1. Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Optimal Control
Instructor: Dr. Moayed Almobaied, Ph.D. Control & Automation
Room: B337
Telephone:
Web-page:
Course Schedule : Monday (14:00—17:00) I414
Control Systems Design, Dr. Moayed
syllabus

2. Course Description Definition of optimization.
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Course Description
Definition of optimization.
Calculus of extrema and parameter optimization by the method of Lagrange multipliers.
Performance measures.
Optimality Principle and Dynamic Programming. Variational calculus and Pontragin’s minimum principle.
Dynamic optimization in control systems for different terminal conditions.
Control Systems Design, Dr. Moayed
syllabus

3. Course Description Hamilton Jacobi-Bellman equation.
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Course Description
Hamilton Jacobi-Bellman equation.
Linear Optimal Control Problem solution (The matrix Riccati equation).
Optimization of discrete control systems.
Numerical solution methods in optimal control problem using Direct Method and Indirect Method Approaches.
Control Systems Design, Dr. Moayed
syllabus

4. Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Course Objectives
To provide basic concepts related to optimal control and its position in optimization.
To teach the calculus of extrema and parameter optimization by the method of Lagrange multipliers.
To teach the Optimality Principle and Dynamic Programming.
To teach variational calculus and Pontragin’s minimum principle.
To provide a solution approach for the Hamilton Jacobi-Bellman equation.
To provide the solution for Linear Optimal Control Problem (The Matrix Riccati Equation).
Control Systems Design, Dr. Moayed
syllabus

5. Prerequisites Feedback Control Systems. Math Courses.
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Prerequisites
Feedback Control Systems.
Math Courses.
Control Systems Design, Dr. Moayed
syllabus

6. Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Textbook
D. E. Kirk, "Optimal Control Theory: An Introduction, New York, NY: Dover, 2004.
B.D.O. Anderson and J.B. Moore, Optimal Control: Linear Quadratic Methods, Dover Books on Engineering, 1989.
Control Systems Design, Dr. Moayed
syllabus

7. Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
References
Daniel Liberzon, Calculus of Variations and Optimal Control Theory: A Concise Introduction, Princeton University Press, Dec 2011.
Michael Athans , Peter L. Falb, Optimal Control: An Introduction to the Theory and Its Applications, Dover Books on Engineering, 2006.
R. F. Stengel, Optimal Control and Estimation, Dover Publications, 1994.
Control Systems Design, Dr. Moayed
syllabus

8. Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Software
Students Will Use MATLAB (2013a or newer) and its Toolboxes while preparing their assignments and projects.
Control Systems Design, Dr. Moayed
syllabus

9. Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Course Outcomes
M.Sc. students who successfully pass this course gain knowledge, skill and competency in the following subjects;
The basic concepts related to optimal control and its position in optimization.
The parameter optimization method in optimal control.
Optimality Principle and Dynamic Programming.
The variational calculus and Pontragin’s minimum principle.
The Hamilton Jacobi-Bellman approach.
Linear Optimal Control Problem (The Matrix Riccati Equation).
Control Systems Design, Dr. Moayed
syllabus

10. Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Outline
Week 1
Introduction to Optimal Control Problem and classifications
Week 2
The parameter optimization by the method of Lagrange multipliers in optimal control problem
Week 3
Week 4
The performance indices in optimal control problem and Dynamic Programming
Control Systems Design, Dr. Moayed
syllabus

11. The calculus of variations and Euler Equations Week 7
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Week 5
The performance indices in optimal control problem and Dynamic Programming
Week 6
The calculus of variations and Euler Equations
Week 7
Week 8
The application of the calculus of variations to basic optimal control problem
Control Systems Design, Dr. Moayed
syllabus

12. The Hamilton-Jacobi-Bellmann approach
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Week 9
Pontragin’s minimum principle and solutions for the minimum time and control effort problems
Week 10
Week 11
The Hamilton-Jacobi-Bellmann approach
Week 12
Linear quadratic Optimal Control Problem (The Matrix Riccati equation)
Control Systems Design, Dr. Moayed
syllabus

13. Numerical methods for optimal control problem
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Week 13
Linear Quadratic Optimal Control Problem (The Algebraic Riccati equation)
Week 14
Numerical methods for optimal control problem
Control Systems Design, Dr. Moayed
syllabus

14. Grading Midterm Exam 20 % Homework (3*5) 15 % Project 15 %
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Grading
Midterm Exam %
Homework (3*5) %
Project %
Final Exam %
Control Systems Design, Dr. Moayed
syllabus

15. Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Grading Policy
Regular attendance of this class is necessary to receive a passing grade.
Weekly problem sets will be typically assigned and will be due one week later.
Cellular phones should be off or on silent ring during class in order to keep classroom distractions at a minimum.
Control Systems Design, Dr. Moayed
syllabus

16. Cheating will not be tolerated and will be dealt with decisively.
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Grading Policy
Cheating will not be tolerated and will be dealt with decisively.
Missed midterms will result in a score of 0. If you have a legitimate reason for missing a midterm, and communicate with me prior to the midterm, you may be able to arrange an alternative solution. The sooner you inform me of your conflict, the better your chances of being able to make up the missed grade. If you inform me about your absence after the midterm, you will receive a 0.
Office Hours (Tentative)
Wed (10 :00—12 :00) ; Mon (11 :00—14 :00) ; Sun, Tue (Tentative).
Control Systems Design, Dr. Moayed
syllabus

17. Islamic University of Gaza Faculty of Engineering
Electrical Engineering Department
Control Systems Design, Dr. Moayed
syllabus