# Advanced Nonlinear Control

Lecturer Kenji FUJIMOTO, Associate Professor School of Engineering / Graduate School of Engineering, 2011 Fall freshmen and sophomores majoring in electro-mechanic engineering (2・1.5hrs / session 1 session / week 15 weeks / semester)

### Course Aims

In this course, you will learn control methods based on nonlinear differential equations, and also analytical methods of (mechanical) performance. From basic items- for example, Lyapunov method, which is one common form of nonlinear analysis, input-output stability, and the evaporation theory- to practical ones like mechatronic modeling and control methods, you will be exposed to a great deal of engineering theory and knowledge. I hope to carry on the lectures mindful of its connections with related fields, such as the mathematics, control engineering, and physics.

### Key Features

Because this course is based on many areas in mathematics, physics, and engineering, it is important that the students review these fields during the course. The lessons themselves are mathematical, so I try to give students both the abstract concept and the examples that follow. Students are given a rather tough paper assignment roughly once every two weeks. Most of them seem to enjoy the assignments better when given a slightly difficult one.

### Contents

1. Introduction
2. Forms of differentiation
3. The basics of nonlinear controls
4. Modeling of mechatronics system and its properties
5. Optimal control
6. Dynamic control
7. Feedback linearity

Mathematics 1, 2 and practical mathematics, control engineering 1, 2, and practice

### Course Schedule

Session Contents
1 Introduction
2 Reviews on differentiation
3 The nonlinear differential equation and equal exchange
4 The balance point and stability, the Lyapunov method
5 Lyapunvs reverse theorem and LaSalle's invariant principle
6 Input-output stability and the small-gain theorem
7 Passivity and the passivity theorem
8 Evaporation and the partial differential equation
9 The Dynamic system and Hamilton's equation
10 Passivity of the Hamiltonian system
11 The basics of nonlinear control design
12 Optimal control, passivity-based control
13 Inverse optimal control, linearization of input & output, Canonical form
14 Linearization of feedback
15 Conclusion

#### Last updated

December 23, 2019

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