CN113223721A - Novel prediction control model for coronavirus pneumonia - Google Patents

Novel prediction control model for coronavirus pneumonia Download PDF

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CN113223721A
CN113223721A CN202110309282.3A CN202110309282A CN113223721A CN 113223721 A CN113223721 A CN 113223721A CN 202110309282 A CN202110309282 A CN 202110309282A CN 113223721 A CN113223721 A CN 113223721A
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coronavirus pneumonia
novel coronavirus
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CN113223721B (en
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张俊锋
张素焕
焦晨旭
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Hangzhou Dianzi University
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    • G—PHYSICS
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    • G16H50/00—ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics
    • G16H50/50—ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics for simulation or modelling of medical disorders
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    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16H—HEALTHCARE INFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR THE HANDLING OR PROCESSING OF MEDICAL OR HEALTHCARE DATA
    • G16H50/00—ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics
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    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16H—HEALTHCARE INFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR THE HANDLING OR PROCESSING OF MEDICAL OR HEALTHCARE DATA
    • G16H50/00—ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics
    • G16H50/80—ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics for detecting, monitoring or modelling epidemics or pandemics, e.g. flu
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Abstract

The invention discloses a novel coronavirus pneumonia prediction control model. The establishment of the model of the invention is realized as follows: step 1, establishing a state space model of a novel coronavirus pneumonia model; step 2, designing a time-varying matrix processing mechanism; step 3, constructing an event trigger condition for the prediction control of the novel coronavirus pneumonia model; step 4, designing a model predictive control framework; step 5, designing an event trigger model prediction controller; step 6, verifying the positive degree of the novel coronavirus pneumonia model prediction control; and 7, verifying the robust stability of the novel coronavirus pneumonia model prediction control. The method utilizes a positive system to carry out SEIR type modeling on the novel coronavirus pneumonia epidemic situation, designs a model predictive controller, optimally analyzes performance indexes and the like, and provides a theoretical method for predicting and estimating the development trend of the novel coronavirus pneumonia epidemic situation and adopting a corresponding control strategy.

Description

Novel prediction control model for coronavirus pneumonia
Technical Field
The invention belongs to the technical field of automation, and relates to a model predictive control, optimization control, state feedback control and other methods based on a novel coronavirus pneumonia epidemic situation.
Background
In recent years, with the development of internet technology and gene sequencing technology, multisource information such as virus gene data is used for analyzing the virus transmission process, and infectious disease modeling methods enter the era of diversified development. Researchers comprehensively utilize mathematical and statistical models to more accurately model and analyze epidemic rules of infectious diseases based on multi-source information. Since the outbreak of new coronavirus pneumonia in 2019, the daily life and economic development of people all over the world are seriously influenced. With the development and continuous diffusion of epidemic situations, how to effectively predict and control the epidemic situations becomes a focus problem. Among these, the SEIR model is a commonly used infectious disease modeling method. After the novel coronavirus pneumonia epidemic situation occurs, a plurality of research teams at home and abroad research and analyze the development situation of the novel coronavirus pneumonia epidemic situation by using a kinetic equation model.
In real life, there are many quantities that are non-negative, e.g., urban traffic flow, network traffic, number of species, concentration of substances, etc. Such non-negative quantity constituted systems can be analyzed with positive system modeling. However, the existing models of infectious diseases use general systematic methods to analyze the virus spreading process and predict the number of infected persons. These models ignore the essential nature of the system, i.e., S, E, I, R the population numbers of the four classes are all non-negative. The method has the advantages that the characteristics are considered, the positive system model is established, the positive system method is adopted for analysis, the accuracy is high, corresponding control measures are adopted, and the applicability is high.
Disclosure of Invention
The invention aims to provide a novel coronavirus pneumonia prediction control model aiming at the development trend of a novel coronavirus pneumonia epidemic situation.
The concrete steps of the model of the invention comprise:
step 1, establishing a state space model of a novel coronavirus pneumonia model;
step 2, designing a time-varying matrix processing method;
step 3, constructing an event trigger condition for the prediction control of the novel coronavirus pneumonia model;
step 4, designing a model predictive control framework;
step 5, designing an event trigger model prediction controller;
step 6, analyzing the positive degree of the novel coronavirus pneumonia model prediction control;
and 7, analyzing the robust stability of the novel coronavirus pneumonia model prediction control.
Step 1, establishing an SEIR model aiming at the epidemic situation of the novel coronavirus pneumonia, acquiring real-time data according to the change of various groups of the SEIR model, and establishing a state space model of the novel coronavirus pneumonia SEIR, wherein the form is as follows:
x(k+1)＝A(k)x(k)+B(k)(α(k)sat(u(k))+(1-α(k))β(k)u(k)), (1)
wherein the content of the first and second substances,
Figure BDA0002989108580000021
the number of various types of crowds in the SEIR model at the moment k is shown, n is the number of the types of the crowds,
Figure BDA0002989108580000022
is the isolation measure taken at time k, α (k) indicates whether the isolation measure u (k) taken is saturated, β (k) indicates whether the isolation measure is taken, and sat (u (k)) is (sat (u (k)), (1(k)),...,sat(um(k)))TWhich represents a function of the saturation vector and,
Figure BDA0002989108580000023
and
Figure BDA0002989108580000024
a weighting matrix representing the k moment is obtained by data collected by the sensor at the k moment (the weighting matrix at all the moments is a time-varying matrix); in consideration of the fact that the SEIR model of the novel coronavirus pneumonia requires that the number of various groups of people is non-negative, the novel coronavirus pneumonia is modeled according to a positive system model.
Step 2, designing a time-varying matrix processing mechanism, which is specifically realized as follows:
assuming that the sensors can acquire a set of values, time-varying matrices a (k) and b (k) are designed to be in the following interval uncertainty set:
Figure BDA0002989108580000025
wherein the content of the first and second substances,
Figure BDA00029891085800000213
and
Figure BDA00029891085800000214
wherein the content of the first and second substances,AandBthe lower bound is represented by the lower bound,
Figure BDA0002989108580000026
and
Figure BDA0002989108580000027
representing an upper bound;
step 3, constructing event trigger conditions for the prediction control of the novel coronavirus pneumonia model, namely taking isolation measures when various crowds meet the isolation conditions, wherein the specific construction form is as follows:
Figure BDA0002989108580000028
wherein the constant ∈ is given and satisfies
Figure BDA0002989108580000029
Error satisfaction
Figure BDA00029891085800000210
Wherein the content of the first and second substances,
Figure BDA00029891085800000211
is the sampling state, ksAnd ks+1Respectively the s-th and (s +1) -th event trigger times, where k e ks,ks+1)，
Figure BDA00029891085800000212
And 4, designing a model predictive control framework, wherein the specific design steps are as follows:
step 4.1 isolation measure constraints for given system state and system inputs:
Figure BDA0002989108580000031
wherein δ > 0 and η > 0.
Step 4.2, designing an event trigger control law:
Figure BDA0002989108580000032
wherein the content of the first and second substances,
Figure BDA0002989108580000033
is the controller gain.
Step 4.3 the following optimization problem is solved by the designed event trigger control law:
Figure BDA0002989108580000034
the performance indicator function here satisfies:
Figure BDA0002989108580000035
wherein x (k + i | k) represents the number of the various groups of people predicted in the step i based on the number of the various groups of people at the kth time in the SEIR model,
Figure BDA0002989108580000036
indicating future time k predictive control measures and, in addition,
Figure BDA0002989108580000037
and
Figure BDA0002989108580000038
step 4.4, constructing a linear complementary positive Lyapunov function V (i, k):
V(i,k)＝x(k+i|k)Tv, (9)
wherein
Figure BDA0002989108580000039
Introducing a robust stability condition:
Figure BDA00029891085800000310
then, the expectation and summation operation is obtained for (10), and the following can be obtained:
Figure BDA00029891085800000311
further, obtain
Figure BDA00029891085800000312
Then, the minimum gamma (k) is calculated to obtain
V(0,k)＝x(k|k)Tv≤γ(k)。 (13)
Step 5, designing an event trigger model prediction controller, which comprises the following specific steps:
if there is a constant μ1＞1,0＜μ2＜1,μ3> 0, gamma (k) > 0 and
Figure BDA0002989108580000041
(Vector)
Figure BDA00029891085800000417
ξ(k),ξ(ι)(k),ζ(k),ζ(ι)(k),
Figure BDA0002989108580000042
so that the following inequality and step 4.4 hold, the state space model established in step 1 is positive, stable, and meets the performance index in step 4.3 based on step 4.2, the feedback controller gain, and the attraction domain gain. For any initial set of states Φ, the states remain in the set Ψ (H)i) In (1). The inequality includes the following:
minγ(k),(14)
Figure BDA0002989108580000043
Figure BDA0002989108580000044
Figure BDA0002989108580000045
Figure BDA0002989108580000046
Figure BDA0002989108580000047
Figure BDA0002989108580000048
Figure BDA0002989108580000049
Figure BDA00029891085800000410
Figure BDA00029891085800000416
the gain of the feedback controller is as follows:
Figure BDA00029891085800000411
the attraction domain gains are as follows:
Figure BDA00029891085800000412
wherein the content of the first and second substances,
Figure BDA00029891085800000413
i 1, 1., m, and p 1., L,
Figure BDA00029891085800000414
and
Figure BDA00029891085800000415
and 6, carrying out a model predictive control positive analysis process as follows:
step 6.1 assume that x (t) e Ψ (H)i) Then there are:
Figure BDA0002989108580000051
wherein DlAnd
Figure BDA0002989108580000052
is a diagonal matrix with diagonal elements of 0 or 1 and
Figure BDA0002989108580000053
(I is an identity matrix),
Figure BDA0002989108580000054
then, in the intervalk∈(kp,kp+1) The inside is as follows:
Figure BDA0002989108580000055
given initial conditions
Figure BDA0002989108580000059
The following can be obtained:
Figure BDA0002989108580000056
for k e (k)p,kp+1) Can obtain the product
Figure BDA0002989108580000057
At event trigger k0At a moment have
Figure BDA0002989108580000058
Reuse of
Figure BDA0002989108580000068
And
Figure BDA0002989108580000069
can obtain the product
Figure BDA0002989108580000061
Thus, the model is established at (k)p,kp+1) The event triggering time within is positive.
Step 6.2 Interval uncertainty method considering time-varying matrix, one can obtain
Figure BDA0002989108580000062
Further, the method can be obtained as follows:
Figure BDA0002989108580000063
further obtain the
Figure BDA0002989108580000066
Derived by recursive derivation
Figure BDA0002989108580000067
Therefore, the interval system model is positive.
Step 7, the robust stability analysis process of the novel coronavirus pneumonia model predictive control is as follows:
according to step 6.1
Figure BDA0002989108580000065
Figure BDA0002989108580000071
Combining step 4.4 to obtain
Figure BDA0002989108580000072
This is equivalent to
Figure BDA0002989108580000073
Further, it is possible to prevent the occurrence of,
Figure BDA0002989108580000074
Figure BDA0002989108580000081
next, consider DlThree value cases of (2):
case 1: dlWhen equal to 0, there is
Figure BDA0002989108580000082
Further, there are
Figure BDA0002989108580000083
In combination with the step 6, it is possible to obtain,
Figure BDA0002989108580000084
the robust stability condition in step 4.4 can thus be established.
Case 2: dlWhen I, the method is similar to that of case 1
Figure BDA0002989108580000091
Further, it is possible to prevent the occurrence of,
Figure BDA0002989108580000092
in combination with the step 6, it is possible to obtain,
Figure BDA0002989108580000093
the robust stability condition in step 4.4 can thus be established.
Case 3: dlNot equal to 0 and DlWhen not equal to I, it can be obtained according to claim 6
Figure BDA0002989108580000094
Figure BDA0002989108580000095
Figure BDA0002989108580000096
Figure BDA0002989108580000097
Figure BDA0002989108580000098
Figure BDA0002989108580000101
Further, in the present invention,
Figure BDA0002989108580000102
in combination with the step 6, it is possible to obtain,
Figure BDA0002989108580000103
the robust stability condition in step 4.4 can thus be established.
The performance index in step 4.3 can be solved by step 5.
The invention has the following beneficial effects:
the invention provides a novel method for predicting and estimating the development trend of the coronavirus pneumonia epidemic situation through methods such as model construction, model prediction controller design, optimal performance index analysis and the like. The method can effectively predict the development trend of the novel coronavirus pneumonia epidemic situation and carry out corresponding control.
Drawings
Fig. 1 is a block diagram of the present invention.
Detailed Description
As shown in fig. 1, the present embodiment provides a model predictive control method based on novel coronavirus pneumonia, which comprises the following specific steps:
step 1, establishing an SEIR model aiming at the epidemic situation of the novel coronavirus pneumonia, acquiring real-time data according to the change of various groups of the SEIR model, and establishing a state space model of the novel coronavirus pneumonia SEIR, wherein the form is as follows:
x(k+1)＝A(k)x(k)+B(k)(α(k)sat(u(k))+(1-α(k))β(k)u(k)), (52)
wherein the content of the first and second substances,
Figure BDA0002989108580000111
the number of various types of crowds in the SEIR model at the moment k is shown, n is the number of the types of the crowds,
Figure BDA0002989108580000112
is the isolation measure taken at time k, α (k) indicates whether the isolation measure u (k) taken is saturated, β (k) indicates whether the isolation measure is taken, and sat (u (k)) is (sat (u (k)), (1(k)),...,sat(um(k)))TWhich represents a function of the saturation vector and,
Figure BDA0002989108580000113
and
Figure BDA0002989108580000114
a weighting matrix representing the k moment is obtained by data collected by the sensor at the k moment (the weighting matrix at all the moments is a time-varying matrix); considering the actual situation that the SEIR model of the novel coronavirus pneumonia requires that the number of various crowds is non-negative, the novel coronavirus pneumonia is processed according to the positive system modelAnd (6) modeling.
Step 2, designing a time-varying matrix processing mechanism, which is specifically realized as follows:
assuming that the sensors can acquire a set of values, time-varying matrices a (k) and b (k) are designed to be in the following interval uncertainty set:
Figure BDA0002989108580000115
wherein the content of the first and second substances,
Figure BDA00029891085800001116
and
Figure BDA00029891085800001117
wherein the content of the first and second substances,AandBthe lower bound is represented by the lower bound,
Figure BDA0002989108580000116
and
Figure BDA0002989108580000117
representing an upper bound;
step 3, constructing event trigger conditions for the prediction control of the novel coronavirus pneumonia model, namely taking isolation measures when various crowds meet the isolation conditions, wherein the specific construction form is as follows:
Figure BDA0002989108580000118
wherein the constant ∈ is given and satisfies
Figure BDA0002989108580000119
Error of the measurement
Figure BDA00029891085800001110
Figure BDA00029891085800001111
Is the sampling state, ksAnd ks+1Respectively the s-th and (s +1) -th event trigger time, whichIn, k is as [ k ]s,ks+1)，
Figure BDA00029891085800001112
And 4, designing a model predictive control framework, wherein the specific design steps are as follows:
step 4.1 isolation measure constraints for given system state and system inputs:
Figure BDA00029891085800001113
wherein δ > 0 and η > 0.
Step 4.2, designing an event trigger control law:
Figure BDA00029891085800001114
wherein the content of the first and second substances,
Figure BDA00029891085800001115
is the controller gain.
Step 4.3 the following optimization problem is solved by the designed event trigger control law:
Figure BDA0002989108580000121
the performance indicator function here satisfies:
Figure BDA0002989108580000122
wherein x (k + i | k) represents the number of the various groups of people predicted in the step i based on the number of the various groups of people at the kth time in the SEIR model,
Figure BDA0002989108580000123
indicating future time k predictive control measures and, in addition,
Figure BDA0002989108580000124
and
Figure BDA0002989108580000125
step 4.4, constructing a linear complementary positive Lyapunov function V (i, k):
V(i,k)＝x(k+i|k)Tv, (60)
wherein
Figure BDA0002989108580000126
Introducing a robust stability condition:
Figure BDA0002989108580000127
then, the expectation and summation operation is obtained for (10), and the following can be obtained:
Figure BDA0002989108580000128
further, obtain
Figure BDA0002989108580000129
Then, the minimum gamma (k) is calculated to obtain
V(0,k)＝x(k|k)Tv≤γ(k)。 (64)
Step 5, designing an event trigger model prediction controller, which comprises the following specific steps:
if there is a constant μ1＞1,0＜μ2＜1,μ3> 0, gamma (k) > 0 and
Figure BDA00029891085800001210
(Vector)
Figure BDA00029891085800001212
ξ(k),ξ(ι)(k),ζ(k),ζ(ι)(k),
Figure BDA00029891085800001211
so that the following inequality and step 4.4 hold, the state space model established in step 1 is positive, stable, and meets the performance index in step 4.3 based on step 4.2, the feedback controller gain, and the attraction domain gain. For any initial set of states Φ, the states remain in the set Ψ (H)i) In (1). The inequality includes the following:
minγ(k), (65)
Figure BDA0002989108580000131
Figure BDA0002989108580000132
Figure BDA0002989108580000133
Figure BDA0002989108580000134
Figure BDA0002989108580000135
Figure BDA0002989108580000136
Figure BDA0002989108580000137
Figure BDA0002989108580000138
Figure BDA00029891085800001318
the gain of the feedback controller is as follows:
Figure BDA0002989108580000139
the attraction domain gains are as follows:
Figure BDA00029891085800001310
wherein the content of the first and second substances,
Figure BDA00029891085800001311
i 1, 1., m, and p 1., L,
Figure BDA00029891085800001312
and
Figure BDA00029891085800001313
and 6, carrying out a model predictive control positive analysis process as follows:
step 6.1 assume that x (t) e Ψ (H)i) Then there are:
Figure BDA00029891085800001314
wherein DlAnd
Figure BDA00029891085800001315
is a diagonal matrix with diagonal elements of 0 or 1 and
Figure BDA00029891085800001316
(I is an identity matrix of appropriate dimensions),
Figure BDA00029891085800001317
then, in the interval k ∈ (k)p,kp+1) The inside is as follows:
Figure BDA0002989108580000141
given initial conditions
Figure BDA0002989108580000148
The following can be obtained:
Figure BDA0002989108580000142
for k e (k)p,kp+1) Can obtain the product
Figure BDA0002989108580000143
At event trigger k0At a moment have
Figure BDA0002989108580000144
Reuse of
Figure BDA0002989108580000146
And
Figure BDA0002989108580000147
can obtain the product
Figure BDA0002989108580000145
Thus, the model is established at (k)p,kp+1) The event triggering time within is positive.
Step 6.2 Interval uncertainty method considering time-varying matrix, one can obtain
Figure BDA0002989108580000151
Further, the method can be obtained as follows:
Figure BDA0002989108580000152
further obtain the
Figure BDA0002989108580000156
Derived by recursive derivation
Figure BDA0002989108580000157
Therefore, the interval system model is positive.
Step 7, the robust stability analysis process of the novel coronavirus pneumonia model predictive control is as follows:
according to step 6.1
Figure BDA0002989108580000154
Combining step 4.4 to obtain
Figure BDA0002989108580000155
Figure BDA0002989108580000161
This is equivalent to
Figure BDA0002989108580000162
Further, it is possible to prevent the occurrence of,
Figure BDA0002989108580000163
next, consider DlThree value cases of (2):
case 1: dlWhen equal to 0, there is
Figure BDA0002989108580000171
Further, there are
Figure BDA0002989108580000172
Combining step 6 can obtain:
Figure BDA0002989108580000173
the robust stability condition in step 4.4 can thus be established.
Case 2: dlWhen I, the method is similar to that of case 1
Figure BDA0002989108580000174
Further, it is possible to prevent the occurrence of,
Figure BDA0002989108580000175
Figure BDA0002989108580000181
combining step 6 can obtain:
Figure BDA0002989108580000182
the robust stability condition in step 4.4 can thus be established. Case 3: dlNot equal to 0 and DlWhen not equal to I, it can be obtained according to claim 6
Figure BDA0002989108580000183
Figure BDA0002989108580000184
Figure BDA0002989108580000185
Figure BDA0002989108580000186
Figure BDA0002989108580000187
Figure BDA0002989108580000188
Further, in the present invention,
Figure BDA0002989108580000189
Figure BDA0002989108580000191
combining step 6 can obtain:
Figure BDA0002989108580000192
the robust stability condition in step 4.4 can thus be established.
The performance index in step 4.3 can be solved by optimizing claim 6.

Claims (8)

1. A novel coronavirus pneumonia prediction control model is characterized in that the model is established as follows:
step 1, establishing a state space model of a novel coronavirus pneumonia model;
step 2, designing a time-varying matrix processing mechanism;
step 3, constructing an event trigger condition for the prediction control of the novel coronavirus pneumonia model;
step 4, designing a model predictive control framework;
step 5, designing an event trigger model prediction controller;
step 6, verifying the positive degree of the novel coronavirus pneumonia model prediction control;
and 7, verifying the robust stability of the novel coronavirus pneumonia model prediction control.
2. The model of claim 1, wherein step 1 is to create an SEIR model for the new coronavirus pneumonia epidemic situation, and to collect real-time data according to the variation of various groups of people of the SEIR model, and to create a state space model of the new coronavirus pneumonia SEIR, and the form is as follows:
x(k+1)＝A(k)x(k)+B(k)(α(k)sat(u(k))+(1-α(k))β(k)u(k)),(1)
wherein the content of the first and second substances,
Figure RE-FDA0003127430290000011
the number of various types of crowds in the SEIR model at the moment k is shown, n is the number of the types of the crowds,
Figure RE-FDA0003127430290000012
is the isolation measure taken at time k, α (k) indicates whether the isolation measure u (k) taken is saturated, β (k) indicates whether the isolation measure is taken, and sat (u (k)) is (sat (u (k)), (1(k)),...,sat(um(k)))TWhich represents a function of the saturation vector and,
Figure RE-FDA0003127430290000013
and
Figure RE-FDA0003127430290000014
a weighting matrix representing the k moment is obtained by data collected by the sensor at the k moment; in consideration of the fact that the SEIR model of the novel coronavirus pneumonia requires that the number of various groups of people is non-negative, the novel coronavirus pneumonia is modeled according to a positive system model.
3. The model for predictive control of coronavirus pneumonia as claimed in claim 2, wherein step 2 designs a time-varying matrix processing mechanism, which is implemented as follows:
assuming that the sensors can acquire a set of values, time-varying matrices a (k) and b (k) are designed to be in the following interval uncertainty set:
Figure RE-FDA0003127430290000015
wherein the content of the first and second substances,
Figure RE-FDA0003127430290000016
and
Figure RE-FDA0003127430290000017
wherein the content of the first and second substances,AandBthe lower bound is represented by the lower bound,
Figure RE-FDA0003127430290000018
and
Figure RE-FDA0003127430290000019
representing an upper bound.
4. The model of claim 3, wherein the step 3 is to construct event triggering conditions for the predictive control of the novel coronavirus pneumonia model, that is, to take isolation measures until various groups of people meet the isolation conditions, and the model is constructed in the following specific manner:
Figure RE-FDA0003127430290000021
wherein the constant ∈ is given and satisfies
Figure RE-FDA0003127430290000022
Error of the measurement
Figure RE-FDA0003127430290000023
Satisfies the following conditions:
Figure RE-FDA0003127430290000024
wherein the content of the first and second substances,
Figure RE-FDA0003127430290000025
is the sampling state, ksAnd ks+1Respectively the s-th and (s +1) -th event trigger times, where k e ks,ks+1)，
Figure RE-FDA0003127430290000026
5. The model for predictive control of coronavirus pneumonia as claimed in claim 4, wherein step 4 is to design a model predictive control framework by the following specific steps:
step 4.1 isolation measure constraints for given system state and system inputs:
Figure RE-FDA0003127430290000027
wherein δ > 0 and η > 0;
step 4.2, designing an event trigger control law:
Figure RE-FDA0003127430290000028
wherein the content of the first and second substances,
Figure RE-FDA0003127430290000029
is the controller gain;
step 4.3 the following optimization problem is solved by the designed event trigger control law:
Figure RE-FDA00031274302900000210
the performance indicator function here satisfies:
Figure RE-FDA00031274302900000211
wherein x (k + i | k) represents the number of the various groups of people predicted in the step i based on the number of the various groups of people at the kth time in the SEIR model,
Figure RE-FDA00031274302900000212
indicating future time k predictive control measures and, in addition,
Figure RE-FDA00031274302900000213
and
Figure RE-FDA00031274302900000214
step 4.4, constructing a linear complementary positive Lyapunov function V (i, k):
V(i,k)＝x(k+i|k)Tv, (9)
wherein
Figure RE-FDA00031274302900000215
Introducing a robust stability condition:
Figure RE-FDA00031274302900000216
then, the expectation and summation operation is obtained for (10), and the following can be obtained:
Figure RE-FDA00031274302900000217
further, obtain
Figure RE-FDA0003127430290000031
Then, the minimum gamma (k) is calculated to obtain
V(0,k)＝x(k|k)Tv≤γ(k)； (13)。
6. The predictive control model for the novel coronavirus pneumonia according to claim 5, wherein the event-triggered model predictive controller is designed in step 5 and is implemented as follows:
if there is a constant μ1＞1,0＜μ2＜1,μ3> 0, gamma (k) > 0 and
Figure RE-FDA0003127430290000032
(Vector)
Figure RE-FDA0003127430290000033
ξ(k),ξ(i)(k),ζ(k),ζ(i)(k),
Figure RE-FDA0003127430290000034
if inequalities (14) - (23) and step 4.4 are satisfied, the state space model established in step 1 is positive and stable based on step 4.2, the feedback controller gain and the attraction domain gain, and meets the performance index in step 4.3; for any initial set of states Φ, the states remain in the set Ψ (H)i) Performing the following steps; the inequality includes the following：
minγ(k), (14)
Figure RE-FDA0003127430290000035
Figure RE-FDA0003127430290000036
Figure RE-FDA0003127430290000037
Figure RE-FDA0003127430290000038
Figure RE-FDA0003127430290000039
Figure RE-FDA00031274302900000310
Figure RE-FDA00031274302900000311
Figure RE-FDA00031274302900000312
Figure RE-FDA00031274302900000313
The gain of the feedback controller is as follows:
Figure RE-FDA00031274302900000314
the attraction domain gains are as follows:
Figure RE-FDA0003127430290000041
wherein the content of the first and second substances,
Figure RE-FDA0003127430290000042
and p 1, L,
Figure RE-FDA0003127430290000043
and
Figure RE-FDA0003127430290000044
7. the model of claim 6, wherein the model predictive control of coronavirus pneumonia comprises the following steps:
step 6.1 assume that x (t) e Ψ (H)i) Then there are:
Figure RE-FDA0003127430290000045
wherein DlAnd
Figure RE-FDA0003127430290000046
is a diagonal matrix with diagonal elements of 0 or 1 and
Figure RE-FDA0003127430290000047
(I is an identity matrix),
Figure RE-FDA0003127430290000048
then, in the interval k ∈ (k)p,kp+1) The inside is as follows:
Figure RE-FDA0003127430290000049
given initial conditions
Figure RE-FDA00031274302900000410
The following can be obtained:
Figure RE-FDA00031274302900000411
for k e (k)p,kp+1) Can obtain the product
Figure RE-FDA00031274302900000412
At event trigger k0At a moment have
Figure RE-FDA0003127430290000051
Reuse of
Figure RE-FDA0003127430290000057
And
Figure RE-FDA0003127430290000058
can obtain the product
Figure RE-FDA0003127430290000052
Thus, the model is established at (k)p,kp+1) The event triggering time within is positive;
step 6.2 considering the interval uncertainty method of the time-varying matrix, the following can be obtained:
Figure RE-FDA0003127430290000053
further, the method can be obtained as follows:
Figure RE-FDA0003127430290000054
further obtain the
Figure RE-FDA0003127430290000055
Derived by recursive derivation
Figure RE-FDA0003127430290000056
Therefore, the interval system model is positive.
8. The model for predictive control of coronavirus pneumonia of claim 7, wherein the robust stability analysis process of the predictive control of the novel coronavirus pneumonia model in step 7 is as follows:
according to step 6.1
Figure RE-FDA0003127430290000061
Combining step 4.4 to obtain
Figure RE-FDA0003127430290000062
Equation (35) is equivalent to:
Figure RE-FDA0003127430290000063
further equivalent to:
Figure RE-FDA0003127430290000071
then consider DlThree value cases of (2):
case 1: dlWhen equal to 0, there is
Figure RE-FDA0003127430290000072
Further, there are:
Figure RE-FDA0003127430290000073
combining step 6 can obtain:
Figure RE-FDA0003127430290000081
the robust stability condition in step 4.4 can thus be found to hold;
case 2: dlWhen I, the method is similar to that of case 1
Figure RE-FDA0003127430290000082
And further:
Figure RE-FDA0003127430290000083
combining step 6 can obtain:
Figure RE-FDA0003127430290000084
the robust stability condition in step 4.4 can thus be found to hold;
case 3: dlNot equal to 0 and DlWhen not equal to I, obtainable according to claim 6
Figure RE-FDA0003127430290000085
Figure RE-FDA0003127430290000086
Figure RE-FDA0003127430290000087
Figure RE-FDA0003127430290000091
Figure RE-FDA0003127430290000092
Figure RE-FDA0003127430290000093
Further:
Figure RE-FDA0003127430290000094
combining step 6 can obtain:
Figure RE-FDA0003127430290000095
the robust stability condition in step 4.4 can thus be established.
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Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2016022650A1 (en) * 2014-08-06 2016-02-11 Regents Of The University Of California Moving-horizon state-initializer for control applications
CN107797451A (en) * 2017-10-21 2018-03-13 辽宁石油化工大学 Uncertain system Delay Dependent Robust constrained forecast control method under unknown disturbances
US10178120B1 (en) * 2015-07-23 2019-01-08 Hrl Laboratories, Llc Method for determining contagion dynamics on a multilayer network
CN111611297A (en) * 2020-05-21 2020-09-01 中南大学 Propagation model establishing method considering parameter time-varying property and prediction method thereof
CN111863276A (en) * 2020-07-21 2020-10-30 集美大学 Hand-foot-and-mouth disease prediction method using fine-grained data, electronic device, and medium
CN112201362A (en) * 2020-10-19 2021-01-08 中国计量大学 New coronary pneumonia epidemic propagation prediction method
US20210045640A1 (en) * 2019-08-16 2021-02-18 Poltorak Technologies, LLC Device and method for medical diagnostics

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2016022650A1 (en) * 2014-08-06 2016-02-11 Regents Of The University Of California Moving-horizon state-initializer for control applications
US10178120B1 (en) * 2015-07-23 2019-01-08 Hrl Laboratories, Llc Method for determining contagion dynamics on a multilayer network
CN107797451A (en) * 2017-10-21 2018-03-13 辽宁石油化工大学 Uncertain system Delay Dependent Robust constrained forecast control method under unknown disturbances
US20210045640A1 (en) * 2019-08-16 2021-02-18 Poltorak Technologies, LLC Device and method for medical diagnostics
CN111611297A (en) * 2020-05-21 2020-09-01 中南大学 Propagation model establishing method considering parameter time-varying property and prediction method thereof
CN111863276A (en) * 2020-07-21 2020-10-30 集美大学 Hand-foot-and-mouth disease prediction method using fine-grained data, electronic device, and medium
CN112201362A (en) * 2020-10-19 2021-01-08 中国计量大学 New coronary pneumonia epidemic propagation prediction method

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
陈友春: "状态空间模型及其在传染病发病率预测中的应用", 《南京医科大学学报》, 28 February 2015 (2015-02-28), pages 275 - 278 *

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