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 smooth G-manifolds M modelled locally convex spaces. As a tool, we discuss existence uniqueness questions for differential equations given by time-dependent fundamental vector fields are L1 in time. then the closures reachable sets controls algebra g G, or within compact subset g. Regularity properties group play an important role.