Controllability in codimension one
Let M be an n-dimensional connected analytic manifold. A nonlinear control system of the form \((*)\quad x'=X(x)+\sum^{s}_{i=1}u_ iX^ i(x),\) \(x\in M\) is said to have codimension one when the Lie algebra generated by the vector fields \(X^ 1,...,X^ s\) has dimension n-1 at every point of M. In this paper it is proved that some necessary conditions formerly obtained by the same author, plus some transversality conditions, turn out to be sufficient for local and global controllability of (*).
scientific article; zbMATH DE number 4008190
scientific article