Control theory for partial differential equations : continuous and approximation theories. 2, Abstract hyperbolic-like systems over a finite time horizon /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Lasiecka, I. (Irena), 1948-
Otros Autores: Triggiani, R. (Roberto), 1942-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2000.
Colección:Encyclopedia of mathematics and its applications ; v. 75.
Temas:
Differential equations, Partial.
Control theory.
Équations aux dérivées partielles.
Théorie de la commande.
MATHEMATICS > Differential Equations > Partial.
Control theory
Differential equations, Partial
Hyperbolische Differentialgleichung
Acceso en línea:Texto completo
Tabla de Contenidos:
  • ""Cover""; ""Half Title""; ""Series Page""; ""Dedication""; ""Title""; ""Copyright""; ""Contents""; ""Preface""; ""Acknowledgments for the First Two Volumes""; ""7 Some Auxiliary Results on Abstract Equations""; ""7.1 Mathematical Setting and Standing Assumptions""; ""7.2 Regularity of Land L * on [0, T]""; ""7.3 A Lifting Regularity Property When eAt Is a Group""; ""7.4 Extension of Regularity of Land L* on [0, â?ž] When eAt Is Uniformly Stable""; ""7.4.1 Direct Statement; Direct Proof""; ""7.4.2 Dual Statement; Dual Proof""
  • 7.5 Generation and Abstract Trace Regularity under Unbounded Perturbation7.6 Regularity of a Class of Abstract Damped Systems
  • 7.6.1 Mathematical Setting and Assumptions
  • 7.6.2 Main Regularity Results
  • 7.6.3 Proof of Theorem 7.6.2.2: Dual Statement (7.6.2.6)
  • 7.7 Illustrations of Theorem 7.6.2.2 to Boundary Damped Wave Equations
  • 7.7.1 Wave Equation with Boundary Damping in the Neumann Be
  • 7.7.2 Wave Equation with Boundary Damping in the Dirichlet BC
  • Notes on Chapter 7
  • References and Bibliography
  • ""8 Optimal Quadratic Cost Problem Over a Preassigned Finite Time Interval: The Case Where the Input â?? Solution Map Is Unbounded, but the Input â?? Observation Map Is Bounded""""8.1 Mathematical Setting and Formulation of the Problem""; ""8.2 Statement of Main Results""; ""8.2.1 The General Case: Theorem 8.2.1.1, Theorem 8.2.1.2, and Theorem 8.2.1.3""; ""8.2.2 The Regular Case: Theorem 8.2.2.1""; ""8.3 The General Case. A First Proof of Theorems 8.2.1.1 and 8.2.1.2 by a Variational Approach: From the Optimal Control Problem to the DRE and the IRE Theorem 8.2.1.3""
  • ""8.3.1 Explicit Representation Formulas for the Optimal Pair {uo, yo} under (h.1), (h.3)""""8.3.2 Estimates on uo ( • ,t; x) and Ryo ( . ,t; x). The Operator Î? ( . , . )""; ""8.3.3 Definition of P(t) and Preliminary Properties""; ""8.3.4 P(t) Solves the Differential Riccati Equation (8.2.1.32)""; ""8.3.5 Differential and Integral Riccati Equations""; ""8.3.6 The IRE without Passing through the DRE""; ""8.3.7 Uniqueness""; ""8.3.8 Proof of Theorem 8.2.1.3""; ""8.4 A Second Direct Proof of Theorem 8.2.1.2: From the Well-Posedness of the IRE to the Control Problem. Dynamic Programming""
  • 8.4.1 Existence and Uniqueness: Preliminaries8.4.2 Unique Local Solution to Eqn. (8.4.1.5)for Q(t, s)
  • 8.4.3 Unique Local Solution to Eqn. (8.4.1. 7) for V(t). Global Solution P(t) under (h.1), (h.2)
  • 8.4.4 Global A Priori Estimates for V and Q. Global Solution P(t) under (H. 1), (H.2), and (H.3)
  • 8.4.5 Recovering the Optimal Control Problem under (H.I), (H.2), and (H.3) for (h.I) and (h.2)]
  • 8.5 Proof of Theorem 8.2.2.1: The More Regular Case
  • 8.5.1 A Preliminary Lemma
  • 8.5.2 Completion of the Proof of Theorem 8.2.2.1
  • 8.5.3 An Auxiliary Lemma

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