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arXiv · 2007.11277

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

Helge Glockner·Joachim Hilgert
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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.

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Helge Glockner, Joachim Hilgert. 2020-07-22. Aspects of control theory on infinite-dimensional Lie groups and G-manifolds. https://arxiv.org/abs/2007.11277

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