M.SC. in Electrical and Electronics Engineering (With Thesis)

EEE 512 | Course Introduction and Application Information

Course Name

Optimal Control

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
EEE 512	Fall/Spring	3	0	3	7.5

Prerequisites	None
Course Language	English
Course Type	Elective
Course Level	Second Cycle
Mode of Delivery	-
Teaching Methods and Techniques of the Course	-
National Occupation Classification	-
Course Coordinator	Doç. Dr. Türker İNCE
Course Lecturer(s)	-
Assistant(s)	-

Course Objectives

The course aims the students: i) to get a solid mathematical background on derivations of optimality conditions for constrained and unconstrained static optimization problems with optimal control problems and ii) to gain skills on finding optimal solutions of a static cost function and a given performance index for a linear time-invariant dynamical system by analytical and numerical methods.

Learning Outcomes

#	Content	PC Sub	* Contribution Level
#	Content	PC Sub	1	2	3	4	5
1	Derive optimality conditions for constraint and unconstrained optimization problems
2	Use numerical solution methods for finding minima of static optimization problems
3	Derive optimality conditions for optimal control of discrete-time and continuous-time linear time-invariant dynamical systems
4	Obtain analytical and numerical solutions for linear quadratic regulator, steady state closed loop control and tracking control problems.

Course Description

Static optimization with and also without constraints. Optimality conditions. Lagrange multipliers. Karush-Kuhn-Tucker conditions. Steepest-descent and Newton methods. Calculus of variations. Optimal control of discrete time and continuous time systems. Linear quadratic regulator, steady state closed loop control and tracking control. Dynamic programming of both discrete time and continuous time systems.

Course Category	Core Courses	X
	Major Area Courses
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week	Subjects	Related Preparation	Learning Outcome
1	Optimality conditions for single variable static optimization.	Frank L. Lewis, Vassilis Srimos, Optimal Control, Second edition, John Wiley & Sons, 1995
2	Optimality conditions for multi variable static optimization	Frank L. Lewis, Vassilis Srimos, Optimal Control, Second edition, John Wiley & Sons, 1995
3	Constrained optimization, Lagrange multipliers, Karush-Kuhn-Tucker conditions.	Frank L. Lewis, Vassilis Srimos, Optimal Control, Second edition, John Wiley & Sons, 1995
4	Numerical methods for static optimization.	Frank L. Lewis, Vassilis Srimos, Optimal Control, Second edition, John Wiley & Sons, 1995
5	Variational calculus.	Frank L. Lewis, Vassilis Srimos, Optimal Control, Second edition, John Wiley & Sons, 1995
6	Optimality conditions for optimal control problems defined as the minimization of a performance index under the given system’s state equations constraints.	Frank L. Lewis, Vassilis Srimos, Optimal Control, Second edition, John Wiley & Sons, 1995
7	Solutions of free initial state, fixed initial state, free final state and fixed final state problems.	Frank L. Lewis, Vassilis Srimos, Optimal Control, Second edition, John Wiley & Sons, 1995
8	Optimal control problems, minimum time and minimum fuel problems.	Frank L. Lewis, Vassilis Srimos, Optimal Control, Second edition, John Wiley & Sons, 1995
9	1. Midterm
10	Linear quadratic regulator problem.	Frank L. Lewis, Vassilis Srimos, Optimal Control, Second edition, John Wiley & Sons, 1995
11	Solving Riccati equation, Kalman gain.	Frank L. Lewis, Vassilis Srimos, Optimal Control, Second edition, John Wiley & Sons, 1995
12	Tracking problem for linear time-invariant systems.	Frank L. Lewis, Vassilis Srimos, Optimal Control, Second edition, John Wiley & Sons, 1995
13	2. Midterm
14	Steady-state closed-loop control problem for linear time-invariant systems.	Frank L. Lewis, Vassilis Srimos, Optimal Control, Second edition, John Wiley & Sons, 1995
15	Dynamical programming.	Frank L. Lewis, Vassilis Srimos, Optimal Control, Second edition, John Wiley & Sons, 1995
16	Review of the Semester

Course Notes/Textbooks	The textbook referenced above and lecture notes
Suggested Readings/Materials	Related Books

EVALUATION SYSTEM

Semester Activities	Number	Weighting	LO 1	LO 2	LO 3	LO 4
Participation
Laboratory / Application	6	60
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project	2	40
Seminar / Workshop
Oral Exams
Midterm
Final Exam
Total

Weighting of Semester Activities on the Final Grade	8	100
Weighting of End-of-Semester Activities on the Final Grade
Total

ECTS / WORKLOAD TABLE

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16	2	32
Study Hours Out of Class	15	4	60
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments			0
Presentation / Jury			0
Project	2	42	84
Seminar / Workshop			0
Oral Exam			0
Midterms			0
Final Exam			0
		Total	224

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	Accesses information in breadth and depth by conducting scientific research in Electrical and Electronics Engineering; evaluates, interprets and applies information		-	-	-	-	X
2	Is well-informed about contemporary techniques and methods used in Electrical and Electronics Engineering and their limitations		-	-	X	-	-
3	Uses scientific methods to complete and apply information from uncertain, limited or incomplete data; can combine and use information from different disciplines		-	X	-	-	-
4	Is informed about new and upcoming applications in the field and learns them whenever necessary.		-	-	X	-	-
5	Defines and formulates problems related to Electrical and Electronics Engineering, develops methods to solve them and uses progressive methods in solutions.		-	-	-	-	X
6	Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs.		-	-	-	X	-
7	Designs and implements studies based on theory, experiments and modeling; analyses and resolves the complex problems that arise in this process.		-	-	-	X	-
8	Can work effectively in interdisciplinary teams as well as teams of the same discipline, can lead such teams and can develop approaches for resolving complex situations; can work independently and takes responsibility.		-	X	-	-	-
9	Engages in written and oral communication at least in Level B2 of the European Language Portfolio Global Scale.		-	-	X	-	-
10	Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form.		X	-	-	-	-
11	Is knowledgeable about the social, environmental, health, security and law implications of Electrical and Electronics Engineering applications, knows their project management and business applications, and is aware of their limitations in Electrical and Electronics Engineering applications.		-	-	X	-	-
12	Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity. Adheres to the principles of research and publication ethics.		-	-	X	-	-