Course detail
Algebraic Theory of Control
FSI-VTR Acad. year: 2023/2024 Summer semester
The students will be provided with the principles of the algebraic theory of discrete linear control. The basic algebraic concepts and methods used in the theory will be discussed. The main interest will be focused on the study of polynomials, because they are the
most important tools of the theory of discrete linear control. First, the fundamentals of the theory of rings and the theory of formal series will be expounded. This will be followed by the study of polynomials (as special cases of formal series) and polynomial matrices from the view-point of the theory of discrete linear control. This will be done with the help of the fundamental knowledge of the theory of rings.
Language of instruction
Czech
Number of ECTS credits
3
Supervisor
Department
Entry knowledge
The knowledge of mathematics gained within the bachelor's study programme.
Rules for evaluation and completion of the course
The graded course-unit credit is awarded on condition of having passed a written test at the end of the semester.
Since the attendance at lectures is not compulsory, it will not be checked, and compensation of possible absence will not be required.
Aims
The goal of the course is to acquaint students with the mathematical principles that form the basis of the algebraic theory of discrete linear control and that are used for solving problems of the theory.
Students will be made familiar with solving mathematical problems that occur in the theory of discrete linear control. Basic problems of this kind concern the synthesis of optimal control, which is reduced to searching for solutions of linear polynomial equations (as the transmission of a system can be expressed by using polynomials).
The study programmes with the given course
Programme N-MAI-P: Mathematical Engineering, Master's, compulsory-optional
Programme N-AIŘ-P: Applied Computer Science and Control, Master's, compulsory
Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
Syllabus
1. Introduction
2.-3. Rings
4.-5. Fields
6.-7. Formal power series
8.-9. Polynomials
10.-11. Polynomial fractions
12.-13. Polynomial matrices