2024 Faculty Courses School of Engineering Department of Systems and Control Engineering Graduate major in Systems and Control Engineering
Optimal Control
- Academic unit or major
- Graduate major in Systems and Control Engineering
- Instructor(s)
- Takeshi Hatanaka
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Fri
- Class
- -
- Course Code
- SCE.C451
- Number of credits
- 100
- Course offered
- 2024
- Offered quarter
- 1Q
- Syllabus updated
- Mar 14, 2025
- Language
- English
Syllabus
Course overview and goals
Control engineering is currently required to address control problems in a layer higher than the traditional ones wherein the focus is placed on stabilization, output regulation or disturbance rejection for physical systems. The objective in such high-level control is often described in the framework of optimization, and, indeed, the mainstream of the advanced researches goes in this direction. Besides, optimization is one of the methodologies which is most broadly employed in engineering and hence learning the foundations and powerful techniques would be helpful for solving a variety of problems which students will encounter in the future. This course starts with introduction to the basic contents like problem formulation, convex analysis, duality and optimality conditions together and then educates classical optimal control and dual decomposition together with model predictive control. The latter half of this course is devoted to the contents such as Markov chain, Markov decision process and game theory which are also closely related to advanced research works.
Course description and aims
In this course, the instructor explains the formulations, solutions and examples of optimal control together with advanced topics. The goal of this course is that students will be able to address various research fields wherein optimization theory and techniques are employed. On the other hand, this course aims at helping
students achieve novel research outcomes by teaching fundamental theory used in advanced researches.
Keywords
Optimal Control, Optimization, Convex Optimization, Duality, Model Predictive Control, Markov Process
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
1) Students must study the contents assigned in the previous class before coming to each class.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Optimization Problem | Students must be able to explain the formulation of optimization problems and examples. |
| Class 2 | Convex Optimization | Students must understand the concept of convexity and be able to explain properties of convex optimization. |
| Class 3 | Duality and KKT Conditions | Students must be able to explain the duality theory and the KKT condition. |
| Class 4 | Subgradient Method and Dual Decomposition | Students must understand a solution to optimization problems, called subgradient method, and the distributed optimization technique called dual decomposition. |
| Class 5 | Optimal Control and Model Predictive Control | Students must be able to explain the formulation and solution of optimal control and the concept of model predictive control. |
| Class 6 | Optimization Toolbox | Students learn how to use Optimization Toolbox. |
| Class 7 | Advanced Topic | Student learn the essence of advanced topics |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
Stephen Boyd and Lieven Vandenberghe: Convex Optimization, Cambridge University Press, ISBN-10: 0521833787
Reference books, course materials, etc.
Dimitri P. Bertsekas, Angelica Nedic and Asuman P. Ozdaglar: Convex Analysis and Optimization, Athena Scientific, ISBN: 1886529450
Evaluation methods and criteria
Students will be assessed on their understanding of the concept of optimization, theory, solution and their applications. The course scores are based on exercise problems.
Related courses
- SCE.C301 ： Linear System Theory
- SCE.C302 ： System Modeling
- SCE.C401 ： System Identification and Estimation
- SCE.C502 ： Hybrid Systems Control
- SCE.C533 ： Network Control Systems
Prerequisites
Students must have successfully completed SCE.C.301 and SCE.C.302 or have equivalent knowledge.
Contact information (e-mail and phone) Notice : Please replace from ”[at]” to ”@”(half-width character).
email: hatanaka[at]sc.e.titech.ac.jp
tel: 03-5734-3316
Office hours
Contact by e-mail in advance to schedule an appointment.