FINITE-TIME AND EXACT-TIME CONTROLLABILITY ON COMPACT MANIFOLDS

摘要

It is first shown that a smooth controllable system on a compact manifold is finite-time controllable. The technique of proof is close to that of Sussmann's orbit theorem, and no rank condition is required.This technique is also used to give a new and elementary proof of the equivalence between controllability for essentially bounded inputs and for piecewise constant ones.Two sufficient conditions for controllability at exact time on a compact manifold are then stated.Some applications, in particular, to linear systems on Lie groups, are given.