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Jacobi Fields in Optimal Control I: Morse and Maslov Indices
- Publication Year :
- 2018
-
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.<br />Comment: Section 2 about the gluing formula completely removed, additional sources added to the introduction, examples added, various typos corrected
- Subjects :
- Mathematics - Optimization and Control
Mathematics - Differential Geometry
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1810.02960
- Document Type :
- Working Paper