### 2022　Nonlinear and Adaptive Control

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Graduate major in Systems and Control Engineering
Instructor(s)
Hayakawa Tomohisa
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Fri3-4(W932)
Group
-
Course number
SCE.C452
Credits
1
2022
Offered quarter
3Q
Syllabus updated
2022/4/20
Lecture notes updated
-
Language used
English
Access Index

### Course description and aims

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.

### Student learning outcomes

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 that will be developed

 ✔ 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/Required learning

Course schedule Required learning
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

### Out-of-Class Study Time (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.

None

None

### Assessment criteria and methods

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

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.