scholarly journals Optimization problem of external dynamic influences for the elimination of vibration phenomena in composite elastic building structures

2021 ◽  
Vol 2094 (4) ◽  
pp. 042065
Author(s):  
V V Provotorov ◽  
Y O Lebedeva ◽  
D Tran ◽  
L N Borisoglebskaya ◽  
E I Vorobyov
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Computational Procedure ◽  
Complex Object ◽  
Modern Theory ◽  
Extensive Literature ◽  
Building Structures ◽  
Bridge Cable ◽  
Metal Building ◽  
Modern Application

Abstract The paper considers the actual task of construction engineering: the elimination of harmful (undesirable) vibration phenomena in composite metal building structures and bridge cable-stayed systems – complete damping and vibration of the bridge cable-stayed system entails the calming of the entire bridge structure. Similar problems arise when designing devices that lead to dynamic rest of network antenna structures. The presentation of the material is based on the main provisions of the modern theory of optimal control of distributed differential systems with network carriers. An extensive literature is devoted to the sanctification of the research of the mentioned problem, however, an exhaustive solution of the problems of controlling elastic structures by external influences of various types (distributed, boundary, starting, and point control) and a comparative analysis of their properties did not find their place in these studies. In addition, the ways of algorithmization of previously obtained results are not always specified. The paper uses a mathematical model describing small oscillations of a spatial string system. It is convenient to use such a system and approaches to the analysis of its mathematical model as a fairly simple fundamental object when considering a more complex object, which is an elastic system of more complex elements. The results of the work are presented in a form that makes it possible to formalize the computational procedure, which is convenient for algorithmizing the process of determining the solution, and therefore for the modern application of computer technology. It remains to add that the work indicates ways to transfer the obtained results to the case of analyzing optimal control problems with carriers on multidimensional network-like domains.

MARKOV MATHEMATICAL MODEL OF DYNAMIC ADAPTIVE TESTING OF AN ACTIVE AGENT

2018 ◽  
pp. 29-35
Author(s):  
N. V. Brovka ◽  
P. P. Dyachuk ◽  
M. V. Noskov ◽  
I. P. Peregudova
Keyword(s):  
Mathematical Model ◽  
Finite State Machine ◽  
Active Agent ◽  
Adaptive Testing ◽  
State Machine ◽  
Learning Activities ◽  
Independent Learning ◽  
Complex Object ◽  
Total Reward ◽  
Finite State

The problem and the goal.The urgency of the problem of mathematical description of dynamic adaptive testing is due to the need to diagnose the cognitive abilities of students for independent learning activities. The goal of the article is to develop a Markov mathematical model of the interaction of an active agent (AA) with the Liquidator state machine, canceling incorrect actions, which will allow mathematically describe dynamic adaptive testing with an estimated feedback.The research methodologyconsists of an analysis of the results of research by domestic and foreign scientists on dynamic adaptive testing in education, namely: an activity approach that implements AA developmental problem-solving training; organizational and technological approach to managing the actions of AA in terms of evaluative feedback; Markow’s theory of cement and reinforcement learning.Results.On the basis of the theory of Markov processes, a Markov mathematical model of the interaction of an active agent with a finite state machine, canceling incorrect actions, was developed. This allows you to develop a model for diagnosing the procedural characteristics of students ‘learning activities, including: building axiograms of total reward for students’ actions; probability distribution of states of the solution of the problem of identifying elements of the structure of a complex object calculate the number of AA actions required to achieve the target state depending on the number of elements that need to be identified; construct a scatter plot of active agents by target states in space (R, k), where R is the total reward AA, k is the number of actions performed.Conclusion.Markov’s mathematical model of the interaction of an active agent with a finite state machine, canceling wrong actions allows you to design dynamic adaptive tests and diagnostics of changes in the procedural characteristics of educational activities. The results and conclusions allow to formulate the principles of dynamic adaptive testing based on the estimated feedback.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

Optimal control strategy for cancer remission using combinatorial therapy: A mathematical model-based approach

2021 ◽  
Vol 145 ◽  
pp. 110789
Author(s):  
Parthasakha Das ◽  
Samhita Das ◽  
Pritha Das ◽  
Fathalla A. Rihan ◽  
Muhammet Uzuntarla ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Strategy ◽  
Optimal Control Strategy ◽  
Combinatorial Therapy ◽  
Model Based ◽  
Cancer Remission

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

scholarly journals Fractional-Order Modelling and Optimal Control of Cholera Transmission

2021 ◽  
Vol 5 (4) ◽  
pp. 261
Author(s):  
Silvério Rosa ◽  
Delfim F. M. Torres
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Sensitivity Analysis ◽  
Fractional Order ◽  
Control Measures ◽  
Time Interval ◽  
Variable Order ◽  
Effectiveness Analysis ◽  
The Cost ◽  
Derivative Order

A Caputo-type fractional-order mathematical model for “metapopulation cholera transmission” was recently proposed in [Chaos Solitons Fractals 117 (2018), 37–49]. A sensitivity analysis of that model is done here to show the accuracy relevance of parameter estimation. Then, a fractional optimal control (FOC) problem is formulated and numerically solved. A cost-effectiveness analysis is performed to assess the relevance of studied control measures. Moreover, such analysis allows us to assess the cost and effectiveness of the control measures during intervention. We conclude that the FOC system is more effective only in part of the time interval. For this reason, we propose a system where the derivative order varies along the time interval, being fractional or classical when more advantageous. Such variable-order fractional model, that we call a FractInt system, shows to be the most effective in the control of the disease.

scholarly journals Identification of Neural Network Model of Robot to Solve the Optimal Control Problem

2021 ◽  
Vol 20 (6) ◽  
pp. 1254-1278
Author(s):  
Elizaveta Shmalko ◽  
Yuri Rumyantsev ◽  
Ruslan Baynazarov ◽  
Konstantin Yamshanov
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Mathematical Model ◽  
Optimal Control ◽  
Neural Network Model ◽  
Software Package ◽  
Control Object ◽  
Robotic Systems ◽  
Object Model ◽  
Modern Machine

To calculate the optimal control, a satisfactory mathematical model of the control object is required. Further, when implementing the calculated controls on a real object, the same model can be used in robot navigation to predict its position and correct sensor data, therefore, it is important that the model adequately reflects the dynamics of the object. Model derivation is often time-consuming and sometimes even impossible using traditional methods. In view of the increasing diversity and extremely complex nature of control objects, including the variety of modern robotic systems, the identification problem is becoming increasingly important, which allows you to build a mathematical model of the control object, having input and output data about the system. The identification of a nonlinear system is of particular interest, since most real systems have nonlinear dynamics. And if earlier the identification of the system model consisted in the selection of the optimal parameters for the selected structure, then the emergence of modern machine learning methods opens up broader prospects and allows you to automate the identification process itself. In this paper, a wheeled robot with a differential drive in the Gazebo simulation environment, which is currently the most popular software package for the development and simulation of robotic systems, is considered as a control object. The mathematical model of the robot is unknown in advance. The main problem is that the existing mathematical models do not correspond to the real dynamics of the robot in the simulator. The paper considers the solution to the problem of identifying a mathematical model of a control object using machine learning technique of the neural networks. A new mixed approach is proposed. It is based on the use of well-known simple models of the object and identification of unaccounted dynamic properties of the object using a neural network based on a training sample. To generate training data, a software package was written that automates the collection process using two ROS nodes. To train the neural network, the PyTorch framework was used and an open source software package was created. Further, the identified object model is used to calculate the optimal control. The results of the computational experiment demonstrate the adequacy and performance of the resulting model. The presented approach based on a combination of a well-known mathematical model and an additional identified neural network model allows using the advantages of the accumulated physical apparatus and increasing its efficiency and accuracy through the use of modern machine learning tools.

scholarly journals Dynamics and optimal control of chemotherapy for low grade gliomas: Insights from a mathematical model

2016 ◽  
Vol 21 (6) ◽  
pp. 1895-1915 ◽  
Author(s):  
Clara Rojas ◽  
Juan Belmonte-Beitia ◽  
Víctor M. Pérez-García ◽  
Helmut Maurer
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Low Grade ◽  
Low Grade Gliomas

Information dualism of the problem of optimum terminal control of dynamic object

2021 ◽  
pp. 85-90
Author(s):  
V.P. Ivanov
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Law ◽  
Computational Algorithms ◽  
Terminal Control ◽  
Dynamic Object ◽  
Nonlinear Mathematical Model ◽  
Dynamical Object

The article deals with the problem of synthesis of terminal control. A functional, a nonlinear mathematical model of a dynamic object, restrictions on the maximum permissible values of control are given. The control law is synthesized. The following statement is proved: the synthesis of the optimal control is carried out using the entire initial mathematical model of the dynamical object, but to calculate the control at any particular moment of time, it is possible to use a reduced (truncated) model, which simplifies the computational algorithms. Thus, there is an informational dualism of the manage- ment task. The approach is an extension of the principle of information redefinition of Yu.B. Germeier to the area of optimal terminal control.

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