Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems: Continuous and Approximation Theories (Encyclopedia of Mathematics and its Applications, Series Number 74)

Lasiecka, Irena,Triggiani, Roberto

ISBN 10: 0521434084 / ISBN 13: 9780521434089

Published by Cambridge University Press, 2000

About this Item

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Bibliographic Details

• Title: Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems: Continuous and Approximation Theories (Encyclopedia of Mathematics and its Applications, Series Number 74)
• Publisher: Cambridge University Press
• Publication Date: 2000
• Language: English
• ISBN 10: 0521434084
• ISBN 13: 9780521434089
• Binding: hardcover
• Condition: Good

About this title

Synopsis

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.

Book Description

This is the first volume of a comprehensive and up-to-date two-volume treatise on the mathematical theory of deterministic control systems modeled by multi-dimensional partial differential equations (distributed parameter systems). Emphasis is placed on boundary/point control and observation. The abstract, unifying treatment is illustrated with many concrete examples. Volume 1 presents the abstract parabolic and hyperbolic settings, including many 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.