论文标题
控制理论的方面无限二维谎言组和G-manifolds
Aspects of control theory on infinite-dimensional Lie groups and G-manifolds
论文作者
论文摘要
我们开发了可能是无限尺寸的谎言组的几何控制理论的各个方面，以及在局部凸空间上模拟的平滑G-manifolds m上。作为一种工具，我们讨论了由时间依赖的基本向量场给出的m m的存在和唯一性问题，这些方程在时间上是l^1。然后，我们讨论M中可及的集合的封闭，以在G的Lie代数中或在Lie代数的紧凑型凸子集中进行对照。谎言组的规律性特性起着重要作用。
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.
