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A Homotopy Algorithm for Approximating Geometric Distributions by Integrable Systems
Abstract In the geometric theory of nonlinear contr …
In the geometric theory of nonlinear control systems, the notion of a distribution and the dual notion of codistribution play a central role. Many results in nonlinear control theory require certain distributions to be integrable. Distributions (and codistributions) are not generically integrable and, moreover, the integrability property is not likely to persist under small perturbations of the system. Therefore, it is natural to consider the problem of approximating a given codistribution by an integrable codistribution, and to determine to what extent such an approximation may be used for obtaining approximate solutions to various problems in control theory. In this note, we concentrate on the purely mathematical problem of approximating a given codistribution by an integrable codistribution. We present an algorithm for approximating an m-dimensional nonintegrable codistribution by an integrable one using a homotopy approach. The method yields an approximating codistribution that agrees with the original codistribution on an m-dimensional submanifold E_0 of R^n.
n an m-dimensional submanifold E_0 of R^n.  +
Authors Willem M. Sluis, Andzrej Banaszuk, John Hauser, Richard M. Murray  +
ID 1995r  +
Source <i>System and Control Letters</i>, 27: (5) 285-291  +
Tag sbhm95-cds  +
Title A Homotopy Algorithm for Approximating Geometric Distributions by Integrable Systems +
Type CDS Technical Report  +
Categories Papers
Modification date
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15 May 2016 06:20:26  +
URL
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ftp://ftp.cds.caltech.edu/pub/cds/techreports/postscript/cds95-025.pdf  +
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A Homotopy Algorithm for Approximating Geometric Distributions by Integrable Systems + Title
 

 

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