Optimal Control Theory for Infinite Dimensional Systems (Systems & Control: Foundations & Applications) - Hardcover

Li, Xungjing; Yong, Jiongmin

Hardcover

ISBN 10: 0817637222 ISBN 13: 9780817637224

Publisher: Birkhäuser, 1994

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.

About this title

Review

"This book goes plenty of new ways, which should be interesting also for the expert on this topic...this book is an excellent matured presentation of the modern subject 'Optimal processes' being also very clearly arranged in its typography."   
--ZAA

Synopsis

Infinite dimensional systems can be used to describe many physical phenomena in the real world. Well-known examples are heat conduction, vibration of elastic material, diffusion-reaction processes, population systems and others. Thus, the optimal control theory for infinite dimensional systems has a wide range of applications in engineering, economics and some other fields. On the other hand, this theory has its own mathematical interests since it is regarded as a generalization for the classical calculus of variations and it generates many interesting mathematical questions. The Pontryagin maximum principle, the Bellman dynamic programming method and the Kalman optimal linear quadratic regulator theory are regarded as the three milestones of modern (finite dimensional) control theory. Since the 1960s, the corresponding theory for infinite dimensional systems has also been developed. The essential difficulties for the infinite dimensional theory come from two aspects: the unboundedness of the differential operator or the generator of the strongly continuous semigroup and the lack of the local compactness of the underlying spaces.

The purpose of this book is to introduce optimal control theory for infinite dimensional systems. The authors present the existence theory for optimal control problems. Some applications are also included in this volume.

About this edition

• Publisher: Birkhäuser
• Publication date: 1994
• ISBN 10: 0817637222
• ISBN 13: 9780817637224
• Binding: Hardcover
• Number of pages: 462