Aspects of control theory on infinite-dimensional Lie groups and G-manifolds

2020/07/22 by Helge Glöckner, Glockner, Helge, Joachim Hilgert +1
Mathematics · #22E65 (primary) #28B05 #34A12 #34H05 #46E30 #46E40 (secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2007.11277

openalex publication_date 2020/07/22 · openalex created_date 2022/08/26 · openalex updated_date 2026/08/01

Abstract

We develop aspects of geometric control theory on Lie groups G which may be infinite dimensional, and on smooth G-manifolds M modelled on locally convex spaces. As a tool, we discuss existence and uniqueness questions for differential equations on M given by time-dependent fundamental vector fields which are L¹ in time. We then discuss the closures of reachable sets in M for controls in the Lie algebra of G, or within a compact convex subset of the Lie algebra. Regularity properties of the Lie group G play an important role.

Related

• Equivalence of Control Systems with Linear Systems on Lie Groups and Homogeneous Spaces
• Control contraction metrics on Lie groups
• Control in the spaces of ensembles of points
• An accessibility condition for discrete-time linear systems on Lie groups
• Solution Curve for Linear Control Systems on Lie Groups