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## Details

Additional Physical Format: | Printed edition: |
---|---|

Material Type: | Document, Internet resource |

Document Type: | Book, Computer File, Internet Resource |

All Authors / Contributors: |
Alexander L Zuyev |

ISBN: | 9783319115320 3319115324 3319115316 9783319115313 |

OCLC Number: | 898493258 |

Description: | 1 online resource. |

Contents: | Basic Results from the Theory of Continuous Semigroups of Operator -- Partial Asymptotic Stability -- Stabilization of a Rotating Body with Euler?Bernoulli Beams -- Reachable Sets and Controllability Conditions -- Observer-Based Stabilization of a Manipulator Based on the Timoshenko Beam Model -- Control and Stabilization of a Rotating Kirchhoff Plate.-Appendices. |

Series Title: | Lecture notes in control and information sciences, 458. |

Responsibility: | Alexander L. Zuyev. |

### Abstract:

℗LThis 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 ℓ́ℓaveragedℓ́ℓ oscillations. The bookℓ́ℓs 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.℗ℓ Finally, a mechanical system consisting of a rigid body with the Kirchhoff plate is considered. Having established that such a℗ℓsystem is not controllable in general, sufficient controllability conditions are proposed for the dynamics on an invariant manifold. Academic researchers and graduate students interested℗ℓ 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 st.

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Publisher Synopsis

"The author discusses several topics on partial stabilization and control for distributed parameter systems with elastic elements. ... Readers interested in stabilization and control theory will find the book useful." (Gheorghe Tigan, zbMATH 1310.93003, 2015) Read more...

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