Jacobi fields in optimal control: Morse and Maslov indices
| Autor: | Ivan Beschastnyi, Andrei A. Agrachev |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Hessian matrix
Pure mathematics media_common.quotation_subject Morse code Inertia law.invention Lagrangian Grassmanian symbols.namesake law Settore MAT/05 - Analisi Matematica Mathematics media_common Applied Mathematics Order (ring theory) State (functional analysis) Optimal control Morse theorems Maslov index Jacobi fields symbols Spectral flow Calculus of variations Analysis Symplectic geometry |
| Popis: | 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 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. |
| Databáze: | OpenAIRE |
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