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arXiv · 1810.02960

Jacobi Fields in Optimal Control I: Morse and Maslov Indices

Andrei Agrachev·Ivan Beschastnyi
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Abstract

In this paper we discuss a general framework based on symplectic geometry for the study of second order conditions in constrained variational problems on curves. Using the notion of L-derivatives we construct Jacobi curves, which represent a generalization of Jacobi fields from the classical calculus of variations, but which also works for non-smooth extremals. This construction includes in particular the previously known constructions for specific types of extremals. We state and prove Morse-type theorems that connect the negative inertia index of the Hessian of the problem to some symplectic invariants of Jacobi curves.

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Andrei Agrachev, Ivan Beschastnyi. 2021-03-22. Jacobi Fields in Optimal Control I: Morse and Maslov Indices. https://arxiv.org/abs/1810.02960

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