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Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems : Continuous and Approximation Theories - Irena Lasiecka

Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems

Continuous and Approximation Theories

Paperback

Published: 25th November 2010
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This is the first volume of a comprehensive and up-to-date treatment of quadratic optimal control theory for partial differential equations over a finite or infinite time horizon, and related differential (integral) and algebraic Riccati equations. The authors describe both continuous theory and numerical approximation. They use an abstract space, operator theoretic approach, based on semigroups methods and unifying across a few basic classes of evolution. The various abstract frameworks are motivated by, and ultimately directed to, partial differential equations with boundary/point control. Volume I includes the abstract parabolic theory (continuous theory and numerical approximation theory) for the finite and infinite cases and corresponding PDE illustrations, and presents numerous new results. These volumes will appeal to graduate students and researchers in pure and applied mathematics and theoretical engineering with an interest in optimal control problems.

Review of the hardback: 'This impressive volume is a superb achievement and will be a must for all those who are interested in the quadratic optimal control of parabolic PDEs and in general in the control of PDEs.' A. Akutowicz, Zentralblatt MATH
Review of the hardback: '... a comprehensive and up-to-date treatment ...'. European Maths Society Journal

Introduction
Analytic Semigroups:
The optimal quadratic cost problem over a preassigned finite time interval: the differential Riccati equation
The optimal quadratic cost problem over a preassigned finite time interval: the algebraic Riccati equation
Illustrations of the abstract theory of chapters 1 and 2 to PDEs with boundary/point controls
Numerical approximations of algebraic Riccati equations
Illustrations of the numerical theory of chapter 4 to parabolic-like boundary/point control PDE problems
Min-max game theory over an infinite time interval and algebraic Riccati equations
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521155670
ISBN-10: 0521155673
Series: Encyclopedia of Mathematics and Its Applications
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 672
Published: 25th November 2010
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 23.4 x 15.6  x 3.4
Weight (kg): 0.93