I. Lasiecka, Roberto Triggiani, Irena Lasiecka

Control Theory for Partial Differential Equations

Volume 1, Abstract Parabolic Systems: Continuous and Approximation Theories

• Gebundenes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 672
• Erscheinungstermin: 1. November 2010
• Englisch
• Abmessung: 240mm x 161mm x 40mm
• Gewicht: 1162g
• ISBN-13: 9780521434089
• ISBN-10: 0521434084
• Artikelnr.: 21224446

Inhaltsangabe

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.