2025 (Current Year) Faculty Courses School of Engineering Department of Systems and Control Engineering Graduate major in Systems and Control Engineering
Nonlinear and Adaptive Control
- Academic unit or major
- Graduate major in Systems and Control Engineering
- Instructor(s)
- Tomohisa Hayakawa
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Class
- -
- Course Code
- SCE.C452
- Number of credits
- 100
- Course offered
- 2025
- Offered quarter
- 3Q
- Syllabus updated
- Apr 1, 2025
- Language
- English
Syllabus
Course overview and goals
This course provides lectures on theory and application of nonlinear and adaptive control systems. Methods of on-line parameter identification and adaptive control for nonlinear systems with uncertain parameters are discussed. To this end, Lyapunov stability theory and Lyapunov functions for general nonlinear systems are examined in the first part of the course.
Course description and aims
By the end of this course, students will be able to:
1) Examine existence and uniqueness of solutions of nonlinear differential equations
2) Understand the notion of Lyapunov stability theory and dissipation theory
3) Characterize passivity and nonexpansivity analogous to positive real and bounded real systems
4) Develop adaptive control laws for linear uncertain systems
Keywords
Existence and uniqueness of solutions of differential equations, Lyapunov stability, Lyapunov functions, Lyapunov equations, Dissipativity, Storage functions, Supply rate, passivity and nonexpansivity, positive real and bounded real systems, KYP equations, Absolute stability theory, Adaptive Control
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
At the beginning of each class, some of the important points learned in the previous class are reviewed. Then the main topics for the day are explained in detail. Students are advised to solve exercise problems at home.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Nonlinear dynamical system (I): Existence and uniqueness of solutions | Characterize sufficient conditions for existence and uniqueness of solutions, Lipschitz continuity |
| Class 2 | Nonlinear dynamical system (II): Lyapunov's stability theory | Learn the definition of Lyapunov stability and understand the Lyapunov functions |
| Class 3 | Nonlinear dynamical system (III): Dissipativity theory | Understand the notion of dissipativity, passivity, and nonexpansivity |
| Class 4 | Positive-real and bounded-real equations and KYP equations | Understand the correspondence between passive/nonexpansive systems and positive-real/bounded-real systems |
| Class 5 | Absolute stability theory (I) | Understand some stability criteria with sector bound nonlinearity |
| Class 6 | Absolute stability theory (II) | Extend the framework with loop shifting and derive circle/Popov criteria |
| Class 7 | Adaptive control | Develop adaptive control laws for linear uncertain systems |
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)
None
Reference books, course materials, etc.
Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach by Wassim M. Haddad and Vijaya Sekhar Chellaboina
Nonlinear Control by Hassan k. Khalil
Applied Nonlinear Control by Jean-Jacques Slotine and Weiping Li
Evaluation methods and criteria
Student's knowledge of nonlinear and adaptive control and their ability to apply them to problems will be assessed.
Final exam 70% and exercise problems 30%.
Related courses
- SCE.A404 ： Nonlinear Dynamics
- SCE.C532 ： Nonlinear Control: Geometric Approach
- TSE.M203 ： Theory of Linear System
Prerequisites
No prerequisite
Contact information (e-mail and phone) Notice : Please replace from ”[at]” to ”@”(half-width character).
hayakawa[at]sc.e.titech.ac.jp, 03-5734-2762
Office hours
Contact by e-mail in advance to schedule an appointment.