Optimal Control Theory
| Title | ΘΕΩΡΙΑ ΒΕΛΤΙΣΤΟΥ ΕΛΕΓΧΟΥ / Optimal Control Theory |
| Code | 0844 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter |
| Coordinator | Nikolaos Karampetakis |
| Common | No |
| Status | Active |
| Course ID | 40000066 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2018-sīmera)
Registered students: 24
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKĪ PLĪROFORIKĪ KAI THEŌRIA SYSTĪMATŌN KAI ELEGCΗOU | Core Courses | 1 | 1 | 10 |
| STATISTIKĪ KAI MONTELOPOIĪSĪ | Elective Courses | 1 | 1 | 10 |
| Academic Year | 2025 – 2026 |
| Class Period | Winter |
| Faculty Instructors |
|
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600290412
|
Course Type 2016-2020
- Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600290412
- At the Website of the School: http://www.math.auth.gr/el/content/%CE%B8%CE%B5%CF%89%CF%81%CE%AF%CE%B1-%CE%B2%CE%AD%CE%BB%CF%84%CE%B9%CF%83%CF%84%CE%BF%CF%85-%CE%B5%CE%BB%CE%AD%CE%B
- eLearning: https://elearning.auth.gr/course/view.php?id=6823
- OpenCourses (eClass): https://opencourses.auth.gr/courses/OCRS288/
- Other: http://eclass.auth.gr/courses/MATH106/
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
General Prerequisites
Calculus, Matrix Theory, Modern Control Theory
General Competences
- Apply knowledge in practice
- Work autonomously
- Work in teams
- Generate new research ideas
- Advance free, creative and causative thinking
Course Content (Syllabus)
The optimal control problem basic mathematical notion from the variational calculus - minimization of functionals - Euler-Lagrance equation - minimization of functional under constraints - optimal control of continuous or discrete time systems with or without state/input constraints - the minimum principle of Pontryagin - the linear quadratic (LQ) regulation and tracking problem - Riccati equation - bang-bang control - Hamilton-Jacobi-Bellman theory - dynamic programming - the linear quadratic Gaussian (LQG) problem - applications in Matlab.
Keywords
optimal control, linear systems, calculus of variations
Educational Material Types
- Notes
- Slide presentations
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
- Use of ICT in Laboratory Teaching
- Use of ICT in Communication with Students
Description
Use of pptx slides for the presentations posted on eclass.auth.gr.
Matlab and Mathematica are used in the courses.
Students are contacted via eclass.auth.gr, while assignments are sent to optimal.control.math.auth@gmail.com
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | |||||
| Laboratory Work | |||||
| Project | |||||
| Written assigments | |||||
| Total |
Student Assessment
Description
The assessment is made by 30% by the delivery of weekly assignments, by 70% by the final examination as well as by the assignment of presentations on specific topics.
Student Assessment methods
- Written Assignment (Summative)
- Performance / Staging (Summative)
- Written Exam with Problem Solving (Formative)
- Labortatory Assignment (Formative)
Bibliography
Additional bibliography for study
1. Burl J.B. (1998). Linear Optimal Control: H2 and H Methods. Addison-Wesley.
2. Lewis F.L. (1995). Optimal Control. 2nd edition. John Wi¬ley and Sons; New York.
3. Donald E. Kirk (1970), Optimal Control Theory : An Introduction, Prentice Hall.
4. D. S. Naidu, (2003), Optimal Control Systems, CRC Press.
5. A. Shina, 2007, Linear systems : optimal and robust control, CRC Press
6. V.M. Tikhomirov, 1999, Ιστορίες για μέγιστα και ελάχιστα, Εκδόσεις Κάτο-πτρο.
7. Καραμπετάκης Ν., (2009), Βέλτιστος Έλεγχος Συστημάτων, Εκδόσεις Ζήτη.
8. Κυβεντίδης Θ., (1994). Λογισμός μεταβολών, Εκδόσεις Ζήτη.
Last Update
24-05-2023
