Classification of stable time-optimal controls on 2-manifolds
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In this paper, we provide a topological classification via graphs of time-optimal flows for generic control systems of the form \(\dot x = F(x) + uG(x)\), x ∈ M, |u| ≤ 1, on two-dimensional orientable compact manifolds, also proving the structural stability of generic optimal flows. More precisely, adding some additional structure to topological graphs, more precisely, rotation systems, and owing to a theorem of Heffter, dating back to the 19th century, we prove that there is a one-to-one correspondence between graphs with rotation systems and couples formed by a system and the 2-D manifold of minimal genus in which the system can be embedded.
KeywordsManifold Control System 19th Century Structural Stability Generic Control
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