Islamic University of Gaza Faculty of Engineering Electrical Engineering Department Optimal Control Instructor: Dr. Moayed Almobaied, Ph.D. Control & Automation Room: B337 Telephone: 2853 E-mail: malmobaied@iugaza.edu.ps Web-page: http://site.iugaza.edu.ps/malmobaied/ Course Schedule : Monday (14:00—17:00) I414 Control Systems Design, Dr. Moayed syllabus

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

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

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

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

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

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

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

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

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

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

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

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

Grading Midterm Exam 20 % Homework (3*5) 15 % Project 15 % Islamic University of Gaza Faculty of Engineering Electrical Engineering Department Grading Midterm Exam 20 % Homework (3*5) 15 % Project 15 % Final Exam 50 % Control Systems Design, Dr. Moayed syllabus

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

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

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