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A list of all pages that have property "Abstract" with value "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.". Since there have been only a few results, also nearby values are displayed.

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• A Homotopy Algorithm for Approximating Geometric Distributions by Integrable Systems  + (In the geometric theory of nonlinear contrIn the geometric theory of nonlinear control systems, the notion of a distribution and</br>the dual notion of codistribution play a central role. Many results in nonlinear control</br>theory require certain distributions to be integrable. Distributions (and codistributions)</br>are not generically integrable and, moreover, the integrability property is not likely to</br>persist under small perturbations of the system. Therefore, it is natural to consider the</br>problem of approximating a given codistribution by an integrable codistribution, and to</br>determine to what extent such an approximation may be used for obtaining approximate</br>solutions to various problems in control theory. In this note, we concentrate on the</br>purely mathematical problem of approximating a given codistribution by an integrable</br>codistribution. We present an algorithm for approximating an m-dimensional nonintegrable</br>codistribution by an integrable one using a homotopy approach. The method yields an</br>approximating codistribution that agrees with the original codistribution on an</br>m-dimensional submanifold E_0 of R^n.n an m-dimensional submanifold E_0 of R^n.)