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SIAM J. Control 13, pp. 1271-1281 (11 pages)
On Controllability by Means of Two Vector Fields
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Add to FacebookA set $S$ of vector fields on a differentiable manifold $M$ is said to be completely controllable if for every pair $(m,m')$ of points of $M$ there exists a trajectory of $S$ from $m$ to $m'$. Here a trajectory of $S$ is a curve which is an integral curve of some $X \in S$ or a finite concatenation of such curves so that, in general, a trajectory of $S$ run in reverse is no longer a trajectory. Our main theorem is: on every connected paracompact manifold of class $C^k $, $2 \leqq k \leqq \infty $, or $k = \omega $, there exists a completely controllable set $S$ consisting of two vector fields of class $C^{k - 1} $.
© 1975 Society for Industrial and Applied Mathematics
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Received May 17, 1974
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