Some properties of the value function and its level sets for affine control systems with quadratic cost
type: Dataset
description: Let $T>0$ fixed. We consider the optimal control problem for analytic affine systems~: $\ds{\dot{x}=f_0(x)+\sum_{i=1}^m u_if_i(x)}$, with a cost of the form~: $\ds{C(u)=\int_0^T \sum_{i=1}^m u_i^2(t)dt}$. For this kind of systems we prove that if there are no minimizing abnormal extremals then the value function $S$ is subanalytic. Secondly we prove that if there exists an abnormal minimizer of corank 1 then the set of end-points of minimizers at cost fixed is tangent to a given hyperplane. We illustrate this situation in sub-Riemannian geometry.
landing page: 1079-2724
keyword: abnormal-minimizers
keyword: infoeu-reposemanticsarticle
keyword: journal-articles
keyword: mathmath-ocmathematics-mathoptimization-and-control-mathoc
keyword: optimal-control
keyword: sub-riemannian-geometry
keyword: subanalyticity
keyword: value-function
issued: 2026-05-09T16:21:24.730905
modified: 2026-05-09T16:21:24.730909
language: en
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Some properties of the value function and its level sets for affine control systems with quadratic cost
type: Distribution
format: HTML
access URL: https://hal.science/hal-00086284
issued: 2026-05-09T16:21:24.736632
modified: 2026-05-09T16:21:24.721753