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 -derivatives we construct Jacobi curves, which represent a generalisation 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.

Jacobi Fields in optimal control: Morse and Maslov indices / Agrachev, A.; Beschatnyi, I.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 214:(2022). [10.1016/j.na.2021.112608]

Jacobi Fields in optimal control: Morse and Maslov indices

Agrachev, A.;
2022-01-01

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 -derivatives we construct Jacobi curves, which represent a generalisation 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.
2022
214
112608
https://arxiv.org/abs/1810.02960
Agrachev, A.; Beschatnyi, I.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/131617
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