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)
Famous quotes containing the word definition:
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)