Abstract
In this chapter we study general properties of attainable sets. We consider families of vector fields F on a smooth manifold M that satisfy the property
In this case the system F is called bracket-generating, or full-rank. By the analytic version of the Orbit Theorem (Corollary 5.17), orbits of a bracket-generating system are open subsets of the state space M.
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© 2004 Springer-Verlag Berlin Heidelberg
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Agrachev, A.A., Sachkov, Y.L. (2004). Attainable Sets. In: Control Theory from the Geometric Viewpoint. Encyclopaedia of Mathematical Sciences, vol 87. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06404-7_8
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DOI: https://doi.org/10.1007/978-3-662-06404-7_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05907-0
Online ISBN: 978-3-662-06404-7
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