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Optimal control

Course Description: The curriculum begins with an introduction to the principles and methodologies of optimal control, focusing on the study and understanding of performance metrics and criteria. Subsequently, it addresses the mathematical and theoretical foundation of the field by studying dynamic programming, calculus of variations, and Pontryagin's principle. In the applied section, the course covers the design of optimal linear controllers and deals with minimum-time problems for systems. The material concludes its content with the computational aspect through the study of steepest descent and quasilinear methods for determining optimal trajectories, leading to numerical optimization using evolutionary and modern optimization techniques such as genetic algorithms.

Credit hours: 3

Objectives of the course :

Provide students with the fundamental knowledge of the principles and scientific theories of optimal control systems.
Developing the necessary skills for controller design using available optimal control theories and specialized software.
Presenting evolutionary algorithms as powerful numerical computational tools for solving constrained optimal dynamic control problems. .

Course outputs :

1. Knowledge and understanding:

This field focuses on building students' theoretical foundation; the course aims to enable students to grasp the concepts of optimality, constraints, feasible solutions, and performance indicators. .
Students gain the ability to explain the principles of random search techniques such as genetic algorithms.
Teaching Strategies: Live Lectures, Classroom Discussions, Self-Directed Learning, and Practice Lessons. .
Assessment methods: Direct assessment through quizzes, assignments, midterm exams, and final exams. Indirect assessment through student course evaluations at the end of the course.

2. Skills:

This aspect covers the analytical, applied, and software capabilities of mechanical engineering, where students learn how to apply optimal control theory using specialized software for its application in the mechanical engineering field, and the ability to formulate optimization problems by identifying problem variables and the objective function. .
As students gain skill in identifying optimal solutions for dynamic systems using the calculus of variations, and identifying optimal solutions for static and dynamic systems using evolutionary algorithms. .
Teaching Strategies: Lectures, Recitation Sections, and Semester Project Work. .
Assessment methods: Direct assessment through quizzes, assignments, midterm and final exams, as well as semester project assessment models. Indirect assessment through opinion poll surveys.

3. Values, Independence, and Responsibility:

This domain aims to develop personal and professional skills. The course focuses on empowering students to work effectively within a team and acquire time management and organization skills while performing tasks.
Teaching Strategies: Problem-Based Learning, Mini-Project Work .
Assessment methods: Direct assessment through oral presentations, small project reports, and graded rubric forms, in addition to indirect assessment via student opinion surveys at the end of the course.

Additional information:

Course Content and Hour Distribution
This advanced course consists of 42 accredited teaching hours, distributed evenly to cover the theoretical and computational aspects of optimal control theory. The curriculum begins with an extensive introduction to the principles and methods of optimal control (6 hours), followed by a study of performance metrics (3 hours). Subsequently, the curriculum allocates equal time to the mathematical depth of the material with 6 hours each for: dynamic programming, calculus of variations, and Pontryagin's principle. In terms of practical and computational aspects, students will study optimal linear regulators and minimum time and fuel problems (6 hours), followed by steepest descent and quasilinearization methods for determining optimal trajectories (6 hours). The course concludes by focusing on numerical optimization using evolutionary optimization techniques (3 hours).

Student assessment activities
The assessment strategy is spread out over the course of the semester to ensure continuous monitoring and to measure students’ analytical skills; 15% of the grade is allocated to homework and quizzes, which are held weekly. Students take the midterm exam in the seventh week, which accounts for 25% of the total grade. In the fifteenth week, the term project is graded with a weight of 10%, while the largest portion of the grade is based on the final exam held in the sixteenth week, with a weight of 50%.

References and learning resources
This course features a rich list of references. Key references include “Optimal Control” by Frank Lewis et al. (2012 edition), and Stengel's "Optimal Control and Estimation" (1994), along with other distinguished references such as Aström's "Stochastic Control" and works by Bryson, Athans, and Naidu. Supporting references include Anderson and Moore's book, "Practical Genetic Algorithms" by Haupt (2004), and Kirk's book on Optimal Control Theory. For e-learning, the course relies on the official course website and the MathWorks website (MATLAB software).

Last update: 2026-05-18