UID:
almafu_9959235949402883
Format:
1 online resource (xxi, 644 pages) :
,
digital, PDF file(s).
ISBN:
1-139-88643-6
,
1-107-26678-5
,
1-107-26321-2
,
1-107-34084-5
Series Statement:
Encyclopedia of mathematics and its applications ;
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
""Cover""; ""Series Page""; ""Dedication""; ""Title""; ""Copyright""; ""Contents""; ""Preface""; ""Acknowledgments for the First Two Volumes""; ""0 Background""; ""0.1 Some Function Spaces Used in Chapter 1""; ""0.2 Regularity of the Variation of Parameter Formula When eAt Is a s.c. Analytic Semigroup""; ""0.2.1 Comments on the Space [X, Y]�""; ""0.2.2 Cases Where [D(A),Y]� =D((�A)�)""; ""0.2.3 Comments on the Proof of Proposition 0.1""; ""Properties (0.9), (0.14)""; ""Property (0.10)""; ""Properties (0.11), (0.12)""; ""Properties (0.13)""; ""0.3 The Extrapolation Space [D(A*)]'""
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""0.4 Abstract Setting for Volume I. The Operator LT in (1.1.9), or LsT in (1.4.1.6), of Chapter 1""""References and Bibliography""; ""1 Optimal Quadratic Cost Problem Over a Preassigned Finite Time Interval: Differential Riccati Equation""; ""1.1 Mathematical Setting and Formulation of the Problem""; ""1.2 Statement of Main Results""; ""1.2.1 The Nonsmoothing Case. Theorem 1.2.1.1: Existence of a Riccati Operator""; ""1.2.2 Two Smoothing Cases. Theorem 1.2.2.1: Classical Differential Riccati Equation and Uniqueness of the Riccati Operator. Theorem 1.2.2.2""; ""1.3 Orientation""
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""1.4 Proof of Theorem 1.2.1.1 with GLr Closed""""1.4.1 Optimality. Explicit Representation Formulas for the Optimal Pair {u0, y0}""; ""1.4.2 L2-Estimatesfor {u0,y0} and Zf-Estimate for Gy0(T; . ; x). Limit Relations as s â?? T""; ""1.4.3 Definition of Operators Î? (T, s ) and P(t) and First Properties""; ""1.4.4 Smoothing Properties of Ls and Ls* at t = T, and on Lp(s,T; . )-Spaces. Pointwise Estimates for u0(t, s; x), y0(t, s; x), and P(t)""; ""1.4.5 Smoothing Properties of Ls and Ls* at t = s. Pointwise Regularity of du0(t,s; x)/dt and dy0(t,s; x)/dt for s 〈 t 〈 T, x ε Y""
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""1.7 The Theory of Theorem 1.2.1.1 Is Sharp. Counterexamples When GLÏ? Is Not Closable""""1.7.1 Counterexample to the Existence of the Optimal Control u0 When GLÏ? Is Not Closable""; ""1.7.2 Assumption (1.2.1.26) Is Only Sufficientfor GLÏ? to Be Closed""; ""1.8 Extension to Unbounded Operators R and G""; ""1.8.1 The Case Where R E £(1)( (â€?A)Î?); Z) and G E £(D((â€?A)Î?); Zf), 0""; ""1A Proof of Lemma 1.5.1.l(iii)""; ""Notes on Chapter 1""
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""Sections 1.1 Through 1.6: The Variational Versus the Direct Method: Case G â? 0""
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English
Additional Edition:
ISBN 0-521-15567-3
Additional Edition:
ISBN 0-521-43408-4
Language:
English
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