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Computational methods for time-scale...

Iravanchy, Shawn.

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Computational methods for time-scale analysis of nonlinear dynamical systems.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Computational methods for time-scale analysis of nonlinear dynamical systems./
Author:	Iravanchy, Shawn.
Description:	163 p.
Notes:	Source: Dissertation Abstracts International, Volume: 64-03, Section: B, page: 1348.
Contained By:	Dissertation Abstracts International64-03B.
Subject:	Engineering, Aerospace. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3085979

Computational methods for time-scale analysis of nonlinear dynamical systems.
Iravanchy, Shawn.

Computational methods for time-scale analysis of nonlinear dynamical systems. - 163 p.

Source: Dissertation Abstracts International, Volume: 64-03, Section: B, page: 1348.

Thesis (Ph.D.)--University of California, Irvine, 2003.

Knowledge of the time-scale structure of a smooth finite dimensional nonlinear dynamical system provides the opportunity for model decomposition, if there are two or more disparate time-scales. A few benefits of such model decomposition are simplified control design and analysis and reduced computational effort in simulation. Singular perturbation theory provides the tools necessary to analyze and decompose a multiple time-scale nonlinear system, provided that it is in <italic>standard form</italic>.Subjects--Topical Terms:

1018395
Engineering, Aerospace.

Computational methods for time-scale analysis of nonlinear dynamical systems.
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100 1 $a Iravanchy, Shawn. $3 1945737
245 1 0 $a Computational methods for time-scale analysis of nonlinear dynamical systems.
300 $a 163 p.
500 $a Source: Dissertation Abstracts International, Volume: 64-03, Section: B, page: 1348.
500 $a Chair: Kenneth D. Mease.
502 $a Thesis (Ph.D.)--University of California, Irvine, 2003.
520 $a Knowledge of the time-scale structure of a smooth finite dimensional nonlinear dynamical system provides the opportunity for model decomposition, if there are two or more disparate time-scales. A few benefits of such model decomposition are simplified control design and analysis and reduced computational effort in simulation. Singular perturbation theory provides the tools necessary to analyze and decompose a multiple time-scale nonlinear system, provided that it is in <italic>standard form</italic>.
520 $a This dissertation contributes to the development of a systematic approach for determining the time-scales and the associated geometric structure in the state-space for a differential equation model in general form. The development began with the Ph.D. research of Bharadwaj[32] and was extended further in the paper by Mease, Bharadwaj, and Iravanchy[31]. The approach proceeds from investigating the behavior of the linear variational dynamics associated with a nonlinear system. By analyzing the propagation of a hyper-sphere of initial conditions which evolves into an hyper-ellipsoid in the tangent space, the time-scale information may be quantified. The time-scale information is characterized by the Lyapunov exponents and vectors, and they are related to the principal axes of the hyper-ellipsoid. The Lyapunov spectrum characterizes the average exponential rates of expansion or decay of nearby trajectories and their associated directions. It is known that the classical eigenspace analysis does not provide the correct information, i.e., eigenvalues and eigenvectors of the linearized dynamics. In this thesis the theory is extended to include dynamical systems that operate in non-Euclidean space, since a state transformation may effectively change the metric. The presentation of the entire theory provides the background for presenting the primary new contributions in this dissertation: the development and application of numerical methods for time-scale analysis.
520 $a A systematic procedure is developed to diagnose, analyze, and extract the time-scale information for the system under study. The procedure includes the detection of the time-scales and their uniformity, the computation of the time-scale information, and the identification of a slow manifold. The algorithms are analyzed to better understand the error behavior, convergence rates, their geometric representation in state space, and the effect of state transformations. (Abstract shortened by UMI.)
590 $a School code: 0030.
650 4 $a Engineering, Aerospace. $3 1018395
650 4 $a Mathematics. $3 515831
650 4 $a Physics, General. $3 1018488
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710 2 0 $a University of California, Irvine. $3 705821
773 0 $t Dissertation Abstracts International $g 64-03B.
790 1 0 $a Mease, Kenneth D., $e advisor
790 $a 0030
791 $a Ph.D.
792 $a 2003
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3085979