Author: Harry Hammond Suber
Publisher:
ISBN:
Category :
Languages : en
Pages : 118

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Author: Noal Cope Harbertson
Publisher:
ISBN:
Category :
Languages : en
Pages : 108

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Author: P. Constantin
Publisher: Springer Science & Business Media
ISBN: 1461235065
Category : Mathematics
Languages : en
Pages : 133

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This work was initiated in the summer of 1985 while all of the authors were at the Center of Nonlinear Studies of the Los Alamos National Laboratory; it was then continued and polished while the authors were at Indiana Univer sity, at the University of Paris-Sud (Orsay), and again at Los Alamos in 1986 and 1987. Our aim was to present a direct geometric approach in the theory of inertial manifolds (global analogs of the unstable-center manifolds) for dissipative partial differential equations. This approach, based on Cauchy integral mani folds for which the solutions of the partial differential equations are the generating characteristic curves, has the advantage that it provides a sound basis for numerical Galerkin schemes obtained by approximating the inertial manifold. The work is self-contained and the prerequisites are at the level of a graduate student. The theoretical part of the work is developed in Chapters 2-14, while in Chapters 15-19 we apply the theory to several remarkable partial differ ential equations.

Author: Charles Li
Publisher: Springer Science & Business Media
ISBN: 1461218381
Category : Mathematics
Languages : en
Pages : 177

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In this monograph the authors present detailed and pedagogic proofs of persistence theorems for normally hyperbolic invariant manifolds and their stable and unstable manifolds for classes of perturbations of the NLS equation, as well as for the existence and persistence of fibrations of these invariant manifolds. Their techniques are based on an infinite dimensional generalisation of the graph transform and can be viewed as an infinite dimensional generalisation of Fenichels results. As such, they may be applied to a broad class of infinite dimensional dynamical systems.

Author: Georgio Eugenio Oscare Giacaglia
Publisher: Springer Science & Business Media
ISBN: 1461264006
Category : Mathematics
Languages : en
Pages : 379

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Book Description
This volume is intended to provide a comprehensive treatment of recent developments in methods of perturbation for nonlinear systems of ordinary differ ential equations. In this respect, it appears to be a unique work. The main goal is to describe perturbation techniques, discuss their ad vantages and limitations and give some examples. The approach is founded on analytical and numerical methods of nonlinear mechanics. Attention has been given to the extension of methods to high orders of approximation, required now by the increased accuracy of measurements in all fields of science and technology. The main theorems relevant to each perturbation technique are outlined, but they only provide a foundation and are not the objective of these notes. Each chapter concludes with a detailed survey of the pertinent literature, supplemental information and more examples to complement the text, when necessary, for better comprehension. The references are intended to provide a guide for background information and for the reader who wishes to analyze any particular point in more detail. The main sources referenced are in the fields of differential equations, nonlinear oscillations and celestial mechanics. Thanks are due to Katherine MacDougall and Sandra Spinacci for their patience and competence in typing these notes. Partial support from the Mathematics Program of the Office of Naval Research is gratefully acknowledged.

Author: Huan-Chi Chris Tseng
Publisher:
ISBN:
Category :
Languages : en
Pages : 274

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The integral manifold concept is used in this thesis for controller design in various problems. A definition and the conditions for the existence of the integral manifold are given. Integral manifolds in linear systems are analyzed with special attention given to how the linear system possesses an input dependent manifold. Flexibility in flexible link robots is shown to be a cause for phase delay, which is reduced by a corrective controller based on the integral manifold concept. For a class of nonlinear systems with nonlinear output, the author designed a nonlinear PI controller that achieve asymptotic tracking and disturbance rejection of bounded signals which are not only unknown but also slowly varying. Finally, we showed the existence of a lower order optimal problem which is equivalent to a singularly perturbed optimal problem with initial conditions restricted to a manifold. Throughout this thesis, results obtained from the manifold approach are shown to be consistent with, and sometimes even extend, some established results in singularly perturbed systems. Keywords: Manipulators; Optimal control. (KR).

Author: M. Fliess
Publisher: Elsevier
ISBN: 1483298752
Category : Technology & Engineering
Languages : en
Pages : 507

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This volume represents most aspects of the rich and growing field of nonlinear control. These proceedings contain 78 papers, including six plenary lectures, striking a balance between theory and applications. Subjects covered include feedback stabilization, nonlinear and adaptive control of electromechanical systems, nonholonomic systems. Generalized state space systems, algebraic computing in nonlinear systems theory, decoupling, linearization and model-matching and robust control are also covered.

Author: Alexander F. Vakakis
Publisher: John Wiley & Sons
ISBN: 3527617876
Category : Science
Languages : en
Pages : 552

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Book Description
This landmark book deals with nonlinear normal modes (NNMs) and nonlinear mode localization. Offers an analysis which enables the study of various nonlinear phenomena having no counterpart in linear theory. On a more theoretical level, the concept of NNMs will be shown to provide an excellent framework for understanding a variety of distinctively nonlinear phenomena such as mode bifurcations and standing or traveling solitary waves.

Author:
Publisher:
ISBN:
Category : Military research
Languages : en
Pages : 424

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Author: Zoran Gajic
Publisher: CRC Press
ISBN: 9780203907900
Category : Technology & Engineering
Languages : en
Pages : 334

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Highlights the Hamiltonian approach to singularly perturbed linear optimal control systems. Develops parallel algorithms in independent slow and fast time scales for solving various optimal linear control and filtering problems in standard and nonstandard singularly perturbed systems, continuous- and discrete-time, deterministic and stochastic, mul