Numerical Methods with Applications in Control

Course Information
TitleΑΡΙΘΜΗΤΙΚΕΣ ΜΕΘΟΔΟΙ ΜΕ ΕΦΑΡΜΟΓΕΣ ΣΤΗ ΘΕΩΡΙΑ ΕΛΕΓΧΟΥ / Numerical Methods with Applications in Control
Code0847
FacultySciences
SchoolMathematics
Cycle / Level2nd / Postgraduate
Teaching PeriodWinter/Spring
CommonNo
StatusActive
Course ID40000069

Programme of Study: PMS Tmīmatos Mathīmatikṓn (2018-sīmera)

Registered students: 12
OrientationAttendance TypeSemesterYearECTS
THEŌRĪTIKĪ PLĪROFORIKĪ KAI THEŌRIA SYSTĪMATŌN KAI ELEGCΗOUCompulsory CourseWinter/Spring-10
Class Information
Academic Year2025 – 2026
Class PeriodSpring
Faculty Instructors
Weekly Hours3
Total Hours39
Class ID
600294324
Type Of Offer
  • Disciplinary Course
Course Type 2021
Specialization / Direction
Mode of Delivery
  • Face to face
  • Distance learning
Digital Course Content
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
  • Greek (Instruction, Examination)
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 as well as 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. 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
  • Retrieve, analyse and synthesise data and information, with the use of necessary technologies
  • Adapt to new situations
  • Make decisions
  • Work autonomously
  • Work in teams
  • Generate new research ideas
  • Be critical and self-critical
  • Advance free, creative and causative thinking
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 controls with PDEs as constraints, Numerical Analysis.
Educational Material Types
  • Notes
  • Slide presentations
  • Multimedia
  • Book
Use of Information and Communication Technologies
Use of ICT
  • Use of ICT in Course Teaching
  • Use of ICT in Communication with Students
  • Use of ICT in Student Assessment
Description
Slides projector, computer, python3, C++, supporting research in numerical analysis and PDEs. Online exercise hours.
Course Organization
ActivitiesWorkloadECTSIndividualTeamworkErasmus
Lectures391.3
Reading Assigment1836.1
Tutorial130.4
Project200.7
Written assigments401.3
Exams50.2
Total30010
Student Assessment
Description
The final grade for this course will be calculated as follows: 1. Midterm: 30% 2. Final exam: 50%.
Student Assessment methods
  • Written Exam with Short Answer Questions (Formative, Summative)
  • Written Exam with Extended Answer Questions (Formative, Summative)
  • Written Assignment (Formative, Summative)
  • Performance / Staging (Formative, Summative)
Bibliography
Additional bibliography for study
-J. Nocedal and S. Wright, “Numerical Optimization”, Springer-Verlag 2006. -E. Polak, “Optimization”, Springer-Verlag 1997.
Last Update
15-09-2025