Controllable dynamic systems and underdetermined systems of differential equations

2011 ◽  
Vol 72 (9) ◽  
pp. 1822-1832
Author(s):  
V. I. Elkin
Keyword(s):  
Differential Equations ◽  
Dynamic Systems ◽  
Underdetermined Systems ◽  
Systems Of Differential Equations

scholarly journals Investigation of rigid dynamic systems on the example of modelling a tape drive mechanism

2020 ◽  
Vol 329 ◽  
pp. 03003
Author(s):  
Ruslan Nigay ◽  
Evgeny Nigay ◽  
Lubov Mironova
Keyword(s):  
Differential Equations ◽  
Dynamic Systems ◽  
Stiff Systems ◽  
Tape Drive ◽  
Elementary Functions ◽  
Drive Mechanism ◽  
System A ◽  
Systems Of Differential Equations ◽  
Numerical Analytical Method ◽  
Higher Order Differential Equations

The features of modeling the dynamics of mechanical systems on the example of the operation of the tape drive mechanism related to real technological processes are stated. An approach to solving stiff systems of differential equations by the numerical-analytical method is noted. The approach is based on solving systems of higher-order differential equations using elementary functions using procedures for precision search for the roots of the characteristic polynomial of the system. A mathematical model of the tape drive mechanism of a VCR is given as an example of a precision electromechanical object.

scholarly journals Grounds for Searching the Best Solution for Controlling the Pressurized Water Reactor in Dynamic Modes when Changing the Controlled Parameters

2021 ◽  
Vol 7 (1) ◽  
pp. 56-61
Author(s):  
Taia Petik ◽  
◽  
Viktoriia Vataman ◽  
Konstantin Beglov ◽  
Anna Lysyuk
Keyword(s):  
Information Technology ◽  
Differential Equations ◽  
Control Systems ◽  
Dynamic Systems ◽  
Quality Criteria ◽  
System Quality ◽  
Complex Dynamic ◽  
Complex Dynamic Systems ◽  
Systems Of Differential Equations ◽  
Analysis And Synthesis

The article focused on the development of information technology for the optimization of control over complex dynamic systems at the stage of their design that should realize possibilities of modeling of linear and nonlinear dynamic systems, the analysis and synthesis of such systems, their optimization on various quality criteria. The purpose of this article is to develop the structure and elements of information technology to optimize the control of complex dynamic systems, including automated control systems. The general structure and functional model of information technology of the analysis and synthesis of control systems includes modeling of dynamic systems in the form of systems of differential equations and transfer functions, integration of systems of differential equations, calculation of system quality criteria, methods for solving various optimization tasks on solutions of optimization problems of dynamic systems is offered.

scholarly journals MODELING THE DEVELOPMENT OF EPIDEMIS BASED ON INFORMATION TECHNOLOGIES OF OPTIMIZATION

2021 ◽  
pp. 47-52
Author(s):  
Olena Nikulina ◽  
Valerii Severyn ◽  
Mariia Naduieva ◽  
Anton Bubnov
Keyword(s):  
Information Technology ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Mathematical Models ◽  
Dynamic Systems ◽  
Information Technologies ◽  
Model Parameters ◽  
Infected People ◽  
Systems Of Differential Equations ◽  
Epidemic Development

Mathematical models of the epidemic have been developed and researched to predict the development of the COVID-19 coronavirus epidemic on thebasis of information technology for optimizing complex dynamic systems. Mathematical models of epidemics SIR, SIRS, SEIR, SIS, MSEIR in theform of nonlinear systems of differential equations are considered and the analysis of use of mathematical models for research of development ofepidemic of coronavirus epidemic COVID-19 is carried out. Based on the statistics of the COVID-19 coronavirus epidemic in the Kharkiv region, theinitial values of the parameters of the models of the last wave of the epidemic were calculated. Using these models, the program of the first-degreesystem method from the module of information technology integration methods for solving nonlinear systems of differential equations simulated thedevelopment of the last wave of the epidemic. Simulation shows that the number of healthy people will decrease and the number of infected peoplewill increase. In 12 months, the number of infected people will reach its maximum and then begin to decline. The information technology ofoptimization of dynamic systems is used to identify the parameters of the COVID-19 epidemic models on the basis of statistical data on diseases in theKharkiv region. Using the obtained models, the development of the last wave of the COVID-19 epidemic in Kharkiv region was predicted. Theprocesses of epidemic development according to the SIR-model with weakening immunity are given, with the values of the model parameters obtainedas a result of identification. Approximately 13 months after the outbreak of the epidemic, the number of infected people will reach its maximum andthen begin to decline. In 10 months, the entire population of Kharkiv region will be infected. These results will allow us to predict possible options forthe development of the epidemic of coronavirus COVID-19 in the Kharkiv region for the timely implementation of adequate anti-epidemic measures.

The Stability Study of Dynamic Systems Using the Leapunov Function Method

2019 ◽  
Vol 34 ◽  
pp. 123-128
Author(s):  
Dumitru Bălă
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Dynamic System ◽  
Dynamic Systems ◽  
Function Method ◽  
Autonomous Systems ◽  
Stability Study ◽  
Systems Of Differential Equations ◽  
Stability Theorems ◽  
The Stability

The paper includes the stability study of some dynamical systems given by systems of differential equations. The paper examines the stability of three dynamic systems using the Leapunov function method. The originality of the paper consists of how we choose the Leapunov function. We apply the stability theorems given by Leapunov for autonomous systems. Stability is an important property of a dynamic system that has applications in the technique.

SOLUTION OF SOME SYSTEMS OF DIFFERENTIAL EQUATIONS IN MATHEMATICAL SYSTEM MAPLE

2013 ◽  
Vol 1 (05) ◽  
pp. 58-65
Author(s):  
Yunona Rinatovna Krakhmaleva ◽  
◽  
Gulzhan Kadyrkhanovna Dzhanabayeva ◽  
Keyword(s):  
Differential Equations ◽  
Systems Of Differential Equations ◽  
Mathematical System

On decomposability of countable systems of differential equations

1993 ◽  
Vol 45 (10) ◽  
pp. 1598-1608
Author(s):  
A. M. Samoilenko ◽  
Yu. V. Teplinskii
Keyword(s):  
Differential Equations ◽  
Systems Of Differential Equations

scholarly journals Differential Games for an Infinite 2-Systems of Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1467
Author(s):  
Muminjon Tukhtasinov ◽  
Gafurjan Ibragimov ◽  
Sarvinoz Kuchkarova ◽  
Risman Mat Hasim
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Differential Games ◽  
Differential Game ◽  
Infinite System ◽  
The State ◽  
Geometric Constraints ◽  
Control Parameters ◽  
Systems Of Differential Equations ◽  
Pursuit And Evasion

A pursuit differential game described by an infinite system of 2-systems is studied in Hilbert space l2. Geometric constraints are imposed on control parameters of pursuer and evader. The purpose of pursuer is to bring the state of the system to the origin of the Hilbert space l2 and the evader tries to prevent this. Differential game is completed if the state of the system reaches the origin of l2. The problem is to find a guaranteed pursuit and evasion times. We give an equation for the guaranteed pursuit time and propose an explicit strategy for the pursuer. Additionally, a guaranteed evasion time is found.

Sign in / Sign up

Export Citation Format

Share Document