5 citations · 5 across the 3 of their papers we have counts for
6 papers · 1 filter
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…
Morse index and determinant of block Jacobi matrices via optimal control
Stefano Baranzini, Ivan Beschastnyi
We describe the relation between block Jacobi matrices and minimization problems for discrete time optimal control problems. Using techniques developed for the continuous case, we…
Index theorems for graph-parametrized optimal control problems
Andrei Agrachev, Stefano Baranzini, Ivan Beschastnyi
In this paper we prove Morse index theorems for a big class of constrained variational problems on graphs. Such theorems are useful in various physical and geometric applications.…
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…