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

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Irena Lasiecka (University of Virginia) Roberto Triggiani (University of Virginia)

Control Theory for Partial Differential Equations

Volume 1, Abstract Parabolic Systems: Continuous and Approximation Theories

Irena Lasiecka (University of Virginia), Roberto Triggiani (University of Virginia), G.-C. Rota , B. Doran

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English

Cambridge University Press
15 April 2000

Mathematics & Sciences; Differential calculus & equations

Series: Encyclopedia of Mathematics and its Applications

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.

By: Irena Lasiecka (University of Virginia), Roberto Triggiani (University of Virginia)
Series edited by: G.-C. Rota, B. Doran, M. Ismail
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: No. 74
Dimensions: Height: 244mm, Width: 165mm, Spine: 43mm
Weight: 1.090kg
ISBN: 9780521434089
ISBN 10: 0521434084
Series: Encyclopedia of Mathematics and its Applications
Pages: 672
Publication Date: 15 April 2000
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Introduction; Part I. Analytic Semigroups: 1. The optimal quadratic cost problem over a preassigned finite time interval: the differential Riccati equation; 2. The optimal quadratic cost problem over a preassigned finite time interval: the algebraic Riccati equation; 3. Illustrations of the abstract theory of chapters 1 and 2 to PDEs with boundary/point controls; 4. Numerical approximations of algebraic Riccati equations; 5. Illustrations of the numerical theory of chapter 4 to parabolic-like boundary/point control PDE problems; 6. Min-max game theory over an infinite time interval and algebraic Riccati equations.

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

'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 '... a comprehensive and up-to-date treatment ...'. European Maths Society Journal