Aspects of control theory on infinite-dimensional Lie groups and G-manifolds
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Publication:6345604
DOI10.1016/J.JDE.2022.10.001zbMath1522.22008arXiv2007.11277MaRDI QIDQ6345604
Helge Glöckner, Joachim Hilgert
Publication date: 22 July 2020
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 L^1 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.
Geometric methods (93B27) Control problems involving ordinary differential equations (34H05) Algebraic methods (93B25) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Attainable sets, reachability (93B03)
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