Control Theory for Partial Differential Equations: Volume 2, Abstract Hyperbolic-like Systems Over a Finite Time Horizon: Continuous and Approximation Theories

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Cambridge University Press, Feb 13, 2000 - Mathematics - 1067 pages
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Originally published in 2000, this is the second 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 unifies 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 2 is focused on the optimal control problem over a finite time interval for hyperbolic dynamical systems. A few abstract models are considered, each motivated by a particular canonical hyperbolic dynamics. 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.
 

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Contents

Preface page
xv
3A Interpolation Intermediate Sobolev Spaces and Their
xvi
Illustrations of the Numerical Theory of Chapter 4
xix
Some Auxiliary Results on Abstract Equations
645
Glossary of Symbols for Chapter l
671
Optimal Quadratic Cost Problem Over a Preassigned Finite Time
673
l9 Motivation Statement of Main Results 608
679
2A Bounded Inversion of + SV 5 V 0
761
Notes on Chapter 3
913
l0 Differential Riccati Equations under Slightly Smoothing
919
Statement of the Main Results
926
Proof of Theorem l0 2 3
936
SecondOrder Hyperbolic Equations with Dirichlet
942
Kirchoff Equation with One Boundary Control
989
EulerBernoulli Equation with One Boundary
1019
Notes on Chapter l0 l059
1059

Optimal Quadratic Cost Problem over a Preassigned Finite Time
764
3B Damped Elastic Operators 285
884
Simplified Hinged BC 204
885

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