2017 Optimal Control

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Academic unit or major
Graduate major in Systems and Control Engineering
Hatanaka Takeshi 
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Course description and aims

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.

Student learning outcomes

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.


Optimal Control, Optimization, Convex Optimization, Duality, Model Predictive Control, Markov Process

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

1) At the beginning of each class, solutions to exercise problems assigned during the previous class are reviewed.
2) Attendance is taken in every class.
3) Students must study the contents assigned in the previous class before coming to each class.

Course schedule/Required learning

  Course schedule Required learning
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 Markov Process and Markov Decision Process Students must understand the formulation, solution and applications of Markov Process and Markov Decision Process
Class 6 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 7 Optimization Toolbox Students learn how to use Optimization Toolbox.
Class 8 Advanced Topics Students must understand the recent research directions associated with optimal control.


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

Assessment criteria and methods

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 (i.e., required knowledge, skills, courses, etc.)

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]ctrl.titech.ac.jp
tel: 03-5734-3316

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