Optimal Control Theory for Infinite Dimensional Systems

✍ Scribed by Xunjing Li, Jiongmin Yong (auth.)

• Publisher: Birkhäuser Basel
• Year: 1995
• Tongue: English
• Leaves: 461
• Series: Systems & Control: Foundations & Applications
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xii
Control Problems in Infinite Dimensions....Pages 1-23
Mathematical Preliminaries....Pages 24-80
Existence Theory of Optimal Controls....Pages 81-129
Necessary Conditions for Optimal Controls — Abstract Evolution Equations....Pages 130-167
Necessary Conditions for Optimal Controls — Elliptic Partial Differential Equations....Pages 168-222
Dynamic Programming Method for Evolution Systems....Pages 223-273
Controllability and Time Optimal Control....Pages 274-318
Optimal Switching and Impulse Controls....Pages 319-360
Linear Quadratic Optimal Control Problems....Pages 361-418
Back Matter....Pages 419-450

✦ Subjects

Mathematics, general