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Generalized optimal control

Вибіркова дисципліна для ОП

First

2021/2022

7 Semester

1

LO 10. Be able to choose methods and algorithms rationally for solving optimization problems, operations research, optimal control and decision-making, data analysis. PLO 23.1. Be able to use professional knowledge, skills and abilities in the field of computational mathematics and computer science to model real processes of different nature.

Distance form

1. Know the basics of: ● real analysis (in particular, sequences, limits, differential calculus, Riemann’s integral, functional series, inverse and implicit functions), ● linear algebra (in particular, linear spaces, linear operators, and quadratic forms), ● differential equations (in particular, first-order ODEs, higher-order ODEs, and systems of ODEs), ● probability theory (in particular, absolutely continuous probability distributions), ● functional analysis (in particular, metric spaces, fixed-point theorem, normed spaces, linear functionals and operators, and Hilbert spaces). 2. Be able to solve problems in real analysis, linear algebra, differential equations, probability theory and functional analysis.

The aim of the discipline "Generalized Optimal Control" is to acquaint students with the basic concepts and provisions of the theory of extreme problems, typical examples of its applications, theorems of weak solvability of partial differential equations on which generalized optimal control problems are based; mastering the basic methods of solving certain classes of problems of variational calculus and optimal control and modern methods of deriving models of mathematical physics. The subject of the discipline "Generalized optimal control" are problems of classical variational calculus and problems of optimal control, examples of application of this theory in models of applied mathematics.

Lectures, recommended literature processing

- Intermediate assessment: 1. Test work no. 1: LO 1.1., LO 1.2, LO 2.1, LO 2.2, LO 2.3 ‒ 30 points/18 points. 2. Test work no. 2: LO 1.3, LO 1.4, LO 2.4, LO 2.5, LO 2.6 ‒ 30 points/18 points. The work in the semester consists of 2 parts. Each part ends with a test with a maximum score of 30 points. - Final assessment: ● is held in the form of an exam – 40 points; ● The results of study to be assessed are: LO 1.1, LO 1.2, LO 1.3, LO 1.4, LO 2.1, LO 2.2, LO LO, LO 2.4, LO 2.5 and LO 2.6; ● The form of exam: written; ● The types of assignments are 2 theoretical questions and 2 exercises.

Ukrainian