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Optimal Control Problems and Riccati Equations for Systems with Unbounded Controls and Partially Analytic Generators-Applications to Boundary and Point Control Problems

  • Irena LasieckaEmail author
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1855)

Abstract

  • 1. Introduction

  • I. Abstract Theory
    • 2. Mathematical Setting and Formulation of the Control Problem
      • 2.1. Dynamics and Related Control Problem

      • 2.2. Singular Estimate Assumptions

      • 2.3. Examples of Point and Boundary Control Models

    • 3. Abstract Results for Control Problems with Singular Estimate
      • 3.1. Finite Horizon Control Problem - Differential Riccati Equation (DRE)

      • 3.2. Infinite Horizon Control Problem - Algebraic Riccati Equations (ARE)

    • 4. Finite Horizon Problem - Proofs
      • 4.1. Characterization of Optimal Solution

      • 4.2. Continuity in Time of Optimal Solutions

      • 4.3. Regularity of Evolution \(\Phi (t,s)\) and of Riccati Operator P(t)

      • 4.4. Singular Estimate and Left-differentiability for the Evolution Operator

      • 4.5. Differential Riccati Equation - DRE

      • 4.6. The Function r(t)

  • II. Applications to Point and Boundary Control Problems
    • 5. Boundary Control Problems for Thermoelastic Plates
      • 5.1. PDE Model

      • 5.2. Semigroup Formulation

      • 5.3. Main Result

      • 5.4. Proof of Theorem 5.1

    • 6. Composite Beam Models with Boundary Control
      • 6.1. PDE Model and Main Results

      • 6.2. Transformations of the Model

      • 6.3. Semigroup Formulation

      • 6.4. Singular Estimate and Completion and Proper Proof of Theorem 6.1

    • 7. Point and Boundary Control Problems in Acoustic-structure Interactions
      • 7.1. Description of the Model

      • 7.2. Semigroup Formulation

      • 7.3. Finite Horizon Control Problem

      • 7.4. Infinite Horizon Control Problem

  • References

Mathematics Subject Classification (2000):

34Gxx 34K30 35K90 42A45 47Axx 47D06 47D07 49J20 60J25 93B28 

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

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