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

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 algebrag of G, or within a compact convex subset of g. Regularity properties of the Lie group G play an important role. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

In this paper, we develop certain aspects of geometric control theory on Lie groups G, including the infinite-dimensional case, and on smooth G-manifolds M modeled on locally convex spaces. We utilize time-dependent fundamental vector fields that are L-1 in time to examine the existence and uniqueness of differential equations on M. We also explore the closures of reachable sets in M for controls in the Lie algebra of G or within a compact convex subset of g, with the regularity properties of Lie group G playing a crucial role.