Optimal Control Methods and State Prediction
| Title | ΜΕΘΟΔΟΙ ΒΕΛΤΙΣΤΟΥ ΕΛΕΓΧΟΥ ΚΑΙ ΠΡΟΒΛΕΨΗ ΚΑΤΑΣΤΑΣΕΩΝ / Optimal Control Methods and State Prediction |
| Code | ΣΜΥ035 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Efthymios Karatzas |
| Common | No |
| Status | Active |
| Course ID | 600025971 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2025-2030)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| STATISTIKĪ, MONTELOPOIĪSĪ KAI YPOLOGISTIKES METHODOI | Elective Courses belonging to the selected specialization | Spring | - | 10 |
| Academic Year | 2025 – 2026 |
| Class Period | Spring |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600268444
|
Course Type 2021
Specific Foundation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600268444
- At the Website of the School:
- eLearning: https://elearning.auth.gr/course/view.php?id=16843
- Other: https://gitlab.com/karmakis2824/auth_math_postgraduate_course
Erasmus
The course is also offered to exchange programme students.
Prerequisites
General Prerequisites
Fundamental numerical and mathematical analysis and a programming language knowledge.
Learning Outcomes
Upon successful completion of the course, students should understand and analyze and solve optimal control problems with constraints, initial value problems and differential equations, systems of linear differential equations, understand the role of continuous problem stability of such systems, the order of accuracy/convergence and various stability properties of numerical methods for the aforementioned systems applications and know the basic numerical methods for initial value problems, as well as their advantages and disadvantages, to be able to implement the aforementioned methods on the computer.
General Competences
- Apply knowledge in practice
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Adapt to new situations
- Make decisions
- Work autonomously
- Work in teams
- Work in an international context
- Work in an interdisciplinary team
- Generate new research ideas
Course Content (Syllabus)
Optimal control with PDE constraints and matrices numerical calculations. Numerical stability, convergence rates, numerical solving and system conditioning of such systems. Elementary orthogonal transformations. QR factorization and least squares solutions. Eigenvalue problem. Calculation of Schur and Jordan forms. The problem of generalized eigenvalues. SVD factorization. Solving systems. Exponential matrix sensitivity. The method of series. The method of matrix factorization. Errors in solving systems. Discretization of continuous systems. Solving PDE optimal control systems. Condition number. Newton's method. The method of sign matrices. The method of eigensystems. The method of generalized eigensystems.
Keywords
Optimal controlς with PDEs as constraints, Numerical Analysis.
Educational Material Types
- Slide presentations
- Multimedia
- 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
- Use of ICT in Student Assessment
Description
Slides projector, computer.
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 75 | ||||
| Seminars | 25 | ||||
| Laboratory Work | 50 | ||||
| Reading Assigment | 150 | ||||
| Exams | |||||
| Total | 300 |
Student Assessment
Description
Αssignment, presentation of assignment, written exams.
Student Assessment methods
- Written Exam with Short Answer Questions (Formative)
- Written Exam with Extended Answer Questions (Formative)
- Written Assignment (Formative)
- Oral Exams (Formative)
- Performance / Staging (Formative)
- Written Exam with Problem Solving (Formative)
- Labortatory Assignment (Formative)
Bibliography
Course Bibliography (Eudoxus)
[1] Αλ. Μπακόπουλος και Ιων. Χρυσοβέργης, “Εισαγωγή στην Αριθμητική Ανάλυση”, Εκδόσεις Συμμετρία.
[2] Γ. Ακριβής και Β. Δουγαλής, “Εισαγωγή στην Αριθμητική Ανάλυση”, Πανεπιστημιακές Εκδόσεις Κρήτης.
Additional bibliography for study
Αναφορές
[1] J. Nocedal and S. Wright, “Numerical Optimization”, Springer-Verlag 2006.
[2] E. Polak, “Optimization”, Springer-Verlag 1997.
[3] M. Asch, “A Toolbox for Digital Twins : From Model-Based to Data-Driven” Society for Industrial and Applied Mathematics SIAM, Philadelphia, 2022.
[4] Α. Quarteroni, R. Sacco, and F. Saleri, “Numerical Mathematics”, Springer-Verlag 2007.
Last Update
15-09-2025
