Algebraic Theory of Control (FSI-VTR-K)

Academic year 2018/2019
Supervisor: doc. Mgr. Jaroslav Hrdina, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
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.
Learning outcomes and competences:
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).
Prerequisites:
The knowledge of mathematics gained within the bachelor's study programme.
Course contents:
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.
Teaching methods and criteria:
The course is taught through lectures explaining the basic principles and theory of the discipline.
Assesment methods and criteria linked to learning outcomes:
The graded course-unit credit is awarded on condition of having passed a written test at the end of the semester.
Controlled participation in lessons:
Since the attendance at lectures is not compulsory, it will not be checked, and compensation of possible absence will not be required.
Type of course unit:
    Guided consultation  1 × 9 hrs. optionally                  
    Controlled Self-study  1 × 17 hrs. optionally                  
Course curriculum:
    Guided consultation 1. Introduction
2.-3. Rings
4.-5. Fields
6.-7. Formal power series
8.-9. Polynomials
10.-11. Polynomial fractions
12.-13. Polynomial matrices
    Controlled Self-study 1. Introduction
2.-3. Rings
4.-5. Fields
6.-7. Formal power series
8.-9. Polynomials
10.-11. Polynomial fractions
12.-13. Polynomial matrices
Literature - fundamental:
1. V.Kučera: Algebraická teorie diskrétního lineárního řízení, Academia, Praha, 1978
2. J.Karásek, J.Šlapal: Teorie okruhů pro diskrétní lineární řízení, FSI VUT v Brně, 2000 (učební text)
Literature - recommended:
1. J.Karásek, J.Šlapal: Teorie okruhů pro diskrétní lineární řízení, FSI VUT v Brně, 2000 (učební text)
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
M2I-K combined study M-AIŘ Applied Computer Science and Control -- GCr 4 Compulsory 2 2 S
M2I-K combined study M-AIŘ Applied Computer Science and Control P linked to branch B-AIR GCr 4 Compulsory 2 2 S