Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course This course serves as an introductory course on the controllability of partial differential equations . Students will be first introduced with the back-stepping technique. Then they will apply this method to basic second order parabolic and hyperbolic equations. This course will prepare students to do research and study advanced problems in partial differential equations.
Course Content Controllability and observability of PDEs (using back-stepping methods)
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator Türker Özsarı
Name of Lecturers Türker Özsarı
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources M. Krstic and A. Smyshlyaev, Boundary Control of PDEs: A Course on Backstepping Designs, SIAM, 2008.

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 1 % 30
Quizzes 0 % 0
Homeworks 5 % 30
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 40
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 3 14 42
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 14 6 84
Exams and Exam Preparations 2 30 60
Total Work Load   Number of ECTS Credits 6 186

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 Ability to comprehend the notion of boundary feedback controllability and observability for PDEs
2 Ability to use the back-stepping transformation to control PDEs
3 Ability to understand the differences between linear and nonlinear PDE models from the point of controllability

Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Introduction
2 Lyapunov Stability
3 Exact Solutions to PDEs, Boundary control of parabolic PDEs
4 Boundary control of parabolic PDEs
5 Observer Design
6 Control of complex-valued PDEs
7 Boundary control of hyperbolic PDEs
8 Beam equations
9 Control of first-order hyperbolic PDEs and delay equations
10 Control of Kuramoto-Sivashinsky, Korteweg-de Vries, and other "exotic" equations
11 Control of Navier-Stokes equations modeling turbulent flows
12 Motion planning for PDEs, Adaptive Control for PDEs
13 Towards Nonlinear PDEs
14 Towards Nonlinear PDEs

Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
All 4 3 3 3 4 1 3 3 3
C1 4 3 3 3 4 1 3 3 3
C2 4 3 3 3 4 1 3 3 3
C3 4 3 3 3 4 1 3 3 3

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant