Infopaket

Applied stability problems

ДВС.2.03

Вибіркова дисципліна для ОП

First

2023/2024

7 Semester

3

PLO2. Be able to use basic principles and methods of mathematical, complex and functional analysis, linear algebra and number theory, analytical geometry, and differential equations, including partial differential equations, probability theory, mathematical statistics and random processes, numerical methods. PLO 5. Be able to develop and use in practice algorithms related to the approximation of functional dependencies, numerical differentiation and integration, solving systems of algebraic, differential and integral equations, solving boundary value problems, finding optimal solutions. PLO 22.2. Have knowledge of the mathematical modeling and optimal management fundamentals, to the extent necessary for the development of applied disciplines and use the relevant knowledge in the chosen profession.

Full-time form

1. Successful mastering of the following disciplines: 1) Mathematical analysis. 2) Functional analysis. 3) Linear algebra 4) Differential equations. 5) Control theory 2. Knowledge: 1. Theoretical foundations and methods of construction, verification, and the study of quantitative and qualitative properties of mathematical models. 2. Principles of analysis and optimization of control systems. 3. Numerical methods for finding solutions of differential equations and systems of differential equations. 3. Skills: 1. Solve the basic problems of differential equations theory. 2. Research the properties of functions. 3. Formulate and solve the main problems of control theory. 4. Apply methods of matrix theory. 4. Possession of: 1. Basic skills in programming and using application packages. 2. Skills of analysis and solving problems of mathematical modeling using algebraic approaches, methods of mathematical and functional analysis, and operations research.

The aim of the course is to enable students to master constructive approaches to system analysis using methods of stability theory, as well as to acquire knowledge of problem formulations in stability theory, theoretical foundations, methods, and their applications.

1. Pichkur V.V., Kapustian O.V., Sobchuk V.V. Teoriia dynamichnykh system. – Lutsk: Vezha-Druk, 2020. – 348 p. 2. Bashniakov O.M., Pichkur V.V. Zadacha syntezu v teorii keruvannia: Navchalnyi posibnyk. – K.: Vyd-vo «Stal», 2012. – 116 p. 3. Harashchenko F.H., Pichkur V.V. Prykladni zadachi teorii stiikosti. – K.: VPTs «Kyivskyi universytet», 2014. – 142 p. 4. Samoilenko A.M., Perestiuk M.O., Parasiuk I.O. Dyferentsialni rivniannia. – K.: Lybid, 2003. – 600 p. 5. Khalil H.K. Nonlinear systems. – NJ.: Prentice Hall, 2002. – 766 p. 6. Parasiuk I.O. Vstup do yakisnoi teorii dyferentsialnykh rivnian. – K.: VPTs «Kyivskyi universytet», 2005. – 88 p. 7. Scheinerman, Edward R. Invitation to Dynamical Systems. – Baltimore: The Johns Hopkins University, 2000. – 289 p. 8. Pichkur V. On practical stability of differential inclusions using Lyapunov functions. Discrete and Continuous Dynamical Systems. Series B., 2017, 22, р. 1977-1986.

Lectures, classes, self-study, study of the recommended sources, homework.

Semester assessment: The maximum number of points a student can obtain is 100 points: 1. Midterm test №1: 30/18 points. 2. Midterm test №2: 30/18 points. 3. Independent work №1: 10/6 points. 4. Independent work №2: 10/6 points. 5. Continuous assessment: 20/12 points.

Ukrainian