# Optimal Control Theory for Infinite Dimensional Systems

• Xunjing Li
• Jiongmin Yong
Book

Part of the Systems & Control: Foundations & Applications book series (SCFA)

1. Front Matter
Pages i-xii
2. Xunjing Li, Jiongmin Yong
Pages 1-23
3. Xunjing Li, Jiongmin Yong
Pages 24-80
4. Xunjing Li, Jiongmin Yong
Pages 81-129
5. Xunjing Li, Jiongmin Yong
Pages 130-167
6. Xunjing Li, Jiongmin Yong
Pages 168-222
7. Xunjing Li, Jiongmin Yong
Pages 223-273
8. Xunjing Li, Jiongmin Yong
Pages 274-318
9. Xunjing Li, Jiongmin Yong
Pages 319-360
10. Xunjing Li, Jiongmin Yong
Pages 361-418
11. Back Matter
Pages 419-450

### Introduction

Infinite dimensional systems can be used to describe many phenomena in the real world. As is well known, heat conduction, properties of elastic­ plastic material, fluid dynamics, diffusion-reaction processes, etc., all lie within this area. The object that we are studying (temperature, displace­ ment, concentration, velocity, etc.) is usually referred to as the state. We are interested in the case where the state satisfies proper differential equa­ tions that are derived from certain physical laws, such as Newton's law, Fourier's law etc. The space in which the state exists is called the state space, and the equation that the state satisfies is called the state equation. By an infinite dimensional system we mean one whose corresponding state space is infinite dimensional. In particular, we are interested in the case where the state equation is one of the following types: partial differential equation, functional differential equation, integro-differential equation, or abstract evolution equation. The case in which the state equation is being a stochastic differential equation is also an infinite dimensional problem, but we will not discuss such a case in this book.

### Keywords

Algebra Finite calculus equation function optimization proof theorem

#### Authors and affiliations

• Xunjing Li
• 1
• Jiongmin Yong
• 1
1. 1.Department of MathematicsFudan UniversityShanghaiChina

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-4260-4
• Copyright Information Birkhäuser Boston 1995
• Publisher Name Birkhäuser Boston
• eBook Packages
• Print ISBN 978-1-4612-8712-4
• Online ISBN 978-1-4612-4260-4