It is a little tough to tell what you are asking because of the limited information. It would be helpful if you would show how these vectors fit in your control scheme. However, I'll start an answer and maybe we can arrive at the one you need.
If you are strictly talking about the positions and velocities without regard for how to control them to achieve those poses, then you are just describing differential, or velocity, kinematics. The arrangement into new pose vectors isn't meaningful in this case.
If you are trying to do this to achieve positional via points which are arrived at with a certain velocity, you may benefit from studying velocity control. Off the top of my head I believe Hollerbach had some seminal work in this, but I could be mistaken.
If you are actually concerned with the robot's position and velocities as states to feed into a controller, then you should study state space control. @Chuck has answered some questions with excellent descriptions of state space, and there are numerous other public sources available.
EDIT BASED ON OP's COMMENT
Thanks for describing the scheme. It would be best to put that into your question since comments can disappear eventually.
You are describing an aspect of robotic controls that is generally called path planning, trajectory generation, or sometimes trajectory planning. Purists will differentiate between path planning and trajectory planning in that path planning refers to the geometry of the path (in operational and/or configuration space) only, whereas trajectory planning includes a time element. So your approach is really about trajectory planning, although the literature doesn't always separate the two like that.
The literature in this field includes planning for robotic manipulators, redundant robots, and mobile robots. Often the path planning problem includes avoiding obstacles or optimizing some run-time criterion. However, there are also many earlier papers which describe the planning aspect of manipulators without regard to obstacles. Frequently those papers describe time-optimal methods for achieving target trajectories.
You may want to start your research looking for work by Bruno Siciliano.