On the curves that may be approached by trajectories of a smooth control affine system
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چکیده
In this paper, we give a characterization of the set of curves that may be approached by trajectories of a smooth control-a ne nonlinear system, in the topology of uniform convergence. This characterization is in terms of the drift vector field and the distribution spanned by the Lie algebra generated by the control vector fields. The characterization is valid on open sets where this distribution has constant rank. These results also characterize the support of di↵usion processes with smooth coe cients. ⇤This work was partially supported by NSERC grant OG0036498, when the author was with Dept. of Mathematics, University of Toronto. 1 http://dx.doi.org/10.1016/S0167-6911(98)00086-3
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On the curves that may be approached by trajectories of a smooth control affine system
In this paper, we give a characterization of the set of curves that may be approached by trajectories of a smooth control-aane nonlinear system, in the topology of uniform convergence. This characterization is in terms of the drift vector eld and the distribution spanned by the Lie algebra generated by the control vector elds. The characterization is valid on open sets where this distribution h...
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