Approximate analysis of non-linear stochastic systems
作者:
SH.A. ASSAF,
L. D. ZIRKLE,
期刊:
International Journal of Control
(Taylor Available online 1976)
卷期:
Volume 23,
issue 4
页码: 477-492
ISSN:0020-7179
年代: 1976
DOI:10.1080/00207177608922174
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
In this paper a method is developed whereby the statistical characteristics of the response of non-linear stochastic systems are calculated with good accuracy. The method consists of the formulation and solution of the differential equations for the statistical characteristics of the processes under consideration. The development is based on the theory of Markov processes. In particular, use is made of Ito's differential rule to obtain a basic result which is used for the formulation of the differential equations. For the solution of the differential equations the method employs an approximate analytic representation of the probability density function of a random process. The representation is in the form of a finite Edgeworth (asymptotic) expansion. The method is quite general and yields accurate results. The treatment is illustrated by examples.
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