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

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

byIrena Lasiecka, Roberto Triggiani

Paperback | November 25, 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.
Title:Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems: Continuous…Format:PaperbackDimensions:672 pages, 9.21 × 6.14 × 1.34 inPublished:November 25, 2010Publisher:Cambridge University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0521155673

ISBN - 13:9780521155670

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Table of Contents

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.

Editorial Reviews

Review of the hardback: '... a comprehensive and up-to-date treatment ...'. European Maths Society Journal