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A Homotopy Algorithm for Approximating Geometric Distributions by Integrable Systems

Sluis, Willem M. and Banaszuk, Andrzej and Hauser, John and Murray, Richard M. (1995) A Homotopy Algorithm for Approximating Geometric Distributions by Integrable Systems. California Institute of Technology . (Unpublished) http://resolver.caltech.edu/CaltechCDSTR:1995.CIT-CDS-95-025

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Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechCDSTR:1995.CIT-CDS-95-025

Abstract

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.


Item Type:Report or Paper (Technical Report)
Group:Control and Dynamical Systems Technical Reports
Record Number:CaltechCDSTR:1995.CIT-CDS-95-025
Persistent URL:http://resolver.caltech.edu/CaltechCDSTR:1995.CIT-CDS-95-025
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28015
Collection:CaltechCDSTR
Deposited By: Imported from CaltechCDSTR
Deposited On:18 Oct 2002
Last Modified:26 Dec 2012 14:28

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