Skip to main content
SpringerLink
Log in
Book cover

Differential and Algebraic Riccati Equations with Application to Boundary/Point Control Problems: Continuous Theory and Approximation Theory

  • Book
  • © 1991

Overview

Editors:
  1. Irena Lasiecka
    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  2. Roberto Triggiani
    View editor publications

    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Lecture Notes in Control and Information Sciences (LNCIS, volume 164)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (11 chapters)

  1. Front Matter

    Download chapter PDF

  2. 1. Introduction: Two abstract classes; statement of main problems

    Pages 1-8

  3. 2. Abstract differential Riccati equation for the first class subject to the analyticity assumption (H.1)=(1.5)

    Pages 8-21

  4. 3. Abstract differential Riccati equations for the second class subject to the trace regularity assumption (H.2)=(1.6)

    Pages 22-31

  5. 4. Abstract differential Riccati equations for the second class subject to the regularity assumptions (H.2R)=(1.8)

    Pages 31-35

  6. 5. Abstract algebraic Riccati equations: Existence and uniqueness

    Pages 35-50

  7. 6. Examples of partial differential equation problems satisfying (H.1)

    Pages 51-71

  8. 7. Examples of partial differential equation problems satisfying (H.2)

    Pages 71-101

  9. 8. Example of a partial differential equation problem satisfying (H.2R)

    Pages 101-107

  10. 9. Numerical approximations of the solution to the abstract differential and algebraic Riccati equations

    Pages 107-126

  11. 10. Examples of numerical approximation for the classes (H.1) and (H.2)

    Pages 126-149

  12. 11. Conclusions

    Pages 149-160
Back to top

Keywords

About this book

This book provides, in a unified framework, an updated and rather comprehensive treatment contered on the theory of ot- pimal control with quadratic cost functional for abstract linear systems with application to boundary/point control problems for partial differential equations (distributed pa- rameter systems). The book culminates with the analysisof differential and algebraic Riccati equations which arise in the pointwisefe- edback synthesis of the optimal pair. It incorporates the critical topics of optimal irregularity of solutions to mi- xed problems for partial differential equations, exact con- trollability, and uniform feedback stabilization. It covers the main results of the theory - which has reached a consi- derable degree of maturity over the last few years - as well asthe authors' basic philosophy behind it. Moreover, it provides numerous illustrative examples of boundary/point control problems for partial differential equations, where the abstract theory applies. However, in line with the purpose of the manuscript, many technical pro- ofs are referred to in the literature. Thus, the manuscript should prove useful not only to mathematicians and theoreti- cal scientists with expertise in partial differential equa- tions, operator theory, numerical analysis, control theory, etc., but also to those who simple wish to orient themselves with the scope and status of the theory presently available. Both continuous theory and numerical approximation theory thereof are included.

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation