Small-time controllability of affine systems and quadratic Lie brackets
Karine Beauchard, Eugenio Pozzoli
Abstract
We prove a new sufficient condition for small-time global exact controllability of finite-dimensional control-affine systems. It points out that, under a natural Lie algebra rank condition, quadratic Lie brackets are the only possible obstacles to controllability. This result extends to infinite-dimensional settings such as the global approximate controllability of diffeomorphisms. It also allows us to interpret recent results in PDE control theory.
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