2019 Nonlinear and Adaptive Control

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Academic unit or major
Graduate major in Systems and Control Engineering
Hayakawa Tomohisa 
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Media-enhanced courses
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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


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, Normal form representation, 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 Sufficient conditions for existence and uniqueness of solutions, Lipschitz continuity
Class 2 Nonlinear dynamical system (II): Lyapunov's stability theory Definition of Lyapunov stability, Lyapunov functions
Class 3 Nonlinear dynamical system (III): Dissipativity theory Notion of dissipativity, passivity and nonexpansivity
Class 4 Positive real and bounded real equations and KYP equations Correspondence between passive/nonexpansive systems and positive real/bounded real systems
Class 5 Normal form representation Characterization of normal forms and internal dynamics
Class 6 Absolute stability theory Stability criteria with sector bound nonlinearity
Class 7 Adaptive control Development of adaptive control laws for linear uncertain systems
Class 8 Final exam



Reference books, course materials, etc.


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

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

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.

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