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On Moment Theory and Controllability of One-Dimensional Vibrating Systems and Heating Processes

  • Book
  • © 1992

Overview

Editors:
  1. Werner Krabs
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Part of the book series: Lecture Notes in Control and Information Sciences (LNCIS, volume 173)

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Table of contents (3 chapters)

  1. Front Matter

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  2. Introduction: Finite-dimensional linear control systems and an outline of infinite-dimensional linear control problems

    Pages 1-25

  3. Optimal damping of vibrations

    Pages 26-116

  4. Optimal control of heating processes

    Pages 117-168

  5. Back Matter

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Keywords

About this book

The main concern of this book is the application of infinite moment theory to the problem of controllability of one-di- mensional vibrating systems (like strings and beams) and heating processes. Distributed as well as boundary control is considered. In the case of vibrating systems trigonometric moment pro- blems are to be investigated which is done on the basis of an abstract moment theory in Hilbert spaces. Equivalently, alsothe theory of linear operator equations on Hilbert spa- ces ( partly with unbounded operators) is applied to the problem of controllability and time-minimal controllability. In the case of heating processes exponential moment problems are to be dealt with which is done on the basis of an ab- stract moment theory in Banach spaces. Time-minimal control- lability is also treated with the aid of the theory of line- aroperator equations on Banach spaces. Some advanced knowledge in functional analyis and on partial differential equations is preassumed for a fluent reader of the book, but parts of it are also readable with basic ma- thematical knowledge (for instance, the finite-dimensional part of the introduction).

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