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**A Homotopy Algorithm for Approximating Geometric Distributions by Integrable Systems +***(In the geometric theory of nonlinear contr … In 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.)*