5 citations · 5 across the 2 of their papers we have counts for
4 papers
Singular extremals of optimal control problems with cost
Andrei Agrachev, Ivan Beschastnyi, Michele Motta
We study the optimal control problem for a control-affine system, where we want to minimize the norm of the control. First, we show how Pontryagin Maximum Principle (PMP) app…
Jacobi Fields in Optimal Control II: One-dimensional Variations
Andrei Agrachev, Ivan Beschastnyi
In this second paper of the series we specify general theory developed in the first paper. Here we study the structure of Jacobi fields in the case of an analytic system and piece-…
Jacobi Fields in Optimal Control I: Morse and Maslov Indices
Andrei Agrachev, Ivan Beschastnyi
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 o…
Symplectic Geometry of Constrained Optimization
A. Agrachev, I. Beschastnyi
These are the notes of rather informal lectures given by the first co-author in UPMC, Paris, in January 2017. Practical goal is to explain how to compute or estimate the Morse inde…