Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 343, Issue -, Pages 186-232Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2022.10.001
Keywords
Infinite-dimensional Lie group; Geometric control theory; Fundamental vector field; G-manifold; Reachable set; Bang-bang principle
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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.
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.
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