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

Continuous and Approximation Theories

AvIrena Lasiecka,Roberto Triggiani

Inbunden, Engelska, 2000

Del 74 i serien Encyclopedia of Mathematics and its Applications

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Beskrivning

Originally published in 2000, this is the first volume of a comprehensive two-volume 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. Both continuous theory and numerical approximation theory are included. The authors use an abstract space, operator theoretic approach, which is based on semigroups methods, and which is 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 1 includes the abstract parabolic theory for the finite and infinite cases and corresponding PDE illustrations as well as various abstract hyperbolic settings in the finite case. It presents numerous fascinating 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.

Produktinformation

Utgivningsdatum:2000-02-13
Mått:165 x 244 x 43 mm
Vikt:1 090 g
Format:Inbunden
Språk:Engelska
Serie:Encyclopedia of Mathematics and its Applications
Antal sidor:672
Förlag:Cambridge University Press
ISBN:9780521434089

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Beräkning och matematisk analys inom Naturvetenskap och teknik

Recensioner i media

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

Innehållsförteckning

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.