Theoretical Framework of Optimal Management
Description: In the discipline, skills and habits are studied on the following issues: basic concepts and definitions of optimal control; classification of optimal control problems; static and dynamic optimization; mathematical methods used in the theory of optimal control; methods for finding the extrema of the functions of the classical analysis of one variable; methods of variation calculus; dynamic programming; basic ideas of linear programming; nonlinear programming.
Amount of credits: 6
Пререквизиты:
- Linear Systems of Automatic Control
Course Workload:
| Types of classes | hours |
|---|---|
| Lectures | 30 |
| Practical works | 30 |
| Laboratory works | |
| SAWTG (Student Autonomous Work under Teacher Guidance) | 30 |
| SAW (Student autonomous work) | 90 |
| Form of final control | Exam |
| Final assessment method | Oral exam |
Component: University component
Cycle: Profiling disciplines
Goal
- provide master students with theoretical knowledge and practical skills for the design and analysis of optimal control systems in various fields such as robotics, automation, economics and others.
Objective
- acquiring knowledge and understanding of more complex control systems using optimal control.
- studying methods of analysis and synthesis of optimal control systems
Learning outcome: knowledge and understanding
- Know and understand the basic principles of optimal control, including an understanding of the concepts of optimality, quality functionals, Pontryagin's maximum principles and dynamic programming.
Learning outcome: applying knowledge and understanding
- apply the acquired knowledge and understanding to analyze and design optimal control systems in various fields, such as automation, robotics, economics and others, as well as to solve practical problems of control optimization in real projects.
Learning outcome: formation of judgments
- form judgments about the applicability and effectiveness of optimal control methods in various practical situations, analyze and select suitable methods for specific systems control problems.
Learning outcome: communicative abilities
- Explain basic concepts and principles of optimal control to others, including specialists and non-specialists, and exchange ideas and discussions on problems in systems control.
Learning outcome: learning skills or learning abilities
- systematize and analyze information in the field of optimal management, study additional materials, conduct research and apply new knowledge and methods in their activities.
Teaching methods
When conducting training sessions, the use of the following educational technologies is provided: - interactive lecture (use of the following active forms of learning: guided (managed) discussion or conversation; moderation; demonstration of slides or educational films; brainstorming; motivational speech); - building scenarios for the development of various situations based on given conditions; - information and communication (for example, classes in a computer class using professional application software packages); - search and research (independent research activities of students during the learning process); - solving educational problems.
Assessment of the student's knowledge
Teacher oversees various tasks related to ongoing assessment and determines students' current performance twice during each academic period. Ratings 1 and 2 are formulated based on the outcomes of this ongoing assessment. The student's learning achievements are assessed using a 100-point scale, and the final grades P1 and P2 are calculated as the average of their ongoing performance evaluations. The teacher evaluates the student's work throughout the academic period in alignment with the assignment submission schedule for the discipline. The assessment system may incorporate a mix of written and oral, group and individual formats.
| Period | Type of task | Total |
|---|---|---|
| 1 rating | Practical work 1 | 0-100 |
| Practical work 2 | ||
| Practical work 3 | ||
| Practical work 4 | ||
| 2 rating | Practical work 5 | 0-100 |
| Practical work 6 | ||
| Practical work 7 | ||
| Practical work 8 | ||
| Total control | Exam | 0-100 |
The evaluating policy of learning outcomes by work type
| Type of task | 90-100 | 70-89 | 50-69 | 0-49 |
|---|---|---|---|---|
| Excellent | Good | Satisfactory | Unsatisfactory | |
| Practical work | A complete, detailed answer to the question posed is given, the totality of conscious knowledge about an object is shown, manifested in the free operation of concepts, the ability to identify its essential and non-essential features, and cause-and-effect relationships. Knowledge about an object is demonstrated against the background of understanding it in the system of a given science and interdisciplinary connections. The answer is formulated in scientific terms, presented in literary language, logical, demonstrative, and demonstrates the student’s author’s position. | A detailed answer to the question posed is given, the ability to identify essential and non-essential features and cause-and-effect relationships is demonstrated. The answer is clearly structured, logical, and stated in scientific terms. However, minor errors or omissions were made, which were corrected by the student with the help of “leading questions.” | An incomplete answer was given. There is illogicality in the presentation. The student finds it difficult to prove. A lot of significant errors in the definitions of terms, concepts, characteristics of facts and phenomena. The answer contains no conclusions. Speech is illiterate. When answering additional questions, the student begins to realize the existence of a connection between knowledge only after prompting from the teacher. | A complete, detailed answer to the question posed is given, the totality of conscious knowledge about an object is shown, manifested in the free operation of concepts, the ability to identify its essential and non-essential features, and cause-and-effect relationships. Knowledge about an object is demonstrated against the background of understanding it in the system of a given science and interdisciplinary connections. The answer is formulated in scientific terms, presented in literary language, logical, demonstrative, and demonstrates the student’s author’s position. |
Evaluation form
The student's final grade in the course is calculated on a 100 point grading scale, it includes:
- 40% of the examination result;
- 60% of current control result.
The final grade is calculated by the formula:
| FG = 0,6 | MT1+MT2 | +0,4E |
| 2 |
Where Midterm 1, Midterm 2are digital equivalents of the grades of Midterm 1 and 2;
E is a digital equivalent of the exam grade.
Final alphabetical grade and its equivalent in points:
The letter grading system for students' academic achievements, corresponding to the numerical equivalent on a four-point scale:
| Alphabetical grade | Numerical value | Points (%) | Traditional grade |
|---|---|---|---|
| A | 4.0 | 95-100 | Excellent |
| A- | 3.67 | 90-94 | |
| B+ | 3.33 | 85-89 | Good |
| B | 3.0 | 80-84 | |
| B- | 2.67 | 75-79 | |
| C+ | 2.33 | 70-74 | |
| C | 2.0 | 65-69 | Satisfactory |
| C- | 1.67 | 60-64 | |
| D+ | 1.33 | 55-59 | |
| D | 1.0 | 50-54 | |
| FX | 0.5 | 25-49 | Unsatisfactory |
| F | 0 | 0-24 |
Topics of lectures
- Introduction
- Basic terms and definitions
- Formulation of the optimal control problem
- Optimality criteria
- Mathematical methods used in static optimization
- Mathematical methods used in dynamic optimization
- Analytical design of regulators
- Linear programming
- Nonlinear programming
Key reading
- Methods of classical and modern theory of automatic control: Textbook in 5 volumes / Ed. K.A. Pupkova, N.D. Egupova. – M.: Publishing house of MSTU im. N.E. Bauman. 2004. – 656 p.
- Handbook on the theory of automatic control / Ed. A.A. Krasovsky. – M.: Nauka, 1987. – 712 p.
- Afanasyev V.N., Kolmanovsky V.B., Nosov V.R. Mathematical theory of design of control systems. – M.: Higher. school, 2008. – 574 p.
- Sage E.P., White C.S., III. Optimal systems management /Trans. from English – M.: Radio and Communications, 2002. – 392 p.
Further reading
- Дорф Р, Бишоп Р. Современные системы управления /Пер. с англ. – М.: Ла-боратория Базовых Знаний, 2002. – 832 с.
- Изерман Р. Цифровые системы управления /Пер. с англ. – М.: Мир, 1984. – 541 с.
