A contact covariant approach to optimal control with applications to sub-Riemannian geometry. (English) Zbl 1350.49022
Summary: We discuss contact geometry naturally related with optimal control problems (and Pontryagin’s maximum principle). We explore and expand the observations of T. Ohsawa [“Contact geometry of the Pontryagin maximum principle”, Autom. J. IFAC 55, 1–5 (2015)], providing simple and elegant characterizations of normal and abnormal sub-Riemannian extremals.
MSC:
| 49K15 | Optimality conditions for problems involving ordinary differential equations |
| 53C17 | Sub-Riemannian geometry |
| 53D10 | Contact manifolds (general theory) |
| 58A30 | Vector distributions (subbundles of the tangent bundles) |
Keywords:
contact geometry; optimal control; Pontryagin’s maximum principle; contact vector field; sub-Riemannian geometry; abnormal extremalReferences:
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