Навчання штучних нейронних мереж за реалізації процесу синтезу мереж Петрі
The important task has been solved in this scientific research related to specific development and verification of the fundamental suitability of the method for automatic synthesis of Petri nets based on the functioning of an artificial neural network. This allows to automate the generating process...
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The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"
2026
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System research and information technologies| _version_ | 1869472201637363712 |
|---|---|
| author | Gurskiy, Alexander Denisenko, Andrey Goncharenko, Alexander |
| author_facet | Gurskiy, Alexander Denisenko, Andrey Goncharenko, Alexander |
| author_institution_txt_mv | [
{
"author": "Alexander Gurskiy",
"institution": "Odesa National University of Technology, Odesa"
},
{
"author": "Andrey Denisenko",
"institution": "Odesа Polytechnic National University, Odesa"
},
{
"author": "Alexander Goncharenko",
"institution": "Odesa National University of Technology, Odesa"
}
] |
| author_sort | Gurskiy, Alexander |
| baseUrl_str | http://journal.iasa.kpi.ua/oai |
| collection | OJS |
| datestamp_date | 2026-06-30T06:14:59Z |
| description | The important task has been solved in this scientific research related to specific development and verification of the fundamental suitability of the method for automatic synthesis of Petri nets based on the functioning of an artificial neural network. This allows to automate the generating process of logical control algorithms. It has been proposed to divide the artificial neural network into separate local networks for the subsequent stepwise training. Such stepwise training is necessary to form the logical control algorithm and to synthesize the appropriate Petri net. The proposed principles can be applied in the early stages of training for an artificial neural network while synthesizing a Petri net. It has been conducted the experiments linked to the training of local neural networks and to implement the formation of an algorithm for logical control of the laboratory machine for processing chemical solutions. As a result of the experiment, it has been determined the fundamental suitability for the stepwise training method of neural networks for generating Petri nets and the automated formation of logical control algorithms. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2026.2.11 |
| first_indexed | 2026-07-01T01:00:23Z |
| format | Article |
| fulltext |
A. A. Gurskiy, A. V. Denisenko, A. E. Goncharenko, 2026
Системні дослідження та інформаційні технології, 2026, № 2 169
UDC 004.896
DOI: 10.20535/SRIT.2308-8893.2026.2.11
TRAINING ARTIFICIAL NEURAL NETWORKS
FOR THE IMPLEMENTATION OF THE PETRI NETS
SYNTHESIS PROCESS
A.A. GURSKIY, A.V. DENISENKO, A.E. GONCHARENKO
Abstract. The important task has been solved in this scientific research related to
specific development and verification of the fundamental suitability of the method for
automatic synthesis of Petri nets based on the functioning of an artificial neural
network. This allows to automate the generating process of logical control algorithms.
It has been proposed to divide the artificial neural network into separate local
networks for the subsequent stepwise training. Such stepwise training is necessary to
form the logical control algorithm and to synthesize the appropriate Petri net. The
proposed principles can be applied in the early stages of training for an artificial neural
network while synthesizing a Petri net. It has been conducted the experiments linked
to the training of local neural networks and to implement the formation of an algorithm
for logical control of the laboratory machine for processing chemical solutions. As a
result of the experiment, it has been determined the fundamental suitability for the
stepwise training method of neural networks for generating Petri nets and the
automated formation of logical control algorithms.
Keywords: artificial neural networks, logical control algorithms, training method,
hybrid system, automatic synthesis of Petri nets.
INTRODUCTION
The synthesis of Petri nets and the development of logical control algorithms for
systems with a logical and dynamic (hybrid) nature of operation are provided using
of appropriate software tools. The evolution of such software is primarily tied to
up-to-date trends in scientific and technological development and in the
development of information and intellectual technologies. The use of artificial
neural networks and the creation of intelligent systems is permitted to eliminate
partially or completely the human participation in some cases, e.g., in a particular
case, to eliminate partially or completely the human participation in the synthesis
of Petri nets based on the appropriate software tools.
PROBLEM STATEMENT
The use of artificial neural networks for the automatic generation of Petri nets been
considered in the scientific article [1], in which has been presented the certain
training methods for artificial neural networks. The disadvantages of these methods
are that they can be described as an imitation of learning processes through trial
and error. It is quite difficult to synthesize Petri nets or to form logical control
algorithms using such methods, also applying the well-known reinforcement
learning principles. These methods may not be effective in the initial stages of
training
A. A. Gurskiy, A. V. Denisenko, A. E. Goncharenko
ISSN 1681–6048 System Research & Information Technologies, 2026, № 2 170
[2, 3], but they are acceptable when the Petri net has already been synthesized and
needs to be corrected.
Therefore, it needs to research the principles of training for an artificial neural
network using known methods for the purpose of implementing automatic synthesis
of Petri nets. It is necessary to consider such methods that can be employed during
the early stages of training. For instance, in a particular case it is able to be the well-
known backpropagation algorithm.
The purpose of the scientific work is to automate process in synthesis of the
control algorithms by implementing automatic synthesis of Petri networks during
the operation of an artificial neural network.
To achieve this purpose, it needs to determine principles for the application of
known methods of training artificial neural networks that can be used to implement
automatic synthesis of Petri nets. In this case, after the training process the artificial
neural network should represent a sequence of transitions nttt ..., 21 ensures:
1
0 ...h J
t tt i nM M M .
In such a case, the marking JM of the formed Petri net is directly achievable
from the marking 0M in the same way as for a Petri net synthesized without the
use of automatic generation methods based on the artificial neural networks.
REVIEW OF THE LITERATURE
One of the first mentioned ideas about the automatic synthesis of Petri nets was in
the work of J. Peterson [4]. It was noted in this work that “the use of Petri net
languages would be in the specification and automatic synthesis of Petri nets. If the
behavior which is desired can be specified as a language, than it may be possible to
automatically synthesize a Petri net whose language is the specified language. This
Petri net can be used as a controller, guaranteeing that all and only the sequences
specified are possible”.
Since that time, it has been appeared the small number of scientific papers tied
to such a concept as the automatic synthesis of Petri nets. The development of the
relevant field of synthesis can be traced based on these scientific works [5–8]. Thus,
it has been presented the principles of synthesis for Petri nets given the composition
rules of individual subnets. However, further development for certain constructing
principles of Petri nets have been shown that their formation is based on an artificial
neural network, representing an intelligent technology for the formation of certain
algorithms. The basic principles of training an artificial neural network for the
constructing of Petri nets are explained in the work [1, 9].
This scientific work is a continuation of the development of this principle for
synthesis of Petri nets and the appropriate principles of training artificial neural
networks using known methods.
MAIN PART
The software application in the form of a virtual stand for the automatic synthesis
of Petri nets based on the Labview environment is being developed in this work.
Training artificial neural networks for the implementation of the Petri nets synthesis process
Системні дослідження та інформаційні технології, 2026, № 2 171
The formed Petri nets are able to represent algorithms for logical control of complex
technological systems. Automatic synthesis of Petri nets is implemented on the
basis of a state graph or a reachability tree [10]. The front panel of the developed
virtual stand, which visualizes the synthesis of Petri nets, is shown in Fig. 1. The
front panel shows a hybrid system with a logical and dynamic nature of operation.
Such a system consists of two parts, such as a continuous-event part and a discrete-
event part. The various modes of operation have been formed from the interaction
of these two parts. A model of such a system can be presented on the basis of
DС-nets [11, 12].
The continuous-event part in continuous space )( , kttX can be described by
equations of state
, 1 , 2 ,( ) ( ( )) ( ) ( ( )) ( ) (1)d d
k o o k k o o k kX t t A u t X t t B u t u t t
and exit
, 3 ,( ) ( ( )) ( ) (2)d
k o o k kY t t C u t X t t
in matrix-differential form, where )( , kttX is continuous-event state vector of the
continuous part; )( , kttY is continuous-event output vector; )( , kttu is continuous
action vector; ( ( ))d
o ku t is vector function for control the operating modes of a
hybrid system [12].
Fig. 1. Front panel of the virtual stand demonstrating the automatic formation of a Petri
nets. These nets reflect the logical control algorithms
A. A. Gurskiy, A. V. Denisenko, A. E. Goncharenko
ISSN 1681–6048 System Research & Information Technologies, 2026, № 2 172
The discrete-event part (or the logical control device) can also be described
by a state equation
1( ) ( ) ( ) ( ) ( ) (3)d d d d d
L k L k L L k L k L kX t X t A v t u t w t
and the output equation of the logical part
( ) ( ) (4)d d
L k L kY t X t
where, ( )d
L kw t is external control action; ( )d
L kX t , 1( )d
L kX t are discrete states
at step tk , tk-1 appropriate to the markings of the Petri net, which represents the
logical part; LA is incident matrix representing the relationship of the elements of
the discrete-event part; ( )d
L kv t is control vector; is transition matrix.
Thus, the functioning of the logical part of the system can be represented using
an automatically generated Petri net.
In the software, application it has been carried out the implementation for
automatic synthesis of Petri nets on the basis of the functioning of an artificial
neural network. As illustrated in Fig. 2 in this case the artificial neural network
interacts with synchronously functioning Petri nets. This interaction is carried out
on the principles of feedback. From these synchronously functioning networks it is
possible to form a Petri net composition showing the required logical control
algorithm. It is shown that each position of the generated Petri net matches a
specific position of the Petri net PNi connected to the neural network NN. In order
to compose a Petri net we need to combine transitions fired simultaneously in
networks PN1…PNm. In this case, according to the diagram shown in Fig. 2, the
neural network will be able to form signals appropriate to the columns of the
incidence matrix LA in the equation of state. It has been determined that the
coefficients of interneuronal connections in the output layer of the neural network
correspond to the incidence matrix of the formed Petri net. The input or hidden
layer of a neural network is linked to the conditions for firing of the Petri net
transitions.
It has been determined that training of an artificial neural network for the
implementation the automatic synthesis of Petri nets must be realized by stages
using the known training methods. One of the known methods may be the
backpropagation algorithm. In this case, the artificial neural network without an
output layer must be divided into separate parts or sectors.
Each such part (sector) may constitute a local neural network performing a
specific functional load, tied to conditions for firing of the certain transition ti
where i=1…n. Thus, the number of such parts (sectors) must correspond to the
number of transitions of the formed Petri net. In Fig. 3, these parts are designated
by input neural t1, t2, t3 of the 1st input layer of the artificial neural network.
The coefficients of interneuron connections of the 1st (input) part of the
artificial neural network are determined in the learning process based on the
training sample. In this case, the learning process should occur in examples of the
data conditions for transition from one state of the system to another or the
conditions for firing transitions of the Petri net.
Training artificial neural networks for the implementation of the Petri nets synthesis process
Системні дослідження та інформаційні технології, 2026, № 2 173
The matrix of coefficients for interneuronal connections of the output layer
for the artificial neural network (the 2nd output part) has been determined quite
simply by subtraction: 1k k jm m W , where 1km is the marking of Petri net at
k+1 step; km is the marking of Petri net at k step; jW is a vector of coefficients for
interneuron connections of neurons for the network output layer which corresponds
to the j-th column of the incidence matrix of the Petri net.
Fig. 2. Diagram which shows the interaction of the artificial neural network and Petri nets
during the formation of a logical control algorithm based on a virtual stand
Thus, training or determination of the coefficients of interneuronal
connections in an artificial neural network can be implemented on the basis of a
state graph or a reachability tree of a Petri net.
It should be conducted the appropriate experiments to determine the
fundamental suitability of the presented principle for automatic synthesis of Petri
nets. These experiments are related to the processes of training artificial neural
networks.
A. A. Gurskiy, A. V. Denisenko, A. E. Goncharenko
ISSN 1681–6048 System Research & Information Technologies, 2026, № 2 174
Fig. 3. Diagram representing the interaction of the local artificial neural networks and Petri
nets in the formation of a logical control algorithm
EXPERIMENTS
The necessary experiments have been performed in the MATLAB\Simulink 5.2
software environment. The MATLAB software environment possesses the
necessary tools for formation and training of the artificial neural networks. These
tools can be used to determine the fundamental suitability of a certain method of
Petri net synthesis based on the functioning of artificial neural networks. The
laboratory machine for processing chemical solutions has been considered (Fig. 4).
The modeling of a chemical solution processing machine in the DC-Net
environment as a hybrid system has been presented in the paper [11]. The
fundamental suitability of the presented principle of automatic synthesis of Petri
nets will be established by examining only a fragment of the logical part in this
paper.
Fig. 4. Technological scheme of the plant for processing chemical solutions
Training artificial neural networks for the implementation of the Petri nets synthesis process
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Thus, the logical control algorithm of such a laboratory machine has been
presented in the form of a Petri net implemented in the DC-Net software
environment (Fig. 5). Each marker in the Ps position of the Petri net defines the
state of the system. Accordingly, in the Petri net shown in Fig. 5, if position P1 is
marked 1( ) 1p , then solution processing mode in tank (container) T1 takes place;
If 2( ) 1p , then the solution overflows from T1 to T2, while valve V2 is open and
10( ) 0p respectively. When 3( ) 1p , the post-processing mode is in progress,
in this case the valve V2 is closed, 10( ) 1p respectively. Next, when 6( ) 0p
the filling mode of the tank T1 begins, while the valve V1 is open. When 6( ) 1p ,
the transition to stop process, 10( ) 0p accordingly, valve V3 is open and the
solution comes out of the tank T2. The reachability tree shown in Fig. 6 can be used
to trace this marking dynamics.
According to marking dynamics it is able to imagine a training sample for
stepwise sequential training of an artificial neural network. It is necessary to show
the conditions or states where a certain transition or is fired and those conditions or
states where it is not fired.
Let us consider transition t2. The transition p firing condition is as follows:
2 1( ) : ( ) 1i ip I t p m g , where ( )ip is marking of input positions of
transition t2, respectively 2( ) 1p ; g is maximum limit value of the mass of the
solution in the tank Т2.
The following executable code must be written in the command window of
MATLAB to generate a local neural network:
» P=[0 0 1 1; 50 60 50 60];
» T=[0 0 0 1];
» net = newff([0 1; 0 70], [2 1],{'tansig','logsig'});
» net.trainParam.epochs=3000;
» net=train(net, P, T);
TRAINLM, Epoch 0/3000, MSE 0.145251/0, Gradient 14.3558/1e-010
TRAINLM, Epoch 18/3000, MSE 2.63998e-013/0, Gradient 5.00017e-
011/1e-010
TRAINLM, Minimum gradient reached, performance goal was not met.
» a = sim(net,P)
a =
0.0000 0.0000 0.0000 1.0000
» gensim(net)
In the present executive code that has been presented, P is the input values of
the neural network; t is the corresponding output values of the neural network.
This P is the value of the position marking p2 and the value of the mass for the
solution in the tank T2.
If the output value t=1 then the transition has fired. In the third line of the
executive code the number of neurons, the number of layers and activation
functions has been set. The last command that is entering to form a neural network
in the Simulink environment is the gensim(net) command. As a result of executing
this command, a local neural network appears, indicated in Fig. 7 as Neural
Network 2.
A. A. Gurskiy, A. V. Denisenko, A. E. Goncharenko
ISSN 1681–6048 System Research & Information Technologies, 2026, № 2 176
Fig. 5. Fragment of а Petri net presented in the modeling environment of DC-Net hybrid
(logical-dynamic) systems
Similarly, we have the ability to write executable code to generate a neural
network that is relative to transition t3.
» P=[0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1; 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1; 0
0 0 0 1 1 1 1 0 0 0 0 1 1 1 1; 303 303 303 303 303 303 303 303 313 313
313 313 270 270 270 270];
» T=[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0];
» net = newff([0 1; 0 1; 0 1; 270 400], [4 1],{'tansig','logsig'});
» net.trainParam.epochs=3000;
» net=train(net, P, T);
TRAINLM, Epoch 0/3000, MSE 0.169168/0, Gradient 472.338/1e-010
TRAINLM, Epoch 25/3000, MSE 8.47449e-008/0, Gradient 0.00443561/1e-010
TRAINLM, Epoch 34/3000, MSE 9.84151e-016/0, Gradient 6.63958e-
011/1e-010
TRAINLM, Minimum gradient reached, performance goal was not met.
» a = sim(net,P)
a =
Columns 1 through 7
0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000
Columns 8 through 14
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Columns 15 through 16
0.0000 0.0000
»
» gensim(net)
According to the set of input values P and output ones t, transition t3 is fired
at 3( ) 1p , 9( ) 1p , and at the solution temperature in tank T2 below 3030К. In
order to eliminate erroneous reactions from the artificial neural network, various
input values P are presented to prevent the transition from being fired.
Training artificial neural networks for the implementation of the Petri nets synthesis process
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For transition t6 the execution code is as follows:
» P=[0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 ; 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1;
0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1; 303 303 303 303 303 303 303 303 313 313
313 313 313 313 313 313];
» T=[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0];
» net = newff([0 1; 0 1; 0 1; 260 400], [4 1],{'tansig','logsig'});
» net.trainParam.epochs=3000;
» net=train(net, P, T);
TRAINLM, Epoch 0/3000, MSE 0.498623/0, Gradient 231.701/1e-010
TRAINLM, Epoch 25/3000, MSE 0.0449965/0, Gradient 17.2122/1e-010
TRAINLM, Epoch 47/3000, MSE 6.36122e-015/0, Gradient 6.95981e-
011/1e-010
TRAINLM, Minimum gradient reached, performance goal was not met.
» a = sim(net,P)
a =
Columns 1 through 7
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Columns 8 through 14
1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Columns 15 through 16
0.0000 0.0000
» gensim(net)
As a result of executing the commands, a local neural network appears,
designated in Fig. 7 as Neural Network 6.
Fig. 6. Fragment of a reachability tree of a Petri net representing the logic control algorithm
of the laboratory machine for processing chemical solutions
Next, it can be determined as a result of the subtraction 1k k jm m W the
coefficients of interneuronal connections for the output layer of the artificial neural
network as follows:
A. A. Gurskiy, A. V. Denisenko, A. E. Goncharenko
ISSN 1681–6048 System Research & Information Technologies, 2026, № 2 178
2 1
2,2 3,2 10,2
0 0 1 0 0 0 0 1 1 1
0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 ;
T
k k
TT
W m m
w w w
3 1
3,3 4,3 9,3
0 0 0 1 0 0 0 0 1 1
0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 ;
T
k k
TT
W m m
w w w
6 1
3,6 7,6 11,6
0 0 0 0 0 1 0 1 1 0
0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 .
T
k k
TT
W m m
w w w
The appropriate artificial neural network has been implemented in the
MATLAB\Simulink software environment. This artificial neural network interacts
with Petri nets on the principles of feedback (Fig. 7). Such interaction is also shown
in Fig. 3. As a result of such interaction at the outputs of the neural network у2….y9
it is formed the sequence of signals appropriate to the rows of the incidence matrix
W of the Petri net.
Fig. 7. Scheme of artificial neural network presented by means of MATLAB\Simulink
environment for synthesis of Petri nets
Also, as a result of the functioning of the artificial neural network, it is formed
the dynamics of the Petri net marking appropriate to the dynamics of the network
marking presented in Fig. 5.
It should be noted that in the MATLAB\Simulink environment it has been
represented the operation of Petri nets on the basis of RS-triggers due to the lack of
an element base for constructing Petri nets.
Training artificial neural networks for the implementation of the Petri nets synthesis process
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RESEARCH RESULTS
As a result of modeling the interaction system for an artificial neural network with
Petri nets, it has been obtained the dynamics of Petri net marking presented in
Fig. 8. In Fig. 8 (left) it is shows the change in time of the Petri net marking in the
absence of a stop signal, at which 6( ) 0p . And in Fig. 8 (right) it is shows a
change in time of the Petri net marking in the presence of a stop signal 6( ) 1.p
At 6( ) 1p , the marker does not move into position p4 since p6 is connected by an
inhibitory arc with transition t3. Consequently, when 6( ) 1p , transition t3 is
closed. As can be seen, the change in marking during the operation of the circuit
with an artificial neural network corresponds to the change in marking of the Petri
net shown in Fig. 5.
Fig. 8. Diagrams of changes in the marking of Petri net over time obtained as a result of the
interaction between the artificial neural network with separate Petri nets
Thus, via training and functioning of the neural network, it has been formed
and presented the work of this fragment of the Petri net shown in Fig. 8. Also,
during the functioning of the artificial neural network, it is provided the sequence
of transitions 1 2, ... nt t t at which:
1 2 4
1 ...i i J
t t tM M M .
In this case, the transition i JM M corresponds to the transition
appropriate to the Petri net synthesized in the DC-Net environment.
The presented results confirm the fundamental suitability of the Petri net
synthesis method on based the functioning of artificial neural networks. Such
method involves the implementation of certain stages.
1. Implementation of the scheme for an artificial neural network interaction
with local Petri nets.
2. Division of the neural network into sectors for subsequent stepwise training.
3. Definition of training data (training sample) based on the state graph or
reachability tree Petri net and implementing of stepwise training for an artificial
neural network.
4. Determination of the incidence matrix which forms Petri net based on the
neural network and the launching of its operation.
A. A. Gurskiy, A. V. Denisenko, A. E. Goncharenko
ISSN 1681–6048 System Research & Information Technologies, 2026, № 2 180
DISCUSSION
If it is compared the presented method for automatic synthesis of Petri nets with
method for the synthesis of similar nets in the DC-Net environment, it is able to
determine the appropriate advantages and disadvantages of the presented method.
The automatic synthesis method is advantageous because it eliminates the need for
a person to construct the Petri net by themselves, as with the DC-Net system
[13, 14]. Based on the functioning of the artificial neural network, it is possible to
visualize the operation of the logical control algorithm represented in the form of a
Petri net. It is only necessary to specify the conditions for the transition from one
state of the system to another to train the artificial neural network. Another
advantage of the presented method is that it can be implemented on the basis of the
MATLAB\Simulink or Labview environment, which in turn allows the generated
control algorithm to be linked to the automation system's hardware.
However, it is important to note a few appropriate shortcomings. One of the
disadvantages is the need to provide a sufficiently amount of data for training the
artificial neural network, both on the conditions for the transition from one state of
the system to another and, otherwise, the conditions under which the appropriate
transitions are prohibited.
If training data is insufficient, then the artificial neural network can be wrong
and present a logical control algorithm which leads to an emergency. This is what
makes the system intelligent. The intelligent system is able to represent what had
not been considered in the training process with a positive or negative result.
It should be noted that the DC-Net environment provides the ability to visually
edit and explore the Petri net, unlike a software application associated with
automatic synthesis.
CONCLUSIONS
It has been solved the problem linked to determination of the principles for the
training of artificial neural networks in the automatic synthesis of Petri nets in the
present work. It is presented the diagram of interaction between a neural network
with Petri nets for their compositions. It has been completed the necessary
experiments linked to the stepwise training of an artificial neural network using
known methods in the MATLAB environment. The performed experiments allow
determining the fundamental suitability of the method for automatic synthesis of
Petri nets in the formation of control algorithms. Thus, performing the assigned
task the further develop the method for automatic synthesis of Petri nets and control
algorithms based on the use of artificial neural networks is received.
The development of the method for automatic synthesis of Petri nets allows
approaching the solution of a practical problem. Such a task is related to the
development of an intelligent system and the appropriate software application. This
software must automatically form some logical control algorithms and Petri nets.
Further development of this scientific direction should be directly related to
the formation of methods for self-learning of neural networks in the automatic
synthesis of Petri nets.
Training artificial neural networks for the implementation of the Petri nets synthesis process
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Received 24.04.2025
A. A. Gurskiy, A. V. Denisenko, A. E. Goncharenko
ISSN 1681–6048 System Research & Information Technologies, 2026, № 2 182
INFORMATION ON THE ARTICLE
Alexander A. Gurskiy, ORCID: 0000-0001-5158-2125, Odesa National University of
Technology, Ukraine, e-mail: gurskiya2017@gmail.com
Andrey V. Denisenko, ORCID: 0000-0002-8610-0082, National University “Odesa
Polytechnics”, Ukraine, e-mail: denisenko.a.v@op.edu.ua
Alexander E. Goncharenko, ORCID: 0000-0003-4959-6469, Odesa National University
of Technology, Ukraine, e-mail: kholod.automatic@gmail.com
НАВЧАННЯ ШТУЧНИХ НЕЙРОННИХ МЕРЕЖ ЗА РЕАЛІЗАЦІЇ ПРОЦЕСУ
СИНТЕЗУ МЕРЕЖ ПЕТРІ / O.O. Гурський, А.В. Денисенко, О.Є. Гончаренко
Анотація. Вирішено актуальне завдання, що пов’язане з розробленням і
перевіркою на принципову придатність методу автоматичного синтезу мереж
Петрі на основі функціонування штучної нейронної мережі. Це дає змогу
автоматизувати процес формування визначених алгоритмів логічного
керування. Таке завдання також є актуальним, оскільки вперше розглянуто
принципи навчання штучних нейронних мереж відомими методами за реалізації
задачі синтезу мереж Петрі. Подано розподілення штучних нейронних мереж на
окремі локальні мережі для поетапного навчання. Таке поетапне навчання
потрібне для синтезу алгоритмів логічного керування та відповідних мереж
Петрі. Запропоновано принципи, які можна застосувати на ранніх стадіях
навчання штучних нейронних мереж за синтезу мереж Петрі. Виконано
експерименти, пов’язані з навчанням локальних нейронних мереж та з
реалізацією формування алгоритму логічного керування. У результаті
проведених експериментів установлено принципову придатність метода
поетапного навчання штучних нейронних мереж для генерації мереж Петрі та
автоматизованого формування алгоритмів логічного керування.
Ключові слова: штучні нейронні мережі, мережа Петрі, алгоритм керування,
методи навчання, логіко-динамічна система, автоматичний синтез мереж Петрі.
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| id | journaliasakpiua-article-365269 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-01T01:00:23Z |
| publishDate | 2026 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/d8/2c38e6ccfd25394db6cb5d3247709fd8.pdf |
| spelling | journaliasakpiua-article-3652692026-06-30T06:14:59Z Training artificial neural networks for the implementation of the Petri nets synthesis process Навчання штучних нейронних мереж за реалізації процесу синтезу мереж Петрі Gurskiy, Alexander Denisenko, Andrey Goncharenko, Alexander artificial neural networks logical control algorithms hybrid system automatic synthesis of Petri nets training method штучні нейронні мережі мережа Петрі алгоритм керування методи навчання логіко-динамічна система автоматичний синтез мереж Петрі The important task has been solved in this scientific research related to specific development and verification of the fundamental suitability of the method for automatic synthesis of Petri nets based on the functioning of an artificial neural network. This allows to automate the generating process of logical control algorithms. It has been proposed to divide the artificial neural network into separate local networks for the subsequent stepwise training. Such stepwise training is necessary to form the logical control algorithm and to synthesize the appropriate Petri net. The proposed principles can be applied in the early stages of training for an artificial neural network while synthesizing a Petri net. It has been conducted the experiments linked to the training of local neural networks and to implement the formation of an algorithm for logical control of the laboratory machine for processing chemical solutions. As a result of the experiment, it has been determined the fundamental suitability for the stepwise training method of neural networks for generating Petri nets and the automated formation of logical control algorithms. Вирішено актуальне завдання, що пов’язане з розробленням і перевіркою на принципову придатність методу автоматичного синтезу мереж Петрі на основі функціонування штучної нейронної мережі. Це дає змогу автоматизувати процес формування визначених алгоритмів логічного керування. Таке завдання також є актуальним, оскільки вперше розглянуто принципи навчання штучних нейронних мереж відомими методами за реалізації задачі синтезу мереж Петрі. Подано розподілення штучних нейронних мереж на окремі локальні мережі для поетапного навчання. Таке поетапне навчання потрібне для синтезу алгоритмів логічного керування та відповідних мереж Петрі. Запропоновано принципи, які можна застосувати на ранніх стадіях навчання штучних нейронних мереж за синтезу мереж Петрі. Виконано експерименти, пов’язані з навчанням локальних нейронних мереж та з реалізацією формування алгоритму логічного керування. У результаті проведених експериментів установлено принципову придатність метода поетапного навчання штучних нейронних мереж для генерації мереж Петрі та автоматизованого формування алгоритмів логічного керування. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2026-06-30 Article Article Peer-reviewed Article application/pdf https://journal.iasa.kpi.ua/article/view/365269 10.20535/SRIT.2308-8893.2026.2.11 System research and information technologies; No. 2 (2026); 169-182 Системные исследования и информационные технологии; № 2 (2026); 169-182 Системні дослідження та інформаційні технології; № 2 (2026); 169-182 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/365269/350717 |
| spellingShingle | штучні нейронні мережі мережа Петрі алгоритм керування методи навчання логіко-динамічна система автоматичний синтез мереж Петрі Gurskiy, Alexander Denisenko, Andrey Goncharenko, Alexander Навчання штучних нейронних мереж за реалізації процесу синтезу мереж Петрі |
| title | Навчання штучних нейронних мереж за реалізації процесу синтезу мереж Петрі |
| title_alt | Training artificial neural networks for the implementation of the Petri nets synthesis process |
| title_full | Навчання штучних нейронних мереж за реалізації процесу синтезу мереж Петрі |
| title_fullStr | Навчання штучних нейронних мереж за реалізації процесу синтезу мереж Петрі |
| title_full_unstemmed | Навчання штучних нейронних мереж за реалізації процесу синтезу мереж Петрі |
| title_short | Навчання штучних нейронних мереж за реалізації процесу синтезу мереж Петрі |
| title_sort | навчання штучних нейронних мереж за реалізації процесу синтезу мереж петрі |
| topic | штучні нейронні мережі мережа Петрі алгоритм керування методи навчання логіко-динамічна система автоматичний синтез мереж Петрі |
| topic_facet | artificial neural networks logical control algorithms hybrid system automatic synthesis of Petri nets training method штучні нейронні мережі мережа Петрі алгоритм керування методи навчання логіко-динамічна система автоматичний синтез мереж Петрі |
| url | https://journal.iasa.kpi.ua/article/view/365269 |
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