=Paper=
{{Paper
|id=Vol-2864/paper42
|storemode=property
|title=Neuro-fuzzy Control System for a Non-deterministic Object in Real Time
|pdfUrl=https://ceur-ws.org/Vol-2864/paper42.pdf
|volume=Vol-2864
|authors=Sergey Ivanov,Nataliia Maksyshko,Mykola Ivanov
|dblpUrl=https://dblp.org/rec/conf/cmis/IvanovMI21
}}
==Neuro-fuzzy Control System for a Non-deterministic Object in Real Time==
https://ceur-ws.org/Vol-2864/paper42.pdf
Neuro‐fuzzy Control System for a Non‐deterministic Object in
Real Time
Sergey Ivanova, Nataliia Maksyshkoa and Mykola Ivanova
a
Zaporizhzhia National University, Zhukovsky str., 66, Zaporizhzhia, 69063, Ukraine
Abstract
In this paper discusses the use of neuro-fuzzy control systems as a tool for managing non-
deterministic objects in real time. This paper discusses modern control tools structural
models of a discrete quasi-invariant automated control system. In this paper the analysis of an
automated control system is presented, which is based on the use of typical models of
discrete automated control systems. According to the proposed solution in the automated
control system in real time it is proposed to use a neuro-fuzzy control system as a function of
the object and the system's transfer ratio. The neuro-fuzzy control system is based on the
learning process of an artificial neural network (ANN), which allows to define the rules of
fuzzy inference (FIS). The paper proposes the ANFIS model, which is implemented by using
the fuzzy system Takagi T., Sugeno M., also is considered an algorithm based on seven fuzzy
rules. In this paper is presented a technique for implementing a neuro-fuzzy control system
for non-deterministic objects by using Matlab. The use of Matlab made possible to create a
model of an adaptive neuro-fuzzy inference system. The paper describes the process of
training a neural network, where a hybrid method is chosen, which is a combination of the
least squares method and the method of decreasing the inverse gradient. The results of testing
a neuro-fuzzy control system of a non-deterministic object are presented, which confirmed
the possibility of using a neuro-fuzzy control model. It is constructed the structure and the
result in the form of a control surface of the neuro-fuzzy ANFIS model. The results presented
in this paper allow to conclude about the possibility of using a neuro-fuzzy control system for
non-deterministic objects in real time.
Keywords 1
Neuro-fuzzy control systems, adaptive neural network (ANN), fuzzy inference system (FIS),
ANFIS model
1. Introduction
One of the methods for constructing modern control systems is the synthesis of intelligent systems
based on neuro-fuzzy systems [1]. The peculiarity of systems of this class is the use of neural
networks and fuzzy logic to control complex dynamic objects that function under conditions of
uncertainty and conflict. Uncertainty in this case it is exists a lack of information, which is necessary
to obtain a quantitative description of the processes occurring in the system, and the complexity of the
control object. The use of classical methods, the description of the control system assumes that the
control objects are described by linear dynamic links of a low order. This assumption often leads to
the fact that classical control systems in practice do not provide the desired indicators of fast and
efficient control. Therefore, the neuro-fuzzy control system, using the procedures of artificial neural
networks and fuzzy logic, makes it possible to identify complex processes both in technology and in
economics. The use of neuro-fuzzy systems makes it possible to solve the problem of constructing
control systems in conditions of uncertainty on the basis of the available statistical and experimental
CMIS-2021: The Fourth International Workshop on Computer Modeling and Intelligent Systems, April 27, 2021, Zaporizhzhia, Ukraine
EMAIL: flydaiver@gmail.com (S. Ivanov); maxishko@ukr.net (N. Maksyshko); nn_iva@ukr.net (M. Ivanov)
ORCID: 0000-0003-1086-0701 (S. Ivanov); 0000-0002-0473-7195 (N. Maksyshko); 0000-0002-1908-0763 (M. Ivanov)
© 2020 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
data obtained about the control object. It should be noted that the use of only one neural network in
the tasks of automated control has a number of disadvantages. This is how the neural network
receives information about the control object in the learning process, and this requires statistical data.
Therefore, this disadvantage can be eliminated by using fuzzy set structures, which allow for the
formalization of fuzzy variables. Therefore, this article is devoted to the actual problem of
constructing a neuro-fuzzy control system for non-deterministic objects in real-time systems.
2. The purpose of the article
The paper is devoted to the construction of a neuro-fuzzy control system for a non-deterministic
object in real time. The paper presents an approach to constructing a model of a neuro-fuzzy control
system for non-deterministic objects, as well as the process of implementing a model of an automated
control system ANFIS.
3. Literature review
Today, in control systems fuzzy sets, the authors Ivanov M., Maksyshko N., Ivanov S. and
Terentieva N. applied a method of modeling multidimensional processes [2].
In the works of Casillas J., Cordуn O. [3], Cordуn O., Herrera F. [4], and Espinosa J., Vandewalle
J. [5], the problems of tuning fuzzy systems based on rules for linguistic variables and an algorithm
for extracting rules are considered.
Authors Wang, D., He, H., Zhao, B. and Liu, D. [6] identified the main advantages of using
optimal control based on a neural network (NN) with feedforward.
In the articles of the authors Guillaume S. [7, 8] and Herrera F. [9], the problems of constructing a
fuzzy inference system (FIS) for modeling and control process are considered, as well as the use of
genetic algorithms for the design of fuzzy systems.
In the work, Anzaklis P.J. [10] considered the issues of hybridization of fuzzy logic systems. The
identified shortcomings in the use of a fuzzy inference system are solved on the basis of a neural
network that is able to learn and take into account previous knowledge.
In the article, Cui R., Yang C., Li Y., and Sharma S. [11] solved the problem of trajectory tracking
and object control in the area of discrete time based on two neural networks (NN). Therefore, the data
during the development of the control system must be specified explicitly.
Using a neuro-fuzzy approach eliminates the above problems. Jang J.S.R. in [12] presented an
architecture and training procedure, which is based on ANFIS.
The results of the study by Boyacioglu M.A. and Avci D. in [13] showed the ability of the ANFIS
system to predict the efficiency of the stock market.
In the works of Takagi T., Sugeno M. [14], a mathematical tool is presented for constructing a
fuzzy model of a system in which fuzzy inferences are used. The authors in their works have shown a
method for identifying a system using its input-output data.
In the work of Zhang H. and Liu D. [15], the methodology of fuzzy logic is presented and
efficiency is proved when working with complex nonlinear systems that contain uncertainties.
New solutions for the use of an artificial neural network and an adaptive neuro-fuzzy inference
system were considered in the work of Suparta, W., Alhasa, K. M. [16]. This paper presents the
theoretical foundations and explains in detail this method, as well as emphasizes its importance for
evaluating the model under study.
Saugat B., Debabrota B., Amit K. and Tibarewala D. [17] examined neural networks and showed
that the Adaptive Neural Fuzzy Inference System (ANFIS) works effectively to deal with
uncertainties.
The problems of assessing the quality of input signals were considered in the work of Kumar1 A.
and Qureshi M.F [18]. This paper provides an overview and analyzes of active filter methods. The
main goal of this work is to develop a highly efficient system that is integrated with the network. This
solution is based on the use of ANFIS, which allows the system to work quickly and give improved
results.
Karaboga, D., Kaya, E. [19] considered two groups of ANFIS parameters: premises and
consequences. These studies explored hybrid ANFIS training approaches to assess ANFIS training.
4. Building a model of a neuro‐fuzzy object control system
To determine the input components of the neuro-fuzzy object control system, the method of
system analysis is applied. This method allows you to analyze the mechanisms of interaction of an
economic object with the environment. Typical procedures correspond to business processes of non-
deterministic discrete objects. The decision to use marketing, resource and production procedures is
made based on an analysis of the degree of compliance, in this case, with business processes in an
economic entity. This approach combines the advantages of the principle of using typical subsystems
of automated control systems and the process approach. To build automated control systems that
operate under conditions of random processes, the automated systems approach can be applied.
However, for automated control systems it is not always possible to obtain a system of equations that
fully described it. Existing automated control systems are conditionally invariant (quasi-invariant) to
external factors. Therefore, the classical structural model of a discrete automated control system is
usually presented in the following form (Fig. 1.).
Figure 1: Structural model of a discrete quasi‐invariant automated control system
The structural model of an automated control system includes a production function and vectors of
controlled variables. Automated control system data depends on:
X n (t ) – vectors of input parameters of the automated system;
F pr – object (enterprise) functions;
(t ) – vectors of external disturbances on the control system.
It should be noted that during the time t , the vector of mismatch x(t ) , is generated, which is
necessary for the analysis and processing of the input data. All components of the structural model of
the control system depend on time, which change in accordance with the period of the switch (time
sampling). The switch is displayed in a discrete automated control system in the form of a switch with
a period T. This period of time in the system is necessary for the analysis and processing of the initial
data from the moment of their arrival to the control of the object. Therefore, τ - the duration of pauses
will be determined by the time between the arrival of the input data and the control of the object. The
closed position of the switch of the automated system characterizes the state when information is
provided for making management decisions in accordance with the transmission ratio. In the case of
an open switch, the automated system is in watch mode. It should be noted that fluctuations of the
input parameters fall into the control system mismatch block and determines the need to transform
managerial decisions. In general, the system of automated control of the object should be considered
as a set of tasks to be solved. According to the proposed solution in an automated control system in
real time, it is proposed to use a neuro-fuzzy control system as a function of the object ( F pr ) and the
system's transfer ratio ( K ( p)) . The model of a neuro-fuzzy system for automated control of non-
deterministic objects is shown in the Figure 2.
Figure 2: Model of a neuro‐fuzzy control system for non‐deterministic objects
The system ensures the adoption of n managerial decisions under the condition of fuzzy input
values. The adaptation of the system is provided at the stage of training the neural network. The
neuro-fuzzy control system is based on the learning process of an artificial neural network (ANN),
which allows to define the rules of fuzzy inference (FIS). As soon as the parameters of the fuzzy
inference are determined, the neural networks operate as usual. This is an integrated model in which a
neural network (ANN) training algorithm is used to determine the parameters of a fuzzy inference
system (FIS). Fuzzy inference system and corresponding membership functions. On the other hand,
the learning mechanism of a neural network does not depend on statistical information, but is standard
for the chosen architecture of an artificial neural network.
The ANFIS model (Adaptive-Network-Based Fuzzy Inference System) ANFIS with the
implementation of the Takagi T., Sugeno M. fuzzy system, which is a five-layer feedforward neural
network, is shown in the Figure 3.
Figure 3: Structural view of ANFIS system.
The input values of the model X 1 and X 2 allow you to determine the mismatch between the
current and planned value of the variable. The output variable Y is the control value of the automated
system.
The first layer of the ANFIS system allows the definition of fuzzy sets of a set of input quantities.
The outputs of the nodes of the layers of this level are the domains of membership functions for
certain input values 1 ( X n ) .
The second level of the system makes it possible to determine the generated fuzzy rules. At this
level, one fuzzy rule will correspond to each layer. The layer of the second level of the system is
connected with the nodes of the first level, which form the formation of the corresponding rules. The
outputs of the layers in the system are calculated as ratios of the input quantities 1 .
The third level allows you to normalize the degree of rule compliance
i i , i 1,.., n. (1)
i
In the system, the non-adaptive layer determines the weight value of the execution of the fuzzy
rule.
The fourth level of the adaptive system determines the contribution of each fuzzy rule to the value
of the output value of the network. The layer of the fourth level determines the contribution of the
fuzzy rule to the value of the output value of the system.
The fifth layer forms the value of the magnitude of the control system
Y Yti, n . (2)
Therefore, the ANFIS automated control system determines that only one fuzzy represents each
value set. The training procedure from the ANFIS neural network has no restrictions on the
modification of membership functions. To ensure the speed of training the neural network and the
adaptability of the software implementation, the model Takagi T., Sugeno M.
The Takagi T., Sugeno M model is based on a high-performance neural network training
procedure. The following indicators are selected to build the model:
Yt , n – output value of the control system per year by months t : t 0,1,..,11;
x t ,1 – the quantity of the first product sold per week (units);
xt ,2 – the quantity of the second item sold per week (units);
x t , HR – the amount of human resources that were used to produce goods.
This choice of variables allows you to determine the position of goods on the market and track the
current changes in the market. As the output value of the control system, the model can be written in
the following form:
xt ,3 xt , HR .
The choice of variables allows determine the position of goods on the market and current changes
in the market. As the output value of the control system, the model can be written in the following
form:
Yti,n a 0 1 Yt 1,1 2 x t ,1 3 x t ,2 4 x t , HR . (3)
Further, it can be seen that all variables affect the formation of fuzzy rules. The rules for the
Takagi T., Sugeno M. model were constructed according to the following algorithm. The algorithm,
which is built of seven fuzzy rules, is as follows:
The Rule1 :
If ( x t ,2 A1 ) and (Yt 1,1 B1 ) and ( x t ,1 C1 ) and ( x t , HR D1 ) Then
Yt1 a 10 11Yt 1,1 21 x t ,1 31 x t ,2 41 x t , HR
The Rule 2 :
If ( x t ,2 A1 ) and (Yt 1,1 B1 ) and ( x t ,1 C1 ) and ( x t , HR D 2 ) Then
Yt 2 a02 12Yt 1,1 22 xt ,1 32 xt , 2 42 xt , HR .
The Rule3 :
If ( x t ,2 A1 ) and (Yt 1,1 B1 ) and ( x t ,1 C 2 ) Then
Yt3 a 03 13Yt 1,1 23 x t ,1 33 x t , 2 43 x t , HR .
The Rule 4 :
If ( xt , 2 A1 ) and (Yt 1,1 B1 ) and ( xt ,1 C3 ) Then
Yt 4 a04 14Yt 1,1 24 xt ,1 34 xt , 2 44 xt , HR .
The Rule5 :
If ( xt ,2 A1 ) and (Yt 1,1 B2 ) Then
Yt5 a05 15Yt 1,1 25 xt ,1 35 xt , 2 5 xt , HR .
The Rule 6 :
If ( xt , 2 A2 ) Then
Yt6 a06 16Yt 1,1 26 xt ,1 36 xt ,2 46 xt , HR .
The Rule 7 :
If ( xt , 2 A3 ) Then
Yt7 a 7 17Yt 1,1 27 xt ,1 37 xt , 2 47 xt , HR .
In the presented rules A1 , A2 , A3 , B1 , B2 , C1 , C2 , C3 are fuzzy sets, where membership functions are
constructed using the built-in algorithm in Matlab. Also, Matlab calculates the coefficients of the
equations 0i , 1i , 1i , i2 , 3i , i4 , i 1,..,7.
Implementation of the ANFIS automated control system model
Matlab applied the implementation of a neuro-fuzzy control system for non-deterministic objects.
Matlab allows you to create a model of an adaptive system of neuro-fuzzy inference, as well as
perform its training is shown in the Figure 4.
Figure 4: Data Entry in ANFIS.
In the process of creating a management system in ANFIS, the statistical values of the demand for
goods in the market for the year were used, as well as the optimistic and pessimistic scenarios of the
production of goods (Table 1).
At the stage of FIS formation, membership functions were selected and the parameters of the fuzzy
inference system were determined. When constructing, Gauss functions (gaussmf) were selected,
which made it possible to display the input and output membership functions of the FIS, shown in
Figure 5.
Table 1
Matching Statistics to Output Values
The months Statistical values of the Optimistic scenario for Pessimistic scenario
demand for goods on the the production of for the production
market for the year, quantity goods, quantity of goods, quantity
January 92619 96760 88478
February 97948 102089 93807
March 99593 103734 95452
April 93251 97392 89110
May 94839 98980 90698
June 97591 101732 93450
July 90192 94333 86051
August 95690 99831 91549
September 103223 107364 99082
October 102629 106770 98488
November 105591 109733 101450
December 117227 121368 113086
Figure 5: Input and output membership functions of FIS.
The next stage is the network training procedure, where a hybrid method is chosen, which is a
combination of the least squares method and the inverse gradient decay method. Also, the number of
training cycles (Epochs) is set equal to 100, after which the testing procedure follows (Fig. 6).
Figure 6: The result of the ANFIS system testing process.
The results of constructing the system are presented in the form of the structure of the ANFIS
model as follows (Fig. 7).
Figure 7: The constructed structure of the neuro‐fuzzy model ANFIS.
In the process of studying the ANFIS model, the built-in Matlab procedure was used to view the
obtained rules of fuzzy inference (Fig. 8).
Figure 8: Procedure for viewing rules in a fuzzy inference system.
To analyze the results obtained, the following values of the input variables were set: the statistical
value of the demand for goods on the market for the year 1,0 e 5 and the optimistic scenario 1,04 e 5 .
To obtain this result, the control effect on the production of goods in the ANFIS system will be equal
to 1,07 e 4 (Fig. 9).
In addition, Matlab obtained control surfaces of the neuro-fuzzy model ANFIS, which is shown in
the Figure 10.
Figure 9: The results of the neuro‐fuzzy control system.
Figure 10: ANFIS neuro‐fuzzy model control surface.
5. Conclusion
A model of a neuro-fuzzy control system for a non-deterministic object in real time is proposed.
Structural models of a discrete quasi-invariant automated control system and a neuro-fuzzy control
system for non-deterministic objects are considered and analyzed.
The analysis of the ANFIS model, carried out using the fuzzy system Takagi T., Sugeno M. An
algorithm constructed from 7 fuzzy rules is considered. The article presents a technique for
implementing a neuro-fuzzy control system for non-deterministic objects using Matlab.
Matlab made it possible to create a solution for an adaptive system of neuro-fuzzy inference, as
well as carry out procedures for its training. The paper presents the results of the work of an adaptive
neuro-fuzzy control system for non-deterministic objects.
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