An Approximate Analysis of Transient Response, Moments, and Power Spectrum for Non-linear Feedback Control over the Internet

Hideki SATOH

An Approximate Analysis of Transient Response, Moments, and Power Spectrum for Non-linear Feedback Control over the Internet

Hideki SATOH

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Moment matrix analysis (MMA) that can derive statistical properties of non-linear equations is presented in this paper. First, non-linear stochastic differential, or difference, equations are approximately expressed by simultaneous linear equations of moments defined at discrete events. Next, by eliminating higher order moments, the simultaneous linear equations are reduced to a linear vector equation of their coefficient matrix and a moment vector comprised of the moments of the system state. By computing the eigenvectors and eigenvalues of the coefficient matrix, we can analyze the moments, transient response, and spectrum of the system state. The behavior of Internet traffic was evaluated by using MMA and computer simulation, and it is shown that MMA is effective for evaluating simultaneous non-linear stochastic differential equations.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E87-A No.9 pp.2331-2338

Publication Date: 2004/09/01

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Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)

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Hideki SATOH, "An Approximate Analysis of Transient Response, Moments, and Power Spectrum for Non-linear Feedback Control over the Internet" in IEICE TRANSACTIONS on Fundamentals, vol. E87-A, no. 9, pp. 2331-2338, September 2004, doi: .
Abstract: Moment matrix analysis (MMA) that can derive statistical properties of non-linear equations is presented in this paper. First, non-linear stochastic differential, or difference, equations are approximately expressed by simultaneous linear equations of moments defined at discrete events. Next, by eliminating higher order moments, the simultaneous linear equations are reduced to a linear vector equation of their coefficient matrix and a moment vector comprised of the moments of the system state. By computing the eigenvectors and eigenvalues of the coefficient matrix, we can analyze the moments, transient response, and spectrum of the system state. The behavior of Internet traffic was evaluated by using MMA and computer simulation, and it is shown that MMA is effective for evaluating simultaneous non-linear stochastic differential equations.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e87-a_9_2331/_p

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@ARTICLE{e87-a_9_2331,
author={Hideki SATOH, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={An Approximate Analysis of Transient Response, Moments, and Power Spectrum for Non-linear Feedback Control over the Internet},
year={2004},
volume={E87-A},
number={9},
pages={2331-2338},
abstract={Moment matrix analysis (MMA) that can derive statistical properties of non-linear equations is presented in this paper. First, non-linear stochastic differential, or difference, equations are approximately expressed by simultaneous linear equations of moments defined at discrete events. Next, by eliminating higher order moments, the simultaneous linear equations are reduced to a linear vector equation of their coefficient matrix and a moment vector comprised of the moments of the system state. By computing the eigenvectors and eigenvalues of the coefficient matrix, we can analyze the moments, transient response, and spectrum of the system state. The behavior of Internet traffic was evaluated by using MMA and computer simulation, and it is shown that MMA is effective for evaluating simultaneous non-linear stochastic differential equations.},
keywords={},
doi={},
ISSN={},
month={September},}

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TY - JOUR
TI - An Approximate Analysis of Transient Response, Moments, and Power Spectrum for Non-linear Feedback Control over the Internet
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2331
EP - 2338
AU - Hideki SATOH
PY - 2004
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E87-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2004
AB - Moment matrix analysis (MMA) that can derive statistical properties of non-linear equations is presented in this paper. First, non-linear stochastic differential, or difference, equations are approximately expressed by simultaneous linear equations of moments defined at discrete events. Next, by eliminating higher order moments, the simultaneous linear equations are reduced to a linear vector equation of their coefficient matrix and a moment vector comprised of the moments of the system state. By computing the eigenvectors and eigenvalues of the coefficient matrix, we can analyze the moments, transient response, and spectrum of the system state. The behavior of Internet traffic was evaluated by using MMA and computer simulation, and it is shown that MMA is effective for evaluating simultaneous non-linear stochastic differential equations.
ER -