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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 mdimensional nonintegrable
codistribution by an integrable one using a homotopy approach. The method yields an
approximating codistribution that agrees with the original codistribution on an
mdimensional submanifold E_0 of R^n. n an
mdimensional 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) 285291 + 
Tag  sbhm95cds + 
Title  A Homotopy Algorithm for Approximating Geometric Distributions by Integrable Systems + 
Type  CDS Technical Report + 
Categories  Papers 
Modification date This property is a special property in this wiki.

15 May 2016 06:20:26 + 
URL This property is a special property in this wiki.

ftp://ftp.cds.caltech.edu/pub/cds/techreports/postscript/cds95025.pdf + 
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A Homotopy Algorithm for Approximating Geometric Distributions by Integrable Systems +  Title 
