Journal of convex analysis· 2026Q2
Minimal points and non-holonomic controllability on compact manifolds
- 0citations
- Q2SCImago
- 2026year
Short summary
Non-holonomic controllability on compact manifolds can be assessed solely on the closure of minimal points, provided the flow has a recursion property and satisfies the Hörmander condition.
AI-generated from the title and abstract; the full text is not read.
Key points
- Non-holonomic controllability on compact manifolds can be determined by examining the Hörmander condition on the closure of minimal points.
- This simplification applies to flows with recursion properties (nonwandering or chain recurrent).
- A 2D example illustrates a chain recurrent flow satisfying the Hörmander condition but lacking controllability.
AI-generated from the title and abstract; the full text is not read.
Abstract
We study the problem of non-holonomic point-to-point controllability for ODEs with drift possessing some recursion property of the flow (it is supposed nonwandering or chain recurrent) and satisfying various versions of the Hörmander condition (also known as Lie bracket generating condition). We show that for the flows on compact manifolds, it suffices to assume the validity of the Hörmander condition on the closure of the set of their minimal points only. Also, we construct a 2-dimensional example of a drift defining a chain recurrent flow and the vector fields defining the non-holonomic constraint, which together satisfy the Hörmander condition, but the flow is not controllable in the direction of the given vector fields.
The authors' abstract, as published at the source. Journal of convex analysis, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Control and Systems Engineering
Control and Systems EngineeringEngineering