A Hamiltonian approach to small time local attainability of manifolds for nonlinear control systems
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Publication:6409109
DOI10.1007/S00245-023-09973-5arXiv2208.13476MaRDI QIDQ6409109
Publication date: 29 August 2022
Abstract: This paper develops a new approach to small time local attainability of smooth manifolds of any dimension, possibly with boundary and to prove H"older continuity of the minimum time function. We give explicit pointwise conditions of any order by using higher order hamiltonians which combine derivatives of the controlled vector field and the functions that locally define the target. For the controllability of a point our sufficient conditions extend some classically known results for symmetric or control affine systems, using the Lie algebra instead, but for targets of higher dimension our approach and results are new. We find our sufficient higher order conditions explicit and easy to use for targets with curvature and general control systems.
Controllability (93B05) Nonlinear systems in control theory (93C10) Generalized manifolds (57P99) Hamilton-Jacobi equations (35F21)
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