Definition
Let be a control system, where belongs to a finite-dimensional manifold and belongs to a control set . Consider the family and assume that every vector field in is complete. For every and every real, denote by the flow of at time .
The orbit of the control system through a point is the subset of defined by
- Remarks
The difference between orbits and attainable sets is that, whereas for attainable sets only forward-in-time motions are allowed, both forward and backward motions are permitted for orbits. In particular, if the family is symmetric (i.e., if and only if ), then orbits and attainable sets coincide.
The hypothesis that every vector field of is complete simplifies the notations but can be dropped. In this case one has to replace flows of vector fields by local versions of them.
Read more about this topic: Orbit (control Theory)
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