Control vector fields on manifolds and attainability
This paper contains a coordinate-free proof of the following statement: if (ξ, U) is a given control vector field on a finite-dimensional manifold of class C3, then any control u ε U steering a point of the manifold to the boundary of its set of attainability satisfies the Pontryagin Maximum Principle. Similar results for control processes in Euclidean spaces (under various restrictions) have been proved by different methods (see e.g. , , ).
KeywordsVector Field Integral Curve Pontryagin Maximum Principle Control Space Continuous Linear Mapping
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