Partial Stabilization and Control of Distributed Parameter Systems with Elastic Elements
Partial Stabilization and Control of Distributed Parameter Systems with Elastic Elements

Author: Alexander L. Zuyev

Publisher: Springer

Published: 2014-11-04

Total Pages: 241

ISBN-13: 3319115324

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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.

Stabilization of Distributed Parameter Systems: Design Methods and Applications
Stabilization of Distributed Parameter Systems: Design Methods and Applications

Author: Grigory Sklyar

Publisher: Springer Nature

Published: 2021-03-01

Total Pages: 139

ISBN-13: 3030617424

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This book presents recent results and envisages new solutions of the stabilization problem for infinite-dimensional control systems. Its content is based on the extended versions of presentations at the Thematic Minisymposium “Stabilization of Distributed Parameter Systems: Design Methods and Applications” at ICIAM 2019, held in Valencia from 15 to 19 July 2019. This volume aims at bringing together contributions on stabilizing control design for different classes of dynamical systems described by partial differential equations, functional-differential equations, delay equations, and dynamical systems in abstract spaces. This includes new results in the theory of nonlinear semigroups, port-Hamiltonian systems, turnpike phenomenon, and further developments of Lyapunov's direct method. The scope of the book also covers applications of these methods to mathematical models in continuum mechanics and chemical engineering. It is addressed to readers interested in control theory, differential equations, and dynamical systems.

Control of Distributed Parameter Systems 1989
Control of Distributed Parameter Systems 1989

Author: M. Amouroux

Publisher: Elsevier

Published: 2014-06-28

Total Pages: 533

ISBN-13: 1483298817

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This volume presents state-of-the-art reports on the theory, and current and future applications of control of distributed parameter systems. The papers cover the progress not only in traditional methodology and pure research in control theory, but also the rapid growth of its importance for different applications. This title will be of interest to researchers working in the areas of mathematics, automatic control, computer science and engineering.

Stability of Elastic Multi-Link Structures
Stability of Elastic Multi-Link Structures

Author: Kaïs Ammari

Publisher: Springer Nature

Published: 2022-01-16

Total Pages: 146

ISBN-13: 3030863514

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This brief investigates the asymptotic behavior of some PDEs on networks. The structures considered consist of finitely interconnected flexible elements such as strings and beams (or combinations thereof), distributed along a planar network. Such study is motivated by the need for engineers to eliminate vibrations in some dynamical structures consisting of elastic bodies, coupled in the form of chain or graph such as pipelines and bridges. There are other complicated examples in the automotive industry, aircraft and space vehicles, containing rather than strings and beams, plates and shells. These multi-body structures are often complicated, and the mathematical models describing their evolution are quite complex. For the sake of simplicity, this volume considers only 1-d networks.

Boundary Stabilization of Thin Plates
Boundary Stabilization of Thin Plates

Author: John E. Lagnese

Publisher: SIAM

Published: 1989-01-01

Total Pages: 184

ISBN-13: 9781611970821

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Presents one of the main directions of research in the area of design and analysis of feedback stabilizers for distributed parameter systems in structural dynamics. Important progress has been made in this area, driven, to a large extent, by problems in modern structural engineering that require active feedback control mechanisms to stabilize structures which may possess only very weak natural damping. Much of the progress is due to the development of new methods to analyze the stabilizing effects of specific feedback mechanisms. Boundary Stabilization of Thin Plates provides a comprehensive and unified treatment of asymptotic stability of a thin plate when appropriate stabilizing feedback mechanisms acting through forces and moments are introduced along a part of the edge of the plate. In particular, primary emphasis is placed on the derivation of explicit estimates of the asymptotic decay rate of the energy of the plate that are uniform with respect to the initial energy of the plate, that is, on uniform stabilization results. The method that is systematically employed throughout this book is the use of multipliers as the basis for the derivation of a priori asymptotic estimates on plate energy. It is only in recent years that the power of the multiplier method in the context of boundary stabilization of hyperbolic partial differential equations came to be realized. One of the more surprising applications of the method appears in Chapter 5, where it is used to derive asymptotic decay rates for the energy of the nonlinear von Karman plate, even though the technique is ostensibly a linear one.

Control of Higher–Dimensional PDEs
Control of Higher–Dimensional PDEs

Author: Thomas Meurer

Publisher: Springer Science & Business Media

Published: 2012-08-13

Total Pages: 373

ISBN-13: 3642300154

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This monograph presents new model-based design methods for trajectory planning, feedback stabilization, state estimation, and tracking control of distributed-parameter systems governed by partial differential equations (PDEs). Flatness and backstepping techniques and their generalization to PDEs with higher-dimensional spatial domain lie at the core of this treatise. This includes the development of systematic late lumping design procedures and the deduction of semi-numerical approaches using suitable approximation methods. Theoretical developments are combined with both simulation examples and experimental results to bridge the gap between mathematical theory and control engineering practice in the rapidly evolving PDE control area. The text is divided into five parts featuring: - a literature survey of paradigms and control design methods for PDE systems - the first principle mathematical modeling of applications arising in heat and mass transfer, interconnected multi-agent systems, and piezo-actuated smart elastic structures - the generalization of flatness-based trajectory planning and feedforward control to parabolic and biharmonic PDE systems defined on general higher-dimensional domains - an extension of the backstepping approach to the feedback control and observer design for parabolic PDEs with parallelepiped domain and spatially and time varying parameters - the development of design techniques to realize exponentially stabilizing tracking control - the evaluation in simulations and experiments Control of Higher-Dimensional PDEs — Flatness and Backstepping Designs is an advanced research monograph for graduate students in applied mathematics, control theory, and related fields. The book may serve as a reference to recent developments for researchers and control engineers interested in the analysis and control of systems governed by PDEs.

Control of Distributed Parameter Systems
Control of Distributed Parameter Systems

Author: S. P. Banks

Publisher: Elsevier

Published: 2014-05-18

Total Pages: 554

ISBN-13: 1483151123

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Control of Distributed Parameter Systems covers the proceedings of the Second IFAC Symposium, Coventry, held in Great Britain from June 28 to July 1, 1977. The book focuses on the methodologies, processes, and techniques in the control of distributed parameter systems, including boundary value control, digital transfer matrix, and differential equations. The selection first discusses the asymptotic methods in the optimal control of distributed systems; applications of distributed parameter control theory of a survey; and dual variational inequalities for external eigenvalue problems. The book also ponders on stochastic differential equations in Hilbert space and their application to delay systems and linear quadratic optimal control problem over an infinite time horizon for a class of distributed parameter systems. The manuscript investigates the semigroup approach to boundary value control and stability of nonlinear distributed parameter systems. Topics include boundary control action implemented through a dynamical system; classical boundary value controls; stability of nonlinear systems; and feedback control on the boundary. The text also focuses on the functional analysis interpretation of Lyapunov stability; method of multipliers for a class distributed parameter systems; and digital transfer matrix approach to distributed system simulation. The selection is a dependable source of data for readers interested in the control of distributed parameter systems.

Control Of Nonlinear Distributed Parameter Systems
Control Of Nonlinear Distributed Parameter Systems

Author: Goong Chen

Publisher: CRC Press

Published: 2001-03-14

Total Pages: 380

ISBN-13: 0824745051

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An examination of progress in mathematical control theory applications. It provides analyses of the influence and relationship of nonlinear partial differential equations to control systems and contains state-of-the-art reviews, including presentations from a conference co-sponsored by the National Science Foundation, the Institute of Mathematics and its Applications, the University of Minnesota, and Texas A&M University.

Computational Collective Intelligence. Technologies and Applications
Computational Collective Intelligence. Technologies and Applications

Author: Jeng-Shyang Pan

Publisher: Springer

Published: 2010-11-06

Total Pages: 529

ISBN-13: 3642167322

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This volume composes the proceedings of the Second International Conference on Computational Collective Intelligence––Technologies and Applications (ICCCI 2010), which was hosted by National Kaohsiung University of Applied Sciences and Wroclaw University of Technology, and was held in Kaohsiung City on November 10-12, 2010. ICCCI 2010 was technically co-sponsored by Shenzhen Graduate School of Harbin Institute of Technology, the Tainan Chapter of the IEEE Signal Processing Society, the Taiwan Association for Web Intelligence Consortium and the Taiwanese Association for Consumer Electronics. It aimed to bring together researchers, engineers and po- cymakers to discuss the related techniques, to exchange research ideas, and to make friends. ICCCI 2010 focused on the following themes: • Agent Theory and Application • Cognitive Modeling of Agent Systems • Computational Collective Intelligence • Computer Vision • Computational Intelligence • Hybrid Systems • Intelligent Image Processing • Information Hiding • Machine Learning • Social Networks • Web Intelligence and Interaction Around 500 papers were submitted to ICCCI 2010 and each paper was reviewed by at least two referees. The referees were from universities and industrial organizations. 155 papers were accepted for the final technical program. Four plenary talks were kindly offered by: Gary G. Yen (Oklahoma State University, USA), on “Population Control in Evolutionary Multi-objective Optimization Algorithm,” Chin-Chen Chang (Feng Chia University, Taiwan), on “Applying De-clustering Concept to Information Hiding,” Qinyu Zhang (Harbin Institute of Technology, China), on “Cognitive Radio Networks and Its Applications,” and Lakhmi C.