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Partial Stabilization and Control of Distributed Parameter Systems with Elastic Elements

  • Alexander L. Zuyev

Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 458)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Alexander L. Zuyev
    Pages 13-38
  3. Alexander L. Zuyev
    Pages 97-130
  4. Back Matter
    Pages 215-232

About this book

Introduction

 This monograph provides a rigorous treatment of problems related to partial asymptotic stability and controllability for models of flexible structures described by coupled nonlinear ordinary and partial differential equations or equations in abstract spaces. The text is self-contained, beginning with some basic results from the theory of continuous semigroups of operators in Banach spaces. The problem of partial asymptotic stability with respect to a continuous functional is then considered for a class of abstract multivalued systems on a metric space. Next, the results of this study are applied to the study of a rotating body with elastic attachments. Professor Zuyev demonstrates that the equilibrium cannot be made strongly asymptotically stable in the general case, motivating consideration of the problem of partial stabilization with respect to the functional that represents “averaged” oscillations. The book’s focus moves on to spillover analysis for infinite-dimensional systems with finite-dimensional controls. It is shown that a family of L2-minimal controls, corresponding to low frequencies, can be used to obtain approximate solutions of the steering problem for the complete system.
The book turns from the examination of an abstract class of systems to particular physical examples. Timoshenko beam theory is exploited in studying a mathematical model of a flexible-link manipulator.  Finally, a mechanical system consisting of a rigid body with the Kirchhoff plate is considered. Having established that such a system is not controllable in general, sufficient controllability conditions are proposed for the dynamics on an invariant manifold.
Academic researchers and graduate students interested  in control theory and mechanical engineering will find Partial Stabilization and Control of Distributed-Parameter Systems with Elastic Elements a valuable and authoritative resource for investigations on the subject of partial stabilization.

Keywords

Controllability Distributed-parameter Systems Flexible Structure Lyapunov’s Direct Method Partial Stabilization

Authors and affiliations

  • Alexander L. Zuyev
    • 1
  1. 1.Institute of Applied Mathematics and MechanicsNational Academy of Sciences of UkraineDonetskUkraine

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-11532-0
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-11531-3
  • Online ISBN 978-3-319-11532-0
  • Series Print ISSN 0170-8643
  • Series Online ISSN 1610-7411
  • Buy this book on publisher's site
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