In the geometric theory of nonlinear control systems, the notion of auddistribution and the dual notion of codistribution play a centraludrole. Many results in nonlinear control theory require certainuddistributions to be integrable. Distributions (and codistributions)udare not generically integrable and, moreover, the integrabilityudproperty is not likely to persist under small perturbations of theudsystem. Therefore, it is natural to consider the problem ofudapproximating a given codistribution by an integrable codistribution,udand to determine to what extent such an approximation may be used forudobtaining approximate solutions to various problems in controludtheory. In this note, we concentrate on the purely mathematicaludproblem of approximating a given codistribution by an integrableudcodistribution. We present an algorithm for approximating anudm-dimensional nonintegrable codistribution by an integrable one usinguda homotopy approach. The method yields an approximating codistributionudthat agrees with the original codistribution on an m-dimensionaludsubmanifold E_0 of R^n.ud
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