the running state of the complex network can be monitored in real time, and the safe and stable running of the network is guaranteed.

Description

State estimation method of event-triggered transmission complex network based on collective member estimation
Technical Field
The invention belongs to the technical field of state estimation, and particularly relates to a state estimation method of an event-triggered transmission complex network based on collective member estimation.
Background
The state information of the system has many important applications in engineering, such as being used for system control, real-time monitoring, and ensuring the safe operation of the system. However, due to physical limitations and the like, especially for a complex network with a more complex structure, it is difficult to obtain all the state variables of the system, and therefore the importance of the state estimation technique is self-evident.
State estimation is one of the basic research topics of control disciplines, and its basic idea is to give an estimate of the state of a system that meets a certain performance index based on the measured output of the system received. In the industry, the transmission of signals is usually limited by resources such as transmission energy and network bandwidth, and event-triggered transmission can solve the problem well, and can greatly reduce unnecessary signal transmission while ensuring the system performance, thereby saving energy and bandwidth resources. In practical applications, bounded noise interference in the system is ubiquitous and, if not handled properly, can seriously affect the estimation of the system state.
Disclosure of Invention
The invention aims to provide a state estimation method of an event-triggered transmission complex network based on collective estimation.
In order to achieve the purpose, the invention adopts the following technical scheme:
the state estimation method of the transmission complex network triggered by the event based on the collective member estimation comprises the following steps:
s1, establishing a state space model of each node of the complex network, as shown in a formula (1):
Figure BDA0002734209280000011
in the formula, k represents a sampling time;
Figure BDA0002734209280000012
for the state of the ith node of a complex network,
Figure BDA0002734209280000013
for the state of the jth node of the complex network,
Figure BDA0002734209280000014
represents nxA Vickers space;
Figure BDA0002734209280000015
for the output of the ith node of a complex network,
Figure BDA0002734209280000016
represents nyA Vickers space;
Figure BDA0002734209280000017
i.e. giTo be defined in a natural number set
Figure BDA0002734209280000018
And nxThe function value is n on the Cartesian product of the Vickers spacexA nonlinear vector value function of values in the Vickers space, g for a real systemiThe second-order partial derivative continuity is met;
A＝(aij)N×Nan external coupling matrix representing a complex network, a if there is a connection between two nodes i and j of the complex networkij> 0, otherwise, aij＝0；aiiSatisfies the following conditions:
Figure BDA0002734209280000021
i＝1，2，…，N，j＝1，2，…，N；
Figure BDA0002734209280000022
an internal coupling matrix representing a complex network;
wherein the content of the first and second substances,
Figure BDA0002734209280000023
respectively represent non-negative in-coupling coefficients;
νi(k) which is indicative of a bounded noise, is,
Figure BDA0002734209280000024
Figure BDA0002734209280000025
represents nνA Vickers space; wherein the content of the first and second substances,
Figure BDA0002734209280000026
represents a known holosymmetric polytope, κiIn the case of a known positive scalar quantity,
Figure BDA0002734209280000027
represents nνA dimension unit matrix;
Bi(k)、Ci(k)、Di(k) are all known time-varying matrices;
xi(0) indicating the initial operating conditions of the complex network,<0，Gi，0>is a known holosymmetric polytope;
s2, establishing a model for transmitting data to the centralized member estimator by each node of the complex network under the scheduling of an event trigger mechanism;
for node i of a complex network, in sequence
Figure BDA0002734209280000028
Represents the times at which the node i sends its output, these times being calculated iteratively by equation (2) below:
Figure BDA0002734209280000029
equation (2) shows the trigger time for the ith node of a complex network
Figure BDA00027342092800000210
Later earliest meeting the trigger condition
Figure BDA00027342092800000211
The time of the node i is the next trigger time of the node i;
wherein the content of the first and second substances,
Figure BDA00027342092800000212
respectively representing the s +1 th trigger time and the s +2 th trigger time of the node i;
Figure BDA00027342092800000213
representing a trigger function set in the event trigger device;
Figure BDA00027342092800000214
indicating a trigger condition, σiThe parameter of which is more than 0 is set,
Figure BDA00027342092800000215
output y representing time k of node ii(k) The trigger time closest to time k
Figure BDA00027342092800000216
Output of (2)
Figure BDA00027342092800000217
The Euclidean norm of the difference between;
under the scheduling of an event trigger mechanism, designing a centralized member estimator for a state space model (1) of each node of the complex network;
wherein the input of the membership estimator
Figure BDA00027342092800000218
Expressed as:
Figure BDA00027342092800000219
formula (3) shows that if the moment k is the trigger moment, the input of the collective estimator is the output of the system node at the moment, otherwise, if the moment k is not the trigger moment, the collective estimator adopts the input of the previous trigger moment as the input of the current moment k;
s3, calculating an estimation parameter K of the collective member estimatori(k)；
At time K, the estimated parameters K of the ensemble estimatori(k) Calculated from the following equation (4):
Figure BDA00027342092800000220
wherein, the meaning of each parameter in the formula (4) is as follows:
Figure BDA0002734209280000031
Figure BDA0002734209280000032
Figure BDA0002734209280000033
Figure BDA0002734209280000034
Figure BDA0002734209280000035
for i ═ 1, 2, …, N, Ji(k) The method is obtained by the following partial derivation operation:
Figure BDA0002734209280000036
in the formula (I), the compound is shown in the specification,
Figure BDA0002734209280000037
an estimated value representing the state of the ith node of the complex network;
B(k)＝diag{B1(k)，B2(k)，…，BN(k)}；C(k)＝diag{C1(k)，C2(k)，…，CN(k)}；
D(k)＝diag{D1(k)，D2(k)，…，DN(k)}；
Figure BDA0002734209280000038
Figure BDA0002734209280000039
wherein the content of the first and second substances,
Figure BDA00027342092800000310
the matrix G (k) represents a fully-symmetrical multi-cell generation matrix in which the true value of the system state is positioned at the time k;
the matrix g (k) is iteratively calculated by the following equation (5):
G(k+1)＝[G1(k+1) G2(k+1) G3(k+1) G4(k+1)] (5)
wherein the content of the first and second substances,
Figure BDA00027342092800000311
the parameter K (K) is K (K) diagk { K1(k)，K2(k)，…，KN(k)}，
K1(k)，K2(k)，…，KN(k) From Ki(k) Respectively taking 1, 2, … and N as the component (i) to obtain;
Figure BDA00027342092800000312
Figure BDA00027342092800000313
an interval matrix with known range;
wherein Δ (k) ═ diag { Δ1(k)，Δ2(k)，…，ΔN(k)}；
Figure BDA00027342092800000314
Figure BDA00027342092800000315
Figure BDA00027342092800000316
Representation matrix
Figure BDA00027342092800000317
Maximum value of the absolute value of the element of (a);
R(k)＝diag{R1(k)，R2(k)，…，RN(k)}；
Figure BDA0002734209280000041
Figure BDA0002734209280000042
Figure BDA0002734209280000043
Figure BDA0002734209280000044
wherein the content of the first and second substances,
Figure BDA0002734209280000045
denotes gi(k，xi(k) P-th component of (1), 2, …, n)x；
Figure BDA0002734209280000046
Is in a closed interval of [0, 1 ]]A variable of the up value;
Figure BDA0002734209280000047
Figure BDA0002734209280000048
Figure BDA0002734209280000049
representation matrix
Figure BDA00027342092800000410
Maximum value of the sum of absolute values of the elements of each column of (1);
Gi(k) a generator matrix of fully symmetric polytope representing the true state of the ith node, given directly by g (k);
<0，Gi(k)>a fully symmetric polytope representing the true state containing the ith node;
for the interval matrix X:
Figure BDA00027342092800000411
wherein the content of the first and second substances,
Figure BDA00027342092800000412
an element representing the qth row and the qth column of the interval matrix X;
Figure BDA00027342092800000413
and
Figure BDA00027342092800000414
is a constant that is known to be a constant,
Figure BDA00027342092800000415
the left end point of the interval is shown,
Figure BDA00027342092800000416
represents the right end of the interval;
the operation mid (X) represents X its midpoint, namely:
Figure BDA00027342092800000417
operations
Figure BDA00027342092800000418
Given by:
Figure BDA00027342092800000419
wherein the content of the first and second substances,
Figure BDA00027342092800000420
Figure BDA00027342092800000421
representing variable definition symbols;
thereby calculating
Figure BDA00027342092800000422
And
Figure BDA00027342092800000423
then calculating to obtain G2(k+1)；
G3(k+1)＝-K(k)∑；
G4(k+1)＝(B(k)-K(k)D(k))Gv；
G (k) has an initial value of G (0) ═ diag { G1，0，G2，0，…，GN，0}，Gj，0Denotes the known matrix, j ═ 1, 2, …, N;
s4, constructing a set member estimator, and calculating a full-symmetry multi-cell estimation set containing the real state of the complex network, wherein the expression of the full-symmetry multi-cell estimation set is shown as a formula (6):
Figure BDA0002734209280000058
wherein, formula (6) represents a fully symmetric multi-cell shape containing the true value of the system state;
center of holosymmetric polycell
Figure BDA0002734209280000051
As shown in equation (7):
Figure BDA0002734209280000052
in the formula (I), the compound is shown in the specification,
Figure BDA0002734209280000053
and representing the estimated value of the ith node state of the complex network, wherein the iterative formula is as follows:
Figure BDA0002734209280000054
in the formula (I), the compound is shown in the specification,
Figure BDA0002734209280000055
represents an initial value of the iteration; generating a matrix g (k) iteratively calculated by equation (5);
when estimator parameter Ki(k) When the formula (4) is adopted, the F-norm of the fully-symmetric polytope obtained by the formulas (6) to (8) is the minimum, that is, the size of the state estimation set containing the real state of the complex network is the minimum in the F-norm sense of the generator matrix.
The invention has the following advantages:
as described above, the present invention provides a method for estimating a state of an event-triggered complex network based on ensemble estimation, which considers a complex network with coupling, time-varying characteristics and nonlinearity (specifically, refer to a state space model (1) of each node of the complex network), and can be used to model complex systems in many projects, and further, the estimation method of the present invention employs an event-triggered transmission mechanism, and can save transmission energy and network bandwidth resources, and recursively calculates a fully-symmetric multi-manifold estimation set including system state truth values at each time by using an ensemble estimation technique and a recursive solution technique, and compared with an ensemble estimation method based on an ellipsoid estimation set, the method based on the fully-symmetric multi-manifold estimation set provided by the present invention has simpler operation, avoids solving matrix inequality, and can directly provide accurate intervals of each state variable of the complex network, each point in the value interval can be used as an estimation of a real state, and the middle point of the interval can be used as an estimation point in practical application. The estimation method can obtain the estimation set of the state of the complex network under the norm bounded noise interference, and has important application for monitoring the running state of the complex network and ensuring the safe and stable running of the network, thereby well meeting the actual application requirement.
Drawings
FIG. 1 is a flow chart of a state estimation method for a complex network based on event triggered transmission of centralized member estimation according to the present invention;
FIG. 2 is a diagram illustrating an actual state trajectory of a first node of a complex network according to an embodiment of the present invention
Figure BDA0002734209280000056
And its state estimation trajectory
Figure BDA0002734209280000057
And a corresponding state, wherein j is 1;
FIG. 3 is a diagram illustrating an actual state trajectory of a first node of a complex network according to an embodiment of the present invention
Figure BDA0002734209280000061
And its state estimation trajectory
Figure BDA0002734209280000062
And a corresponding state, wherein j is 2;
FIG. 4 is a diagram illustrating an actual state trajectory of a second node of a complex network according to an embodiment of the present invention
Figure BDA0002734209280000063
And its state estimation trajectory
Figure BDA0002734209280000064
And a corresponding state, wherein j is 1;
FIG. 5 is a diagram illustrating an actual state trajectory of a second node of a complex network according to an embodiment of the present invention
Figure BDA0002734209280000065
And its state estimation trajectory
Figure BDA0002734209280000066
And a corresponding state, wherein j is 2;
FIG. 6 is a diagram illustrating an actual state trajectory of a third node of the complex network according to an embodiment of the present invention
Figure BDA0002734209280000067
And its state estimation trajectory
Figure BDA0002734209280000068
And a corresponding state, wherein j is 1;
FIG. 7 is a diagram illustrating an actual state trajectory of a third node of the complex network according to an embodiment of the present invention
Figure BDA0002734209280000069
And its state estimation trajectory
Figure BDA00027342092800000610
And a corresponding state, wherein j is 2;
fig. 8 is a schematic diagram of trigger information of measurement output of each node of the complex network according to an embodiment of the present invention.
Detailed Description
The basic idea of the invention is as follows:
a state estimation method of an event-triggered transmission complex network is provided, and the method is based on an ensemble estimation technology, and utilizes the known information of a system model and a noise boundary to recursively calculate an estimation set containing a system state truth value.
However, since the directly calculated estimation set usually does not have a regular shape, which results in a heavy calculation burden and affects the real-time application of the estimation algorithm, the embodiment of the present invention uses a set with a simpler shape and containing the system state truth as the estimation set, and the fully symmetric polycythemia is such a set.
Compared with a plurality of ellipsoids used in collective estimation, the method and the device for estimating the system state based on the total-symmetry multi-cell collective estimation algorithm have the advantages that the system state is estimated, the accuracy is higher, the operation is simpler, and the method and the device are suitable for online application.
The general definition of a fully symmetric polytope is first given below, as follows:
for a given vector
Figure BDA00027342092800000611
And matrix
Figure BDA00027342092800000612
Figure BDA00027342092800000613
Showing the dimension of the m in the Euclidean space,
Figure BDA00027342092800000614
represents the set of all m rows and n columns of the matrix,
Figure BDA00027342092800000615
represents a fully symmetrical multicellular form, denoted by<c，M>。
Wherein c represents the center of a fully symmetric polytope;
m denotes a generator matrix of a fully symmetric polytope, s denotes a vector,
Figure BDA00027342092800000616
representing an infinite norm of the vector s.
The invention is described in further detail below with reference to the following figures and detailed description:
as shown in fig. 1, the method for estimating the state of the transport complex network triggered by the event based on the estimation of the centralized member includes the following steps:
s1, establishing a state space model of each node of the complex network, as shown in a formula (1):
Figure BDA0002734209280000071
in the formula, k represents a sampling time;
Figure BDA0002734209280000072
for the state of the ith node of a complex network,
Figure BDA0002734209280000073
for the state of the jth node of the complex network,
Figure BDA0002734209280000074
represents nxThe Vickers space.
Figure BDA0002734209280000075
For the output of the ith node of a complex network,
Figure BDA0002734209280000076
represents nyThe Vickers space.
Figure BDA0002734209280000077
I.e. giTo be defined in a natural number set
Figure BDA0002734209280000078
And nxThe function value is n on the Cartesian product of the Vickers spacexA nonlinear vector value function of values in the Vickers space, g for a real systemiAnd the second-order partial derivative continuity is satisfied.
A＝(aij)N×NAn external coupling matrix representing a complex network, a if there is a connection between two nodes i and j of the complex networkij> 0, otherwise, aij＝0；aiiSatisfies the following conditions:
Figure BDA0002734209280000079
i＝1，2，…，N，j＝1，2，…，N。Γ＝diag{γ1，γ2，...，γ nx0 denotes the internal coupling matrix of the complex network.
Wherein, γ1，γ2，...，γnxAre respectively provided withRepresenting a non-negative in-coupling coefficient.
νi(k) Which is indicative of a bounded noise, is,
Figure BDA00027342092800000710
Figure BDA00027342092800000711
represents nνA Vickers space; wherein the content of the first and second substances,
Figure BDA00027342092800000720
represents a known holosymmetric polytope, κiIn the case of a known positive scalar quantity,
Figure BDA00027342092800000721
represents nvA dimension unit matrix.
Bi(k)、Ci(k)、Di(k) Are all known time-varying matrices.
xi(0) Indicating the initial operating conditions of the complex network,<0，Gi，0>is a known holosymmetric polytope.
And S2, establishing a model for transmitting data to the centralized member estimator by each node of the complex network under the scheduling of an event trigger mechanism.
For node i of a complex network, in sequence
Figure BDA00027342092800000712
Represents the times at which the node i sends its output, these times being calculated iteratively by equation (2) below:
Figure BDA00027342092800000713
equation (2) shows the trigger time for the ith node of a complex network
Figure BDA00027342092800000714
Later earliest meeting the trigger condition
Figure BDA00027342092800000715
The time of the node i is the next trigger time of the node i.
Wherein the content of the first and second substances,
Figure BDA00027342092800000716
respectively representing the s +1 th and s +2 th trigger time of the node i.
Figure BDA00027342092800000717
Representing the trigger function set in the event trigger device.
Figure BDA00027342092800000718
Indicating a trigger condition, σiThe parameter of which is more than 0 is set,
Figure BDA00027342092800000719
output y representing time k of node ii(k) The trigger time closest to time k
Figure BDA0002734209280000081
Output of (2)
Figure BDA0002734209280000082
The euclidean norm of the difference between.
Under the scheduling of an event triggering mechanism, a state space model (1) of each node of a complex network is designed into a centralized estimator.
Wherein the input of the membership estimator
Figure BDA0002734209280000083
Expressed as:
Figure BDA0002734209280000084
and (3) indicating that if the moment k is the trigger moment, the input of the centralized member estimator is the output of the system node at the moment, otherwise, if the moment k is not the trigger moment, the input of the previous trigger moment is adopted by the centralized member estimator as the input of the current moment k.
S3, calculating an estimation parameter K of the collective member estimatori(k)。
At time K, the estimated parameters K of the ensemble estimatori(k) Calculated from the following equation (4):
Figure BDA0002734209280000085
wherein, the meaning of each parameter in the formula (4) is as follows:
Figure BDA0002734209280000086
Figure BDA0002734209280000087
Figure BDA0002734209280000088
Figure BDA0002734209280000089
Figure BDA00027342092800000810
for i ═ 1, 2, …, N, Ji(k) The method is obtained by the following partial derivation operation:
Figure BDA00027342092800000811
in the formula (I), the compound is shown in the specification,
Figure BDA00027342092800000812
an estimate representing the state of the ith node of the complex network.
B(k)＝diag{B1(k)，B2(k)，…，BN(k)}；C(k)＝diag{C1(k)，C2(k)，…，CN(k)}；
D(k)＝diag{D1(k)，D2(k)，…，DN(k)}；
Figure BDA00027342092800000815
；
Figure BDA00027342092800000813
Wherein the content of the first and second substances,
Figure BDA00027342092800000814
the matrix g (k) represents the fully symmetric polytope generator matrix in which the true values of the system state are located at time k.
The matrix g (k) is iteratively calculated by the following equation (5):
G(k+1)＝[G1(k+1) G2(k+1) G3(k+1) G4(k+1)] (5)
wherein the content of the first and second substances,
Figure BDA0002734209280000091
K(k)＝diag{K1(k)，K2(k)，…，KN(k)}，
wherein, K1(k)，K2(k)，…，KN(k) From Ki(k) And (4) obtaining the compound I by respectively taking 1, 2, … and N.
Figure BDA0002734209280000092
Figure BDA0002734209280000093
Is a range matrix with known ranges.
Wherein Δ (k) ═ diag { Δ1(k)，Δ2(k)，…，ΔN(k)}；
Figure BDA0002734209280000094
||Δi(k)||max≤1，||Δi(k)||maxRepresentation matrix deltai(k) Maximum value of the absolute value of the element(s).
R(k)＝diag{R1(k)，R2(k)，…，RN(k)}；
Figure BDA0002734209280000095
i＝1，2，…，N；
Figure BDA0002734209280000096
Figure BDA0002734209280000097
Figure BDA0002734209280000098
Wherein the content of the first and second substances,
Figure BDA0002734209280000099
denotes gi(k，xi(k) P-th component of (1), 2, …, n)x；
Figure BDA00027342092800000910
Is in a closed interval of [0, 1 ]]A variable of the up value; s e {1, 2, …, nx}，t∈{1，2，…，nx}。
Figure BDA00027342092800000911
Representation matrix
Figure BDA00027342092800000912
The maximum value of the sum of the absolute values of the elements of each column.
Gi(k) The generator matrix of the fully symmetric polytope, which represents the true state of the ith node, is given directly by g (k).
<0，Gi(k)>Representing a fully symmetric polytope containing the true state of the ith node.
For the interval matrix X:
Figure BDA00027342092800000913
wherein the content of the first and second substances,
Figure BDA00027342092800000914
an element representing the qth row and the qth column of the interval matrix X;
Figure BDA00027342092800000915
and
Figure BDA00027342092800000916
is a constant that is known to be a constant,
Figure BDA00027342092800000917
the left end point of the interval is shown,
Figure BDA00027342092800000918
indicating the right end of the interval.
The operation mid (X) represents X its midpoint, namely:
Figure BDA0002734209280000101
operations
Figure BDA0002734209280000102
Given by:
Figure BDA0002734209280000103
wherein the content of the first and second substances,
Figure BDA0002734209280000104
Figure BDA0002734209280000105
representing variable definition symbols.
Thereby calculating
Figure BDA0002734209280000106
And
Figure BDA0002734209280000107
then calculating to obtain G2(k+1)。
G3(k+1)＝-K(k)∑。
G4(k+1)＝(B(k)-K(k)D(k))Gv。
G (k) has an initial value of G (0) ═ diag { G1，0，G2，0，…，GN，0}，Gj，0Representing the known matrix, j ═ 1, 2, …, N.
S4, constructing a set member estimator, and calculating a full-symmetry multi-cell estimation set containing the real state of the complex network, wherein the expression of the full-symmetry multi-cell estimation set is shown as a formula (6):
Figure BDA0002734209280000108
wherein equation (6) represents a fully symmetric polytope containing the true value of the system state.
Center of holosymmetric polycell
Figure BDA0002734209280000109
As shown in equation (7):
Figure BDA00027342092800001010
in the formula (I), the compound is shown in the specification,
Figure BDA00027342092800001011
representing a complex networkThe iterative formula of the estimated values of the i node states is as follows:
Figure BDA00027342092800001012
in the formula (I), the compound is shown in the specification,
Figure BDA00027342092800001013
represents an initial value of the iteration; the generator matrix g (k) is iteratively calculated by equation (5).
When estimator parameter Ki(k) When the formula (4) is adopted, the F-norm of the fully-symmetrical multi-cell shape obtained by the formulas (6) to (8) is minimum, namely the size of a state estimation set containing the real state of the complex network is minimum in the F-norm meaning of a generation matrix, so that a better state estimation effect is ensured.
The method for estimating the state of the event-triggered transmission complex network based on the collective estimation provided by the invention is described below by combining experiments to verify the effectiveness of the method provided by the invention.
During the experiment: and taking the experimental step length as 25, and inputting the system output given by the platform into a computer as the input of an estimator by adopting an event triggering mechanism on a semi-physical simulation platform capable of acquiring the real-time state of the system.
By using the state estimation method provided by the invention, a full-symmetry multi-manifold estimation set and an estimation value are generated by using MATLAB software and are compared with a real value of a system state provided by a platform.
Fig. 2 to 7 show the true values of the state variables of a complex network with three nodes totaling six state variables, and the range of the central point of the fully-symmetric multi-manifold estimation set and the true state calculated by the method of the present invention. Wherein:
the real values of the first state variables of the first node of the complex network are given by the solid lines in fig. 2
Figure BDA0002734209280000111
The dotted line shows the correspondence of the central point of the fully-symmetrical multi-cell estimation set
Figure BDA0002734209280000112
Is estimated by
Figure BDA0002734209280000113
The dot-dash line and the double-dashed line respectively show the values calculated from the estimation set
Figure BDA0002734209280000114
Upper and lower bounds. As can be seen from fig. 2:
the upper and lower bounds calculated by the estimation set of the system state obtained by the method of the invention can contain the true value of the state variable
Figure BDA0002734209280000115
Further, the estimated values corresponding to the points in the estimated set
Figure BDA0002734209280000116
And
Figure BDA0002734209280000117
the goodness of fit of (2) is higher.
The real values of the second state variables of the first node of the complex network are given by the solid lines in fig. 3
Figure BDA0002734209280000118
The dotted line shows the correspondence of the central point of the fully-symmetrical multi-cell estimation set
Figure BDA0002734209280000119
Is estimated by
Figure BDA00027342092800001110
The dot-dash line and the double-dashed line respectively show the values calculated from the estimation set
Figure BDA00027342092800001111
Upper and lower bounds of (1); as can be seen from fig. 3:
the upper and lower bounds calculated by the estimation set of the system state obtained by the method of the invention can contain the truth of the state variableReal value
Figure BDA00027342092800001112
Further, the estimated values corresponding to the points in the estimated set
Figure BDA00027342092800001113
And
Figure BDA00027342092800001114
the goodness of fit of (2) is higher.
The real value of the first state variable of the second node of the complex network is given by the solid line in fig. 4
Figure BDA00027342092800001115
The dotted line shows the correspondence of the central point of the fully-symmetrical multi-cell estimation set
Figure BDA00027342092800001116
Is estimated by
Figure BDA00027342092800001117
The dot-dash line and the double-dashed line respectively show the values calculated from the estimation set
Figure BDA00027342092800001118
Upper and lower bounds of (1); as can be seen from fig. 4:
the upper and lower bounds calculated by the estimation set of the system state obtained by the method of the invention can contain the true value of the state variable
Figure BDA00027342092800001119
Further, the estimated values corresponding to the points in the estimated set
Figure BDA00027342092800001120
And
Figure BDA00027342092800001121
the goodness of fit of (2) is higher.
The real value of the second state variable of the second node of the complex network is given by the solid line in fig. 5
Figure BDA00027342092800001122
The dotted line shows the correspondence of the central point of the fully-symmetrical multi-cell estimation set
Figure BDA00027342092800001123
Is estimated by
Figure BDA00027342092800001124
The dot-dash line and the double-dashed line respectively show the values calculated from the estimation set
Figure BDA00027342092800001125
Upper and lower bounds of (1); as can be seen from fig. 5:
the upper and lower bounds calculated by the estimation set of the system state obtained by the method of the invention can contain the true value of the state variable
Figure BDA00027342092800001126
Further, the estimated values corresponding to the points in the estimated set
Figure BDA00027342092800001127
And
Figure BDA00027342092800001128
the goodness of fit of (2) is higher.
The real value of the first state variable of the third node of the complex network is given by the solid line in fig. 6
Figure BDA00027342092800001129
The dotted line shows the correspondence of the central point of the fully-symmetrical multi-cell estimation set
Figure BDA00027342092800001130
Is estimated by
Figure BDA00027342092800001131
The dot-dash line and the double-dashed line respectively show the values calculated from the estimation set
Figure BDA0002734209280000121
Upper and lower bounds of (1); as can be seen from fig. 6:
the upper and lower bounds calculated by the estimation set of the system state obtained by the method of the invention can contain the true value of the state variable
Figure BDA0002734209280000122
Further, the estimated values corresponding to the points in the estimated set
Figure BDA0002734209280000123
And
Figure BDA0002734209280000124
the goodness of fit of (2) is higher.
The real values of the second state variable of the third node of the complex network are given by the solid line in fig. 7
Figure BDA0002734209280000125
The dotted line shows the correspondence of the central point of the fully-symmetrical multi-cell estimation set
Figure BDA0002734209280000126
Is estimated by
Figure BDA0002734209280000127
The dot-dash line and the double-dashed line respectively show the values calculated from the estimation set
Figure BDA0002734209280000128
Upper and lower bounds of (1); as can be seen from fig. 7:
the upper and lower bounds calculated by the estimation set of the system state obtained by the method of the invention can contain the true value of the state variable
Figure BDA0002734209280000129
Further, the estimated values corresponding to the points in the estimated set
Figure BDA00027342092800001210
And
Figure BDA00027342092800001211
the goodness of fit of (2) is higher.
Fig. 8 shows a sequence of trigger instants for three nodes of a complex network. Wherein, the asterisk represents the trigger moment of the output of the first node, the circle represents the trigger moment of the output of the second node, and the plus sign represents the trigger moment of the output of the third node.
As can be easily found from fig. 8, the event trigger mechanism adopted by the state estimation method in the present invention can effectively reduce the frequency of system data transmission, thereby saving energy and network bandwidth resources.
The method considers the influence of high-order terms of nonlinear function Taylor expansion in a complex network dynamic equation, and the calculated fully-symmetrical multi-cell shape estimation set necessarily comprises a true value of a system state; moreover, by using the set member estimator parameters, the obtained full-symmetry multi-cell estimation set can be ensured to have the minimum F radius, so that the estimation precision is ensured; in addition, the method is given in a recursion mode, so that the running state of the complex network can be monitored in real time, and the safe and stable running of the network is guaranteed.
It should be understood, however, that the description herein of specific embodiments is not intended to limit the invention to the particular forms disclosed, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims.

Claims (1)

1. A method for estimating the state of a transport complex network triggered by an event based on an estimation of an aggregator, characterized in that,
the method comprises the following steps:
s1, establishing a state space model of each node of the complex network, as shown in a formula (1):
Figure FDA0003513754100000011
in the formula, k tableShowing the sampling time;
Figure FDA0003513754100000012
for the state of the ith node of a complex network,
Figure FDA0003513754100000013
for the state of the jth node of the complex network,
Figure FDA0003513754100000014
represents nxA Vickers space;
Figure FDA0003513754100000015
for the output of the ith node of a complex network,
Figure FDA0003513754100000016
represents nyA Vickers space;
Figure FDA0003513754100000017
i.e. giTo be defined in a natural number set
Figure FDA0003513754100000018
And nxThe function value is n on the Cartesian product of the Vickers spacexA nonlinear vector value function of values in the Vickers space, g for a real systemiThe second-order partial derivative continuity is met;
A＝(aij)N×Nan external coupling matrix representing a complex network, a if there is a connection between two nodes i and j of the complex networkij> 0, otherwise, aij＝0；aiiSatisfies the following conditions:
Figure FDA0003513754100000019
i＝1，2，...，N，j＝1，2，...，N；
Figure FDA00035137541000000110
an internal coupling matrix representing a complex network;
wherein, γ1，γ2，...，
Figure FDA00035137541000000111
Respectively represent non-negative in-coupling coefficients;
vi(k) which is indicative of a bounded noise, is,
Figure FDA00035137541000000112
Figure FDA00035137541000000113
represents nvA Vickers space; wherein the content of the first and second substances,
Figure FDA00035137541000000114
represents a known holosymmetric polytope, κiIn the case of a known positive scalar quantity,
Figure FDA00035137541000000115
represents nvA dimension unit matrix;
Bi(k)、Ci(k)、Di(k) are all known time-varying matrices;
xi(0) indicating the initial operating conditions of the complex network,<0，Gi，0>is a known holosymmetric polytope;
s2, establishing a model for transmitting data to the centralized member estimator by each node of the complex network under the scheduling of an event trigger mechanism;
for node i of a complex network, in sequence
Figure FDA00035137541000000116
Represents the times at which the node i sends its output, these times being calculated iteratively by equation (2) below:
Figure FDA00035137541000000117
equation (2) shows the trigger time for the ith node of a complex network
Figure FDA00035137541000000118
Later earliest meeting the trigger condition
Figure FDA00035137541000000119
The time of the node i is the next trigger time of the node i;
wherein the content of the first and second substances,
Figure FDA00035137541000000120
respectively representing the s +1 th trigger time and the s +2 th trigger time of the node i;
Figure FDA0003513754100000021
representing a trigger function set in the event trigger device;
Figure FDA0003513754100000022
indicating a trigger condition, σiThe parameter of which is more than 0 is set,
Figure FDA0003513754100000023
output y representing time k of node ii(k) The trigger time closest to time k
Figure FDA0003513754100000024
Output of (2)
Figure FDA0003513754100000025
The Euclidean norm of the difference between;
under the scheduling of an event trigger mechanism, designing a centralized member estimator for a state space model (1) of each node of the complex network;
wherein the input of the membership estimator
Figure FDA0003513754100000026
Expressed as:
Figure FDA0003513754100000027
formula (3) shows that if the moment k is the trigger moment, the input of the collective estimator is the output of the system node at the moment, otherwise, if the moment k is not the trigger moment, the collective estimator adopts the input of the previous trigger moment as the input of the current moment k;
s3, calculating an estimation parameter K of the collective member estimatori(k)；
At time K, the estimated parameters K of the ensemble estimatori(k) Calculated from the following equation (4):
Figure FDA0003513754100000028
wherein, the meaning of each parameter in the formula (4) is as follows:
Figure FDA0003513754100000029
Figure FDA00035137541000000210
Figure FDA00035137541000000211
J(k)＝diag{J1(k)，J2(k)，…，JN(k) 1, 2, …, N, J for ii(k) The method is obtained by the following partial derivation operation:
Figure FDA00035137541000000212
in the formula (I), the compound is shown in the specification,
Figure FDA00035137541000000213
an estimated value representing the state of the ith node of the complex network;
B(k)＝diag{B1(k)，B2(k)，...，BN(k)}；C(k)＝diag{C1(k)，C2(k)，...，CN(k)}；
D(k)＝diag{D1(k)，D2(k)，…，DN(k)}；
Figure FDA00035137541000000214
Figure FDA00035137541000000215
wherein the content of the first and second substances,
Figure FDA00035137541000000216
the matrix G (k) represents a fully-symmetrical multi-cell generation matrix in which the true value of the system state is positioned at the time k;
the matrix g (k) is iteratively calculated by the following equation (5):
G(k+1)＝[G1(k+1) G2(k+1) G3(k+1) G4(k+1)] (5)
wherein the content of the first and second substances,
Figure FDA0003513754100000031
K(k)＝diag{K1(k)，K2(k)，...，KN(k)}；
wherein, K1(k)，K2(k)，...，KN(k) From Ki(k) Respectively taking 1, 2, … and N as the component (i) to obtain;
Figure FDA0003513754100000032
Figure FDA0003513754100000033
an interval matrix with known range;
wherein Δ (k) ═ diag { Δ1(k)，Δ2(k)，…，ΔN(k)}；
Figure FDA0003513754100000034
||Δi(k)||max≤1，||Δi(k)||maxRepresentation matrix deltai(k) Maximum value of the absolute value of the element of (a);
R(k)＝diag{R1(k)，R2(k)，…，RN(k)}；
Figure FDA0003513754100000035
Figure FDA0003513754100000036
Figure FDA0003513754100000037
Figure FDA0003513754100000038
wherein the content of the first and second substances,
Figure FDA0003513754100000039
denotes gi(k，xi(k) Of)The p-th component, p ═ 1, 2, …, nx；
Figure FDA00035137541000000310
Is in a closed interval of [0, 1 ]]A variable of the up value; s e {1, 2, …, nx}，t∈{1，2，…，nx}；
Figure FDA00035137541000000311
Representation matrix
Figure FDA00035137541000000312
Maximum value of the sum of absolute values of the elements of each column of (1);
Gi(k) a generator matrix of fully symmetric polytope representing the true state of the ith node, given directly by g (k);
<0，Gi(k)>a fully symmetric polytope representing the true state containing the ith node;
for the interval matrix X:
Figure FDA00035137541000000313
wherein the content of the first and second substances,
Figure FDA00035137541000000314
an element representing the qth row and the qth column of the interval matrix X;
x qoand
Figure FDA0003513754100000041
is a constant that is known to be a constant,x qothe left end point of the interval is shown,
Figure FDA0003513754100000042
represents the right end of the interval;
the operation mid (X) represents X its midpoint, namely:
Figure FDA0003513754100000043
operations
Figure FDA0003513754100000044
Given by:
Figure FDA0003513754100000045
wherein the content of the first and second substances,
Figure FDA0003513754100000046
Figure FDA0003513754100000047
representing variable definition symbols;
thereby calculating
Figure FDA0003513754100000048
And
Figure FDA0003513754100000049
then calculating to obtain G2(k+1)；
G3(k+1)＝-K(k)∑；
G4(k+1)＝(B(k)-K(k)D(k))Gv；
G (k) has an initial value of G (0) ═ diag { G1，0，G2，0，…GN，0}，Gj，0Denotes the known matrix, j ═ 1, 2, …, N;
s4, constructing a set member estimator, and calculating a full-symmetry multi-cell estimation set containing the real state of the complex network, wherein the expression of the full-symmetry multi-cell estimation set is shown as a formula (6):
Figure FDA00035137541000000410
wherein, formula (6) represents a fully symmetric multi-cell shape containing the true value of the system state;
center of holosymmetric polycell
Figure FDA00035137541000000411
As shown in equation (7):
Figure FDA00035137541000000412
in the formula (I), the compound is shown in the specification,
Figure FDA00035137541000000413
and representing the estimated value of the ith node state of the complex network, wherein the iterative formula is as follows:
Figure FDA00035137541000000414
in the formula (I), the compound is shown in the specification,
Figure FDA00035137541000000415
represents an initial value of the iteration; generating a matrix g (k) iteratively calculated by equation (5);
when estimator parameter Ki(k) When the formula (4) is adopted, the F-norm of the fully-symmetric polytope obtained by the formulas (6) to (8) is the smallest, and the size of the state estimation set including the true state of the complex network is the smallest in the F-norm sense of the generator matrix.
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