Control Theory for Partial Differential Equations: Continuous and Approximation Theories

by Irena Lasiecka , Roberto Triggiani

• ISBN13: 9780521155670
• ISBN10: 0521155673
• Format: Paperback
• Copyright: 2010-11-25
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Introduction

Analytic Semigroups:

The optimal quadratic cost problem over a preassigned finite time interval: the differential Riccati equation

The optimal quadratic cost problem over a preassigned finite time interval: the algebraic Riccati equation

Illustrations of the abstract theory of chapters 1 and 2 to PDEs with boundary/point controls

Numerical approximations of algebraic Riccati equations

Illustrations of the numerical theory of chapter 4 to parabolic-like boundary/point control PDE problems

Min-max game theory over an infinite time interval and algebraic Riccati equations

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