###### Brief Information

- Name : Topics in Applied Mathematics 응용수학특강
- Lecturer : 이종우 Lee Jong-woo
- Semester : 2016 Fall
- Major : BS, Mathematics
- Textbook
- Syllabus : Syllabus_2016-5-2__Topics on Applied Mathematics.pdf
- Key words
- calculus of variations, optimal control, mathematical optimization theory, Euler-Lagrange equation, Hamiltonian eqaution

## References

- Control theory | Wolfram MathWorld
- Calculus of Variations | Wikipedia
- Optimal Control | Wikipedia
- Mathematical optimization | Wikipedia
- Optimization Theory | Wolfram MathWorld

## Summary

###### Control Theory

The mathematical study of how to manipulate the parameters affecting the behavior of a system to produce the desired or optimal outcome. – Control theory | Wolfram MathWorld

###### Calculus of Variations

A field of mathematical analysis that deals with maximizing or minimizing functionals, which are mappings from a set of functions to the real numbers. – Calculus of Variations | Wikipedia

###### Optimal Control Theory

**Optimal control theory**, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. – Optimal Control | Wikipedia

###### Control System / Dynamic System

A control system, i.e., dynamic system is composed of three components: **time**, **state**, and **controls**. A control system is used to describe the state that varies by time and controls. The number of controls can be one or more. However, we first consider the dynamic systems with one control. The control system is written as follows in equations.

where is time, is the state function, and is the control function.

###### Theorems of the Euler-Lagrange Equation

###### Theorem of the Hamiltonian Equation