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.
$latex \frac{dx}{dt}=f(x(t)), u(t))$
where $latex t$ is time, $latex x(f)$ is the state function, and $latex u(t)$ is the control function.
Theorems of the Euler-Lagrange Equation
Theorem of the Hamiltonian Equation
$latex H(p,x,u,t)=F(x,u,t)+pf(x,u)$
