Задачі автоматизованого керування динамічними процесами системного забезпечення безпеки України на основі моделей імпульсних процесів у когнітивних картах. Частина 1. Забезпечення демографічної безпеки
The paper provides a cognitive map (CM) of demographic security and a dynamic model of CM impulse processes described as a difference equations system (Robert’s equations). The external control vector for the CM impulse process is implemented by means of varying the CM nodes’ coordinates. A closed-l...
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| author | Romanenko, Viktor Miliavskyi, Yurii |
| author_facet | Romanenko, Viktor Miliavskyi, Yurii |
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| description | The paper provides a cognitive map (CM) of demographic security and a dynamic model of CM impulse processes described as a difference equations system (Robert’s equations). The external control vector for the CM impulse process is implemented by means of varying the CM nodes’ coordinates. A closed-loop control system for the CM impulse process is proposed. It includes a multivariate discrete controller designed based on an automated control theory method, which generates the chosen control actions. We solve a discrete controller design problem for automated control of dynamic processes to ensure demographic security. The controller suppresses external and internal disturbances during CM impulse processes control based on the invariant ellipsoids method. The paper presents an algorithm for CM weights identification based on the recurrent least squares method. We present the results of a qualitative research study on dynamic processes related to demographic security in Ukraine under various disturbances during martial law. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2025.3.06 |
| first_indexed | 2025-11-09T02:11:02Z |
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V. Romanenko, Y. Miliavskyi, 2025
76 ISSN 1681–6048 System Research & Information Technologies, 2025, № 3
TIДC
ПРОБЛЕМИ ПРИЙНЯТТЯ РІШЕНЬ ТА
УПРАВЛІННЯ В ЕКОНОМІЧНИХ, ТЕХНІЧНИХ,
ЕКОЛОГІЧНИХ І СОЦІАЛЬНИХ СИСТЕМАХ
UDC 62.50
DOI: 10.20535/SRIT.2308-8893.2025.3.06
AUTOMATED CONTROL OF DYNAMIC SYSTEMS
FOR ENSURING UKRAINE’S SECURITY USING COGNITIVE
MAP IMPULSE PROCESS MODELS.
PART 1. DEMOGRAPHIC SECURITY
V. ROMANENKO, Y. MILIAVSKYI
Abstract. The paper provides a cognitive map (CM) of demographic security and a
dynamic model of CM impulse processes described as a difference equations system
(Robert’s equations). The external control vector for the CM impulse process is im-
plemented by means of varying the CM nodes’ coordinates. A closed-loop control
system for the CM impulse process is proposed. It includes a multivariate discrete
controller designed based on an automated control theory method, which generates
the chosen control actions. We solve a discrete controller design problem for auto-
mated control of dynamic processes to ensure demographic security. The controller
suppresses external and internal disturbances during CM impulse processes control
based on the invariant ellipsoids method. The paper presents an algorithm for CM
weights identification based on the recurrent least squares method. We present the
results of a qualitative research study on dynamic processes related to demographic
security in Ukraine under various disturbances during martial law.
Keywords: cognitive map, demographic security, invariant ellipsoid, linear matrix
inequalities, impulse process.
INTRODUCTION
To study the dynamic processes for system ensuring of Ukraine’s demographic
security we use cognitive modelling, which is one of the most relevant areas of
scientific and practical research of complex systems of different nature now.
Cognitive modeling is based on the notion of a cognitive map (CM), which is a
weighted directed graph, its nodes reflect coordinates (factors, concepts) of the
complex system and weighted edges (arcs) of the graph describe interrelations
between CM nodes. When disturbances affect CM nodes, we can observe impulse
transitional process, its dynamics is described by the difference equation [1]:
n
j
jiji kyaky
1
),()1( (1)
where nikykyky iii ,...,2,1),1()()( , ija — weight of an edge connecting
the j -th node and the i -th one. Equation (1) describes the free motion of the i -th
Automated control of dynamic systems for ensuring Ukraine’s security using cognitive…
Системні дослідження та інформаційні технології, 2025, № 3 77
node of CM without external control impact. We can write this equation in vec-
tor-matrix form:
),()1( kYAkY (2)
where )1()()( kYkYkY , A is a weighted adjacency matrix of the CM of
size nn .
In order to implement control of the CM impulse process (2) based on mod-
ern control theory it is necessary to be able to physically change some coordinates
of CM nodes as control actions. Then we can describe the forced motion of the
CM impulse process under external control as the difference equation:
),()()1( kUBkYAkY (3)
where )1()()( kUkUkU — vector of controls increments with size nm .
The operator fills the control matrix )( mnB and in its simplest form uses ones
and zeros.
If the CM has unmeasurable coordinates, they can be included into equation
(3) as disturbances. In such a case the impulse process (3) will be written as
),()()()1( kkUBkYAkY (4)
where )1()()( kkk — vector of unmeasurable coordinates (disturbances).
PROBLEM STATEMENT
The first problem is to create a controlled dynamic model of CM impulse process
describing multivariate demographic process in Ukraine. The second problem is
to research and develop the system for suppressing constrained internal and exter-
nal disturbances by means of control of the demographic security CM impulse
process during martial law. The third problem is to implement an adaptive CM
impulse process control under unknown or unmeasurable coefficients of the adja-
cency matrix A; this control should combine procedures of the matrix A elements’
estimation during the transient process and usage of these estimates of the matrix
 for a control vector design. The forth problem is to perform a simulation of the
designed closed-loop control system and to research dynamic processes’ quality
with respect to ensuring demographic security of Ukraine under different distur-
bances during martial law.
CREATION OF A DEMOGRAPHIC SECURITY COGNITIVE MAP
Fig. 1 represents the schema of the CM of demographic security of Ukraine, de-
veloped based on cause and effect relations during martial law. The CM nodes
have the following meaning:
0 — state support of families with children; 1 — average salary of a worker;
2 — consumer price index; 3 — export volume; 4 — import volume; 5 — popula-
tion in Ukraine; 6 — real GDP of Ukraine; 7 — inflation rate; 8 — migration out
of Ukraine; 9 — birth rate; 10 — unemployment rate; 11 — death rate; 12 — mil-
itary events, spends on the war.
The following CM nodes coordinates can be varied as control actions:
state support of families with children ( )(1 ku );
V. Romanenko, Y. Miliavskyi
ISSN 1681–6048 System Research & Information Technologies, 2025, № 3 78
average salary of a worker ( )(2 ku );
export volume ( )(3 ku );
import volume ( )(4 ku ).
Adjacency matrix A of the CM impulse process has the following form:
0000000000000
5.003.00002.000001.00
000015.05.045.01.000000
5.002.0035.015.02.00002.015.07.0
5.000002.03.01.015.01.03.003.0
2.00000005.0035.035.04.03.00
3.04.04.04.0001.004.05.007.00
08.01.08.07.0001.000005.00
00002.07.01.0000000
00002.004.002.00000
003.003.08.0006.00000
007.00065.06.003.03.04.000
0000000000000
A
Consider main disturbances affecting the demography, to implement control
of the demographic security under martial law:
1. Mass migration of population out of Ukraine because of the threat to life
under missile attacks on civilian targets in all regions and because of occupation
of the territories.
Fig. 1. Demographic security CM
Automated control of dynamic systems for ensuring Ukraine’s security using cognitive…
Системні дослідження та інформаційні технології, 2025, № 3 79
2. High death rate because of military actions at the front and because of
missile attacks over all territory of Ukraine.
3. Low birth rate because of young men population in the army, migration,
unemployment rate increase and general uncertainty about the future affecting
willingness of people to have children.
All these disturbances are practically impossible to describe mathematically
using probabilistic indicators, specifically, to find their distributions, research
their stationarity, analyse their fluctuations calculating their variance, find correla-
tions etc. We can only set up limitations on their amplitude when describing the
disturbances.
PROBLEM OF SUPPRESSING CONSTRAINED INTERNAL AND EXTERNAL
DISTURBANCES DURING CONTROL OF DEMOGRAPHIC SECURITY
COGNITIVE MAP IMPULSE PROCESS
Studies [3–5] present the theoretical foundations on the suppression of arbitrary
constrained external disturbances in terms of invariant ellipsoids based on the de-
sign of a static state feedback, which minimizes the size of the invariant ellipsoid
of the dynamical system. In this case, we implemented a robust control, where the
analysis and synthesis problems are reduced to equivalent conditions in the form
of linear matrix inequalities (LMI), solved numerically on the basis of semi-
definite programming. In [5] we solve the problem of suppression of constrained
external disturbances based on the invariant ellipsoids approach in the implemen-
tation of a closed-loop control system of impulse processes in CM of cryptocur-
rency on financial markets.
The general model of the dynamics of impulse processes (2) is decomposed
into two interrelated systems of difference equations:
);()()1( 1 kZDkXAkX (5)
)()()1( 2 kXkZAkZ . (6)
Here X is the vector of measurable coordinates of CM nodes which are to
be stabilized later; Z is the vector of CM coordinates considered as disturbances.
The matrices 1A , D , 2A , are parts of the adjacency matrix of the initial model
(2). The matrices D , show the relationships between the first (5) and the sec-
ond (6) parts of the initial CM (2). The increments of coordinates )(kZ are tak-
en into account as external constrained disturbances with unknown probabilistic
characteristics in the first system of equations (5) of the CM model.
We designed a control vector to suppress constrained perturbations )(kZ
by implementing static state controller in the feedback loop
)()( kXKkU p , (7)
which acts directly on the measured nodes coordinates X of the first impulse
process equations system (5) according to the controlled model:
)()()()1( 1 kZDkUBkXAkX (8)
The control is performed by changing the resources of the CM nodes, which
are affected by the vector )(kU .
V. Romanenko, Y. Miliavskyi
ISSN 1681–6048 System Research & Information Technologies, 2025, № 3 80
In this paper, the change in the weight coefficients )(1 kA with respect to
the known estimated values of the matrix 1Â is proposed to be considered as the
internal perturbations in the CM impulse process model (5) of the demographic
situation. For this purpose, in [4, 5] we modify the model (5) as follows:
)()()()1( 11 kZDkXAkXAkX , (9)
where )(
var111 kAAA is the change in the adjacency matrix of CM (5) during
the sampling period, )(
var1 kA is the real unknown value of the matrix 1A , which
changes as the demographic system evolves.
Let us denote the increment of internal perturbations in (9) as )()(1 kykA
)(kw . Then the equation of the uncontrolled impulse process (9) will be
written as:
,
)(
)(
)()()1( 11
kZ
kw
DIkXAkX (10)
where the vectors and matrices have the following dimensions: nX dim ;
pZ dim ; nw dim ; )(1 nnA ; )( pnD , I is a unit matrix of dimension
nn . We assume that the internal and external perturbations are jointly con-
strained by the norm l , so that:
1
)(
)(
])()([sup
)(
)(
2/1
kZ
kw
kZkw
kZ
kw TT . (11)
In [3] invariant ellipsoids on state variables are proposed to describe the
characteristic of the effect of disturbances of the type (11) on the trajectory of a
dynamic discrete system (10). For the CM they take the form:
0},1:)({ 1
PXPXRkX Tn
X , (12)
if from XX )0( the condition XkX )( follows for all discrete moments
of time ,...3,2,1k . Then the matrix P is called the matrix of the ellipsoid X .
In [4; 5] the condition of invariance of the ellipsoid (12) under disturbances (11)
is proven. According to it, invariance is guaranteed when the following LMI is met:
0
)1(
1 1
11
T
T DDI
PPAA . (13)
ALGORITHM FOR A STATE CONTROLLER DESIGN FOR THE COGNITIVE
MAP IMPULSE PROCESS
The state equation of the controlled CM impulse process (10) under additional
internal disturbances )(kw takes the form:
)(
)(
)()()1( 11
kZ
kw
DIkUBkXAkX . (14)
When the state controller (7) is applied, the equation of the closed-loop CM
impulse process control system is written as follows:
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Системні дослідження та інформаційні технології, 2025, № 3 81
)(
)(
)()()()1( 11
kZ
kw
DIkXBKAkX p . (15)
It is assumed that the pair )( 1 BA in the model (14) is controllable. Then
the LMI (13) for the closed-loop system looks like:
0
)1(
)()(
1 1
11
T
T
pp
DDI
PBKAPBKA . (16)
We consider the minimization of the trace of the ellipsoid matrix (12) as the
optimality criterion for the design of the controller (7):
1min,)( * trP , (17)
This ensures minimization of the size of the invariant ellipsoid (12) with the
largest suppression of disturbances
)(
)(
kZ
kw
, which are constrained only by the
maximum range (11). After multiplying the factors in the inequality (16), we obtain:
0
)1(
)(
1 T
1TTTT
1
T
1
T
11
DDI
PBPKBKBPKAPABKPAA pppp . (18)
Inequality (18) is nonlinear with respect to P and pK , which need to be op-
timized. In [3] a replacement PKL p and introduction of an additional con-
straint is done:
0
PL
LR
T , (19)
where TRR . This inequality is equivalent to T
pp
T PKKLLPR 1 according
to the Schur’s formula at 0P . Then to meet inequality (18) it is sufficient that:
0
)1(
)(
1 1
1111
T
TTTTT DDI
PBRBBLABLAPAA . (20)
Minimization of criterion (17) under constraints (19), (20) is performed with
respect to variables RLP ,, using semi-definite programming method by using
Matlab-based SeDuMi Toolbox. Then the matrix pK̂ of the optimal state control-
ler (7) is defined as:
1ˆˆˆ PLK p (21)
with the estimated values of RLP ˆ,ˆ,ˆ,̂ , providing minimization of criterion (17)
under constraints (19), (20).
PROBLEM OF THE COGNITIVE MAP WEIGHTS IDENTIFICATION BASED
ON THE RECURRENT LEAST SQUARES METHOD
The model of the controlled CM impulse process (3) of the “input-output” type
can be represented as:
)()()( 11
1 kUBqkYqAI . (22)
V. Romanenko, Y. Miliavskyi
ISSN 1681–6048 System Research & Information Technologies, 2025, № 3 82
Weighting coefficients of the adjacency matrix A are usually determined by
applying expert estimates based on cause-and-effect relations. In the process of
evolving of the demographic situation, these coefficients in the model (22) will
change over time, depending on changes in the influence of the CM nodes on
each other. So the problem of adaptive control of the CM implulse process ap-
pears, when both estimation of the parameters (coefficients) of the adjacency ma-
trix 1A and design of the control vector )(kU must be performed simultaneously.
Let us describe the equation (22) coordinate-wise (for each CM node):
).()1()1()(
1
kkubkyaky i
n
j
iijiji
(23)
It is assumed that the disturbances )(ki , caused by inaccurate measuring of
the CM nodes coordinates and inaccurate knowledge of the model coefficients,
are white noise. This assumption is plausible because )(),( kuky ii in model (23)
are presented in the form of the first differences, i.e. increments. It should also be
taken into account that the structure of the matrix 1A is known and some of the
coefficients ija are obviously equal to zero (in those cases when there are no con-
nections between the corresponding CM nodes).
Let us write model (23) as follows:
),()()1()( kkXkubky ii
T
iiii (24)
where T]...[
11 ijPiji aa consists of the non-zero coefficients in the i-th row of
matrix 1A , )]1(,...,)1([)( 1 kYkYkX
ijPj
T
i is a vector of measured CM
nodes coordinates.
The current estimate of the vector i is denoted by )(ˆ ki . To estimate the
weight coefficients of the matrix 1A we apply the recurrent least squares method [6–9]:
))1(ˆ)()1()()(()1(ˆ)(ˆ kkXkubkykKkk i
T
iiiiiii ;
)1()()()1(
)()1()(1
1
)(
kPkXkXkP
kXkPkX
kK i
T
iii
ii
T
i
i ; (25)
)1()()()1(
)()1()(1
1
)1()(
kPkXkXkP
kXkPkX
kPkP i
T
iii
ii
T
i
ii .
The recurrent procedure (25) should be performed for each CM node
,)(kyi ni ,...,2,1 at each sampling period. We use the obtained estimates
)(ˆ ki as the coefficients values of the adjacency matrix 1A at the current sam-
pling period in the control algorithm (7), (20), (21). For parametric identification
of the adjacency matrix 1A , we can also apply non-recurrent identification meth-
ods outlined in [10].
EXPERIMENTAL RESEARCH OF THE SYSTEM SUPPRESSING CONSTRAINED
INTERNAL AND EXTERNAL DISTURBANCES DURING CONTROL OF THE
DEMOGRAPHIC SECURITY COGNITIVE MAP IMPULSE PROCESS
To ensure demographic security in Ukraine it is reasonable to stabilize the follow-
ing coordinates X of the CM on Fig. 1: 0, 1, 2, 3, 4, 5, 6, 9. The following coor-
Automated control of dynamic systems for ensuring Ukraine’s security using cognitive…
Системні дослідження та інформаційні технології, 2025, № 3 83
dinates Z are considered as disturbances affecting the demographic security: 7, 8,
10, 11, 12. After decomposition of the model (2) into models (5) and (6) we con-
clude that although model (2) is unstable, state equations (5) and (6) are stable.
Control actions )(1 ku , )(2 ku , )(3 ku , )(4 ku are fed to the nodes 0, 1, 3, 4
respectively. So matrix B in the controlled impulse process equation (8) is the
following:
T
00010000
00001000
00000010
00000001
B
During simulation of closed-loop control system dynamics of the CM im-
pulse process based on the proposed method, we applied step impulse with unit
amplitude as an external disturbance at the initial time moment fed to the node
(12) — military events, spends on the war. Internal disturbances are generated as
following: at each sampling period non-zero coefficients of the matrix 1A are var-
ied under the formula )()( 1var1 kAkA , where )(k is a normal random variable
(Gaussian white noise) for the control only values of 1A are used while var1A are
applied as unknown internal disturbance. Initial levels of all the CM nodes coor-
dinates are taken equal to zero for simplicity.
Fig. 2 shows the transient processes of the CM nodes coordinates, Fig. 3 —
their increments. Here solid lines denote transient process under control, dashed
lines — without control. Fig. 4 shows control actions changes.
y0(kT0) y1(kT0) y2(kT0) y3(kT0) y4(kT0)
y5(kT0) y6(kT0) y7(kT0) y8(kT0) y9(kT0)
y10(kT0) y11(kT0) y12(kT0)
Fig. 2. CM nodes coordinates
V. Romanenko, Y. Miliavskyi
ISSN 1681–6048 System Research & Information Technologies, 2025, № 3 84
CONCLUSIONS
The paper considers important problem of demographic security under martial
law in Ukraine. Possible approach to solve this problem was suggested based on
5 10 15 20
-1
0
1
y
0
5 10 15 20
-1
0
1
y
1
5 10 15 20
-1
0
1
y
2
5 10 15 20
-1
0
1
y
3
5 10 15 20
-1
0
1
y
4
5 10 15 20
-1
0
1
y
5
5 10 15 20
-1
0
1
y
6
5 10 15 20
-1
0
1
y
7
5 10 15 20
-1
0
1
y
8
5 10 15 20
-1
0
1
y
9
5 10 15 20
-1
0
1
y
10
5 10 15 20
-1
0
1
y
11
5 10 15 20
-1
0
1
y
12
Fig. 3. CM nodes coordinates increments
Fig. 4. Control actions
Automated control of dynamic systems for ensuring Ukraine’s security using cognitive…
Системні дослідження та інформаційні технології, 2025, № 3 85
the CM impulse processes modelling and control. Specifically, the CM of demo-
graphic security was created and the control method for suppressing disturbances
based on invariant ellipsoids was applied. As a result, the control system was de-
signed and the simulation was performed.
Based on the simulation results, we can conclude that the suggested ap-
proach will help to stabilize very dangerous and unstable demographic process
initiated by increase of the military spends and the military events intensity.
Without control this process leads to the catastrophic depopulation of Ukraine.
Under the suggested control, the simulation demonstrates that despite significant
decrease of the population at the beginning, we are able to stabilize it at some
level and stop this process. Main control actions the government should apply are:
export increase and import decrease, average salary increase and support of the
families with children. The latter two of them are necessary to increase birth rate
and decrease migration, while the former two actions are necessary to prevent
inflation and stabilize economy.
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Received 10.12.2024
V. Romanenko, Y. Miliavskyi
ISSN 1681–6048 System Research & Information Technologies, 2025, № 3 86
INFORMATION ON THE ARTICLE
Viktor D. Romanenko, ORCID: 0000-0002-6222-3336, Educational and Research
Institute for Applied System Analysis of the National Technical University of Ukraine
“Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine, e-mail: romanenko.viktorroman@
gmail.com
Yurii L. Miliavskyi, ORCID: 0000-0003-0882-3418, Educational and Research Institute
for Applied System Analysis of the National Technical University of Ukraine “Igor
Sikorsky Kyiv Polytechnic Institute”, Ukraine, e-mail: yuriy.milyavsky@gmail.com
ЗАДАЧІ АВТОМАТИЗОВАНОГО КЕРУВАННЯ ДИНАМІЧНИМИ
ПРОЦЕСАМИ СИСТЕМНОГО ЗАБЕЗПЕЧЕННЯ БЕЗПЕКИ УКРАЇНИ НА
ОСНОВІ МОДЕЛЕЙ ІМПУЛЬСНИХ ПРОЦЕСІВ У КОГНІТИВНИХ
КАРТАХ. ЧАСТИНА 1. ЗАБЕЗПЕЧЕННЯ ДЕМОГРАФІЧНОЇ БЕЗПЕКИ /
В.Д. Романенко, Ю.Л. Мілявський
Анотація. Наведено когнітивну карту (КК) демографічної безпеки, на основі
якої описано динамічну модель імпульсних процесів КК у вигляді системи різ-
ницевих рівнянь (рівнянь Робертса). Виконано вибір зовнішнього вектора ке-
рувальних дій імпульсним процесом КК, який реалізується шляхом варіювання
координат вершин КК. Реалізовано замкнену систему керування імпульсним
процесом КК, до складу якої входить синтезований на основі методів теорії
автоматичного керування багатовимірний дискретний регулятор, який формує
вибрані керувальні дії. Розв’язано задачу проєктування дискретного регулято-
ра для автоматизованого керування динамічними процесами для забезпечення
демографічної безпеки. Функція регулятора полягає у приглушенні зовнішніх
та внутрішніх збурень при керуванні імпульсними процесами КК на основі ме-
тоду інваріантних еліпсоїдів. Наведено алгоритм ідентифікації вагових коефі-
цієнтів КК на основі рекурентного методу найменших квадратів. Подано ре-
зультати дослідження якості динамічних процесів стосовно забезпечення
демографічної безпеки в Україні в разі дії різноманітних збурень в умовах во-
єнного стану.
Ключові слова: когнітивна карта, демографічна безпека, інваріантний еліпсо-
їд, лінійні матричні нерівності, імпульсний процес.
|
| id | journaliasakpiua-article-343063 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-11-09T02:11:02Z |
| publishDate | 2025 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/1e/e2e070a5b7351a6b0984ce02888f931e.pdf |
| spelling | journaliasakpiua-article-3430632025-11-09T00:01:30Z Automated control of dynamic systems for ensuring Ukraine’s security using cognitive map impulse process models. Part 1. Demographic security Задачі автоматизованого керування динамічними процесами системного забезпечення безпеки України на основі моделей імпульсних процесів у когнітивних картах. Частина 1. Забезпечення демографічної безпеки Romanenko, Viktor Miliavskyi, Yurii когнітивна карта демографічна безпека інваріантний еліпсоїд лінійні матричні нерівності імпульсний процес cognitive map demographic security invariant ellipsoid linear matrix inequalities impulse process The paper provides a cognitive map (CM) of demographic security and a dynamic model of CM impulse processes described as a difference equations system (Robert’s equations). The external control vector for the CM impulse process is implemented by means of varying the CM nodes’ coordinates. A closed-loop control system for the CM impulse process is proposed. It includes a multivariate discrete controller designed based on an automated control theory method, which generates the chosen control actions. We solve a discrete controller design problem for automated control of dynamic processes to ensure demographic security. The controller suppresses external and internal disturbances during CM impulse processes control based on the invariant ellipsoids method. The paper presents an algorithm for CM weights identification based on the recurrent least squares method. We present the results of a qualitative research study on dynamic processes related to demographic security in Ukraine under various disturbances during martial law. Наведено когнітивну карту (КК) демографічної безпеки, на основі якої описано динамічну модель імпульсних процесів КК у вигляді системи різницевих рівнянь (рівнянь Робертса). Виконано вибір зовнішнього вектора керувальних дій імпульсним процесом КК, який реалізується шляхом варіювання координат вершин КК. Реалізовано замкнену систему керування імпульсним процесом КК, до складу якої входить синтезований на основі методів теорії автоматичного керування багатовимірний дискретний регулятор, який формує вибрані керувальні дії. Розв’язано задачу проєктування дискретного регулятора для автоматизованого керування динамічними процесами для забезпечення демографічної безпеки. Функція регулятора полягає у приглушенні зовнішніх та внутрішніх збурень при керуванні імпульсними процесами КК на основі методу інваріантних еліпсоїдів. Наведено алгоритм ідентифікації вагових коефіцієнтів КК на основі рекурентного методу найменших квадратів. Подано результати дослідження якості динамічних процесів стосовно забезпечення демографічної безпеки в Україні в разі дії різноманітних збурень в умовах воєнного стану. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2025-09-29 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/343063 10.20535/SRIT.2308-8893.2025.3.06 System research and information technologies; No. 3 (2025); 76-86 Системные исследования и информационные технологии; № 3 (2025); 76-86 Системні дослідження та інформаційні технології; № 3 (2025); 76-86 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/343063/330991 |
| spellingShingle | когнітивна карта демографічна безпека інваріантний еліпсоїд лінійні матричні нерівності імпульсний процес Romanenko, Viktor Miliavskyi, Yurii Задачі автоматизованого керування динамічними процесами системного забезпечення безпеки України на основі моделей імпульсних процесів у когнітивних картах. Частина 1. Забезпечення демографічної безпеки |
| title | Задачі автоматизованого керування динамічними процесами системного забезпечення безпеки України на основі моделей імпульсних процесів у когнітивних картах. Частина 1. Забезпечення демографічної безпеки |
| title_alt | Automated control of dynamic systems for ensuring Ukraine’s security using cognitive map impulse process models. Part 1. Demographic security |
| title_full | Задачі автоматизованого керування динамічними процесами системного забезпечення безпеки України на основі моделей імпульсних процесів у когнітивних картах. Частина 1. Забезпечення демографічної безпеки |
| title_fullStr | Задачі автоматизованого керування динамічними процесами системного забезпечення безпеки України на основі моделей імпульсних процесів у когнітивних картах. Частина 1. Забезпечення демографічної безпеки |
| title_full_unstemmed | Задачі автоматизованого керування динамічними процесами системного забезпечення безпеки України на основі моделей імпульсних процесів у когнітивних картах. Частина 1. Забезпечення демографічної безпеки |
| title_short | Задачі автоматизованого керування динамічними процесами системного забезпечення безпеки України на основі моделей імпульсних процесів у когнітивних картах. Частина 1. Забезпечення демографічної безпеки |
| title_sort | задачі автоматизованого керування динамічними процесами системного забезпечення безпеки україни на основі моделей імпульсних процесів у когнітивних картах. частина 1. забезпечення демографічної безпеки |
| topic | когнітивна карта демографічна безпека інваріантний еліпсоїд лінійні матричні нерівності імпульсний процес |
| topic_facet | когнітивна карта демографічна безпека інваріантний еліпсоїд лінійні матричні нерівності імпульсний процес cognitive map demographic security invariant ellipsoid linear matrix inequalities impulse process |
| url | https://journal.iasa.kpi.ua/article/view/343063 |
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