Advanced Nonlinear Control

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

Requirements and recommended courses

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

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