Geometry of Optimal Control Problems and Hamiltonian Systems
By Andrei A. Agrachev. 2005
64 citations recorded by the source corpus.
These notes are based on the mini-course given in June 2004 in Cetraro, Italy, in the frame of a C.I.M.E. school. Of course, they contain much more material that I could present in the 6 hours course. The main goal is to give an idea of the general variational and dynamical nature of nice and powerful concepts and results mainly known in the narrow framework of Riemannian Geometry. This concerns Jacobi fields, Morse's index formula, Levi Civita connection, Riemannian curvature and related topics. I tried to make the presentation as light as possible: gave more details in smooth regular situations and referred to the literature in more complicated cases.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/5800a5b0cfa4e73a0ee77f2dd3f9402841fd025b
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In Geometry and Topology
- Davide Barilari
- Andrei A. Agrachev
- Ugo V. Boscain
- Fabrice Baudoin
- Nicola Garofalo
- Paul W. Y. Lee
- Yuri L. Sachkov
- A. Ardentov
In Mathematical Physics
- Ugo V. Boscain
- Davide Barilari
- Fabrice Baudoin
- Andrei A. Agrachev
- Nicola Garofalo
- Paul W. Y. Lee
- Yuri L. Sachkov
- A. Ardentov
In Statistical and Nonlinear Physics
- Fabrice Baudoin
- Nicola Garofalo
- Yuri L. Sachkov
- Paul W. Y. Lee
- A. Ardentov
- Ugo V. Boscain
- Andrei A. Agrachev
- Davide Barilari
Citations in the corpus
- A Comprehensive Introduction to Sub-Riemannian Geometry (2019, background): “The study of Lagrange multipliers through the theory of Morse problems have been initiated in [AG98], see also the survey [Agr08].”
- Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries (2011, methodology): “In their preprint [2] Agrachev and Lee have used a notion of Ricci tensor, denoted by Ric, which was introduced by the first author in [1].”
- Optimal transportation under nonholonomic constraints (2007, background): “First, we recall some basic notions in the geometry of optimal control problems; see [2, 14] and the references therein for the details.”
- Conjugate points in nilpotent sub-Riemannian problem on the Engel group (2012, background): “ 1 +o(u5 1). Finally, g(u 1) is a comparison function for −(d0 0(u 1) + d02(u 1)) therefore it follows from Lemma 2 that d0 0(u 1)+d02(u 1) < 0 for u 1 ∈ (0,π). 8 Lemma 6. For any u 1 ∈ (0,π), x ∈ [0,1], we have J0 1(u 1,x) < 0 Proof. If u 1 ∈ (0,π), then J0 1(u 1,0) < 0 (see Lemma 4), J 1 ”