Research and Development of Algorithmic Transport Control Systems

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IJTSRD
Education
Volume 4 Issue 5
International Journal of Trend in Scientific Research and Development (IJTSRD) 
Volume 5 Issue 6, September-October 2021 Available Online: www.ijtsrd.com e-ISSN: 2456 – 6470 
 
@ IJTSRD   |   Unique Paper ID – IJTSRD46388   |   Volume – 5   |   Issue – 6   |   Sep-Oct 2021 
Page 172 
Research and Development of 
Algorithmic Transport Control Systems 
Turdibekov Kamolbek Khamidovich, Yakubov Mirjalil Sagatovich, 
Sulliev Absaid Khurramovich, Soliev Elyor Nigmatovich, Halikov Sarvar Salikhjanovich 
Tashkent State Transport University, Tashkent, Uzbekistan 
 
ABSTRACT 
The necessity of a systematic approach is shown when considering 
the problems of transport systems management. The effectiveness of 
the algorithmic approach is shown for the creation of an automated 
system for identification and optimization of management processes 
for complex systems. Experimental statistical methods are proposed 
for solving the problem in the field of complex systems for the 
development of modeling control algorithms. 
The necessity of an algorithmic approach to the development of a 
methodology for creating an information reference system in the field 
of transport is shown. 
The developments are investigated by algorithmic mathematical 
models of processes in the transport system. 
 
 
KEYWORDS: Algorithmic systems, control of complex systems, 
mathematical models, performance criteria, regression equation, 
active experiment methods, Taylor series, communications operator 
 
 
 
 
 
 
 
 
 
 
 
 
How to cite this paper: Turdibekov 
Kamolbek Khamidovich | Yakubov 
Mirjalil Sagatovich | Sulliev Absaid 
Khurramovich 
| 
Soliev 
Elyor 
Nigmatovich 
| 
Halikov 
Sarvar 
Salikhjanovich 
"Research 
and 
Development of Algorithmic Transport 
Control 
Systems" 
Published 
in 
International Journal 
of Trend in Scientific 
Research 
and 
Development (ijtsrd), 
ISSN: 
2456-6470, 
Volume-5 | Issue-6, 
October 
2021, 
pp.172-176, URL: 
www.ijtsrd.com/papers/ijtsrd46388.pdf 
 
Copyright © 2021 by author (s) and 
International Journal of Trend in 
Scientific Research and Development 
Journal. This is an 
Open Access article 
distributed under the 
terms of 
the Creative Commons 
Attribution License (CC BY 4.0) 
(http://creativecommons.org/licenses/by/4.0) 
 
Technical progress in the transport system and the 
associated intensification of production dictate new 
problems in the management of sectors of the national 
economy, which are presented in the form of complex 
systems. 
 Complexes of tasks are methods of analysis and 
synthesis of complex systems, since they solve the 
problems of determining the behavior of an object 
and predicting it, forming criteria for the efficiency of 
transport objects and optimizing its modes. This 
opportunity gives us an algorithmic approach to the 
construction of mathematical models of complex 
systems [1,2]. 
The methods of mathematical description and 
modeling of production processes considered in the 
literature provide a solution to a wide range of 
practical problems. However, they refer only to 
discrete production processes and do not cover a 
significant number of continuous production 
processes common in the national economy. 
If discrete production processes observed in transport 
are characterized by the following features: 1) 
operating on individual parts, semi-finished products, 
units, etc., from which the product is ultimately 
assembled, and 2) the possibility of dividing the 
production process into separate elementary acts, 
called operations, then the class of continuous 
production processes is devoid of these features. 
A systematic analysis of complex systems 
encountered in practice shows that solving problems 
of operational and high-quality control of them 
necessitates identifying information flows, forming a 
control algorithm, centralizing control, developing a 
modeling algorithm and objectivity criteria, taking 
into account such factors as the randomness of 
deviations from the planned modes of operation,  
 
 
 
IJTSRD46388 
International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 
@ IJTSRD   |   Unique Paper ID – IJTSRD46388   |   Volume – 5   |   Issue – 6   |   Sep-Oct 2021 
Page 173 
multidimensionality, poor observability, poor 
controllability, unsteadiness of subsystems, lack of 
technical means of quality control of processed 
products, etc. 
The multidimensionality of the elements of the 
system is one of the features in determining the 
complexity of the system [3]. Production processes 
existing in transport are multidimensional and, being 
elements of a complex system, have their own 
characteristics. However, the multidimensionality of 
the elements of a complex system, when forming 
performance criteria, can lead to contradictory 
situations, which dictates the need for a compromise 
decision. Presence of elements at the input
 and at 
the output 
 of vector quantities allows you to use the 
methods of vector optimization. 
A priori estimates of some technological processes 
have shown that the level of their observability and 
controllability is very low and is within 18% -40% of 
the total state space. Consequently, from the 
classification point of view, we can say that the 
processes in transport are related to weakly 
observable, poorly controlled and non-stationary 
processes, in which quasi-stationarity areas can be 
identified at short time intervals. 
For these processes, it is advisable to study the object 
as a converter of information. At the same time, the 
main attention is paid to the relationships associated 
with the paths of information passage through their 
possible transmission channels in order to achieve 
greater dynamism and efficiency of control. 
So, let T- be a fixed subset of real positive numbers 
(the set of considered moments of time), X, U, Y, Z - 
sets of any nature. The elements of the indicated sets 
will be called as follows: tϵT - moment of time; xϵX - 
input, uϵU- control, yϵY - output signals, zϵZ- state. In 
the subsequent states, input, output and control 
signals will be considered as functions of time, and 
their values at time t will be denoted z(t), x(t), 
y(t)respectively [4,5]. 
Due to the fact that the main production processes are 
complex, that is, with many input and output 
variables, the task is to build a mathematical model 
for a multidimensional object
. It can be formulated 
as follows: according to the results of experimental-
statistical observations, it is necessary to find an 
estimate of the object operator that is optimal in some 
sense. In this case, the requirement is imposed that 
the estimate is close to the true 
. value in the sense 
of some criterion, that is, the requirement for the 
proximity of the vector random function at the output 
of the model must be fulfilled
 
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)
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t
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to the vector output variable of the object 
 
To determine the optimal operator by the criterion of 
the minimum mean square of the error in this case, 
the loss function, which depends on the output 
variables of the object
)
(t
Y
and the model
, and 
not on the operator, should take the form: 
[
]
[
]
∑
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(
)
(
)
(
),
(
t
Y
t
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W
t
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t
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, 
where the weights are determined by the significance 
of 
each 
of 
the 
output 
variables
 
In the case of determining mathematical models 
under normal operating conditions, to determine the 
optimal estimates of operator 
 by the criterion of 
the minimum mean square of the error, the basic 
equation for the observation time T can be 
represented as a system of integral equations, 
including auto and cross-correlation functions of the 
variables under consideration [5,6]. 
The main mathematical apparatus for processing the 
results of observations when using methods of 
planning an experiment is regression analysis. The 
regression analysis procedure consists in estimating 
the regression coefficients using the least squares 
method (OLS), followed by statistical analysis of the 
resulting regression model. 
 In this case, the mathematical description is 
presented in the form of a segment of the Taylor 
series: 
...
1
2
1
0
+
+
+
+
=
∑
∑
∑
=
=
=
L
i
ii
ii
L
j
i
ij
ij
L
i
i
i
x
x
x
Y
β
β
β
β
 
Using the results of the experiment, it is possible to 
determine only the sample regression coefficients b0, 
bi, bij, bii, which are only estimates for the theoretical 
regression coefficients β0, βi, βij, βii. 
The regression equation obtained from experience is 
written 
...
1
2
1
0
+
+
+
+
=
∑
∑
∑
=
=
=
∧
L
i
ii
ii
L
j
i
j
i
ij
L
i
i
i
x
b
x
x
b
x
b
b
Y
 
where 
 is the output predicted by the equation. 
International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 
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Page 174 
Following the established tradition in many fields of 
science, we will evaluate the properties of complex 
systems using numerical characteristics. Each of the 
numerical characteristics used to assess the properties 
of a complex system must satisfy at least the 
following requirements: 1) be a value that depends on 
the process of the system's functioning, which, if 
possible, 
is simply calculated based on the 
mathematical description of the system; 2) give a 
visual representation of one of the properties of the 
system; and 3) allow, within the limits of the possible, 
a simple approximate estimate based on experimental 
data. One of the main properties of a complex system 
that characterizes its quality of work is the efficiency 
indicator. Under the indicator of the effectiveness of a 
complex system, we mean a numerical characteristic 
in the form of an efficiency criterion (CE). 
For production processes, the problem of multicriteria 
optimization is formulated as follows: Let the process 
parameters be described by an “n” dimensional input 
vector X ) 
(vector 
of 
parameters) 
, and the quality of 
functioning is estimated by a π dimensional vector - 
function Y (efficiency vector) [6,7]. 
whose 
components are given real functions of the variable X. 
The optimal solution is a certain value of the vector X 
from the set of possible solutions Х
, which 
gives a combination of the levels of the selected 
parameters 
which corresponds to a 
certain optimum of the efficiency vector Y. 
Let us consider the problems of algorithmic control of 
complex systems in the transport system. The 
problem of algorithmic construction of mathematical 
models can be formulated as follows: according to the 
results of the experiment, it is necessary to find the 
optimal, in a sense, an estimate of the object operator 
. In this case, the requirement of closeness of the 
vector random function at the output of the model 
to the vector output variable of the 
object 
should be highlighted. 
The algorithm provides for the possibility of 
obtaining the best estimate 
in the sense of the 
minimum mean square of the error for any number of 
input variables in the class of all possible operators. 
Let us give an algorithm for constructing a static 
model of a control object under normal operating 
conditions [7]. 
Let there be a linear correlation between Уand 
 
 
The model building algorithm is as follows: 
1. Variables of equation (1) are normalized. 
2. Coefficients of paired correlations between 
process variables are calculated. 
3. A system of normal equations is compiled. 
4. By solving the system of normal equations, the 
values of the standardized regression coefficients 
are obtained. 
5. For practical use of the resulting model, it is 
necessary to return to the natural scale. 
6. Calculate the multiple correlation coefficient. 
7. Calculate the residual variance. 
8. Calculate the calculated value of the Fisher 
criterion. 
9. The model is considered adequate if 
 
Where 
is the tabular value of the Fisher 
criterion for the selected significance level of n 
degrees of freedom. 
10. The significance of the coefficients of the 
multiple regression equation is assessed by t - ratio. 
Coefficient 
differs significantly from zero if 
 at the selected significance level and the 
number of degrees of freedom. When 
, 
the coefficient 
 differs insignificantly from zero, 
and in this case the th variable is excluded from 
consideration. 
If the regression equation does not adequately 
describe the process (which is established by clause 
9), then proceed to the construction of a nonlinear 
regression model. 
In this case, the regression equation looks like this: 
 
To simplify the solution of the problem of 
determining the coefficients of the last equation, all 
its second-order terms are considered as new 
variables: 
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where:
, 
q - the number of terms in the last sum of equation (2) 
 
Further, 
the procedure 
for determining 
the 
coefficients of equation (2) completely coincides with 
the above procedure (1-10). Nonlinear equation (2) is 
considered as a linear equation with 
 2 with 
input variables [8]. 
As mentioned above, when constructing mathematical 
models by methods of active experimentation, the 
relationship equations between У and X can be 
implemented in the form of Taylor series. It is most 
convenient to look for this connection in the class of 
linear functions. If the resulting model does not 
satisfy the conditions of adequacy, then go to plans of 
a higher order. 
 In other words, the communication operator must be 
sought in the class of nonlinear functions. 
The proposed algorithm makes it possible to reliably 
evaluate and refine the unknown parameters of linear 
models and can serve as a tool for automated 
processing of experimental results. 
Linear type models 
 
where  is the number of independent variables, are 
the simplest approximating functions. 
The algorithm performs the following sequence of 
calculations: 
1. The average values are calculated for the rows of 
the planning matrix. 
2. Line-by-line variances are determined. 
3. The hypothesis about the homogeneity of the 
sample estimates is tested. 
4. The variance of the reproducibility of the mean 
value of the function is estimated. 
5. The hypothesis about the significance of the 
difference between the maximum and minimum 
values of the optimization parameter is tested 
using the Student's t-test. 
6. This difference is considered significant if 
 for the significance level 
and degrees of freedom ƒ=kmax+kmin. 
7. The coefficients of the regression equation are 
calculated. 
8. The variance of the regression coefficients is 
estimated. 
9. The significance of the coefficients of the 
regression equation is checked using the Student's 
t-test. The 
coefficient 
is 
significant 
if 
 (ƒ1, 
 ) 
10. The residual variance is estimated. 
11. Testing the hypothesis about the adequacy of the 
representation of the response surface by the 
linear regression equation is carried out according 
to the Fisher criterion [9]. 
Adequacy check according to the chosen method is 
possible if the number of significant coefficients of 
the regression equation is at least one less than the 
number of rows of the planning matrix. 
When these two values are equal, it is necessary to 
reduce the dimension of the polynomial by discarding 
one of its terms. It is proposed to discard the term of 
the normalized equation with the minimum, in 
absolute value, coefficient, i.e. this contributes less to 
the increase in residual variance. 
 If the linear model turns out to be inadequate, then go 
to higher-order models (for example, second-order 
plans): 
 (3) 
Nonlinear designs, unlike linear ones, do not 
simultaneously satisfy several optimality criteria. 
Therefore, in each case, it is necessary to choose the 
plan that best suits the research objectives. Items 6 
and further for the Hartley plan with five factors will 
have the following meanings: 
1. The coefficients of the regression equation are 
calculated: 
2. The variance of the regression coefficients is 
estimated. 
3. The covariance of the regression coefficients is 
calculated. 
4. The proportion of the variance of the response 
function due to the linear terms of the regression 
equation is calculated. 
5. The significance of this fraction of the variance 
from zero is checked. 
6. To assess the significance of the group of 
coefficients at the terms of the second order, the 
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proportion of the variance of the response 
function caused by them is calculated: 
7. The significance of the variance associated with 
terms of the second order from zero is checked. 
8. The residual variance is estimated. 
9. The hypothesis about the adequacy of the 
representation of the response surface by the 
nonlinear regression equation according to 
Fisher's criterion is tested. 
One of the main sources of increasing production 
efficiency is improving the quality and productivity 
of technological equipment [10,11]. 
For the effective functioning of the system, it is 
necessary to fulfill a number of conditions of a 
general and special nature, set forth in the form of 
general system requirements, as well as requirements 
for 
information, 
software, 
technical 
and 
organizational types of support. 
System-wide requirements contain a number of 
conditions to ensure the effective functioning of the 
system as a whole. 
The software must contain programs that implement 
the functions of monitoring and controlling processes 
based on microprocessor technology. 
The technical support of the system, on the one hand, 
must be sufficient for the implementation of all 
information, control and auxiliary functions of the 
system, and on the other hand, it must have minimal 
hardware redundancy. 
The organizational support of the system should be 
presented in the form of operating instructions, 
including the form of the system and the regulations 
for its operation in the form of descriptions of the 
functional, technical and organizational structures of 
the system, as well as instructions and regulations for 
the operating personnel on the operation of the 
system. 
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