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Elements of optimal control

ДВС.4.01.01

Вибіркова дисципліна для ОП

Second

2021/2022

4 Semester

4

PLO1. To identify problem situations, perform their research based on a systematic approach, make informed choices of methods and models for the formation of effective management decisions, and apply models and methods of decision-making in forecasting the development of the enterprise and in the domain of computer science. LO21.3. To develop software for modern computing systems.

Full-time form

1. Know: Mathematical analysis, functional analysis, theory of differential equations, algebra, and numerical methods in the scope of the first four university courses. 2. Be able to read, understand, and analyze mathematical texts. Implement programs in one general-purpose programming language. Confidently read literature in English. 3. Possess skills: working with a computer, searching for information on the Internet, using translation tools, and creating mathematical texts and presentations.

The goal of the discipline is to provide students with competence in mathematical approaches to optimal control problems. To create a sufficient understanding of the main theoretical concepts along with the acquisition of practical skills in the implementation and application of relevant algorithms. Within the framework of the discipline, students get acquainted with the mathematical apparatus of the theory of optimal control and the corresponding algorithms. Both practical implementation and application, and theoretical research of such algorithms are practiced. Students also practice presenting the results of their research.

1. Klyushin D.A, Lyashko S.I., Nomirovsky D.A., Petunin Yu.,I., Semenov V.V. Generelized solutions of operator equations and extreme elements //Springer.- 2012.- New York, Dordrecht, Heidelberg, London.- 200p. 2. Lyashko S.I. Obobschennoe upravlenie lineynyimi sistemami. K.: Naukova dumka, 1998. – 472 s. 3. Lyashko I.I., Didenko V.P., Tsitritskiy O.E. Filtratsiya shumov. K.: Naukova dumka. 1979, -230 s. 4. Lions Zh.-L. Optimalnoe upravlenie sistemami, opisyivaemyie uravneniyami s chastnyimi proizvodnyimi. - M.: Mir, 1972. - 415s. 5. Vasilev F.P. Metodyi resheniya ekstremalnyih zadach. – M.: Nauka. – 1981. – 400 s. 6. Butkovskiy A.G. Metodyi upravleniya sistemami s raspredelennyimi parametrami. – M.: Nauka. – 1975. – 568 s. 7. Alekseev V.M., Tihomirov V.M., Fomin S.V. Optimalnoe upravlenie. – M.: Nauka. – 1979. – 430 s. 8. Yang L. Lektsii po variatsionnomu ischisleniyu i teorii optimalnogo upravleniya. – M.: Mir. – 1974. – 488 s.

Lectures, implementation of the project, preparation of the report.

Semester assessment: 1. Modular control work - 20 points/12 points. 2. Implementation of the project - 20 points/12 points. 3. Report – 20 points/12 points. Final evaluation (in the form of an exam): - the maximum number of points that can be obtained by a student: 40 points; - learning outcomes that will be assessed: PH1.1, PH1.2, PH1.3, PH2.1; - form of implementation and types of tasks: written. Types of tasks: 4 written tasks - two general theoretical questions and two tasks for substantiating the properties of the algorithm. Each task is valued at 10 points.

Ukrainian