李代数子代数的收敛实现
Convergent realizations of Lie subalgebras
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中文总结 AI 辅助
研究有限余维李代数子代数在局部解析向量场意义下收敛实现的刻画，给出性质推广及在控制理论中的应用，恢复并阐明控制仿射系统相关的一些结果。
中文摘要 AI 辅助
自Guillemin和Sternberg的开创性工作以来，已知有限余维的李代数子代数可实现为形式幂级数上形式向量场的子代数。在本笔记中，我们刻画了在局部解析向量场意义下允许收敛实现的李代数子代数。我们对输出实现问题给出了这些性质的推广。我们在控制理论背景下给出了这些代数结果的重新表述和应用。特别是，我们恢复并阐明了关于控制仿射系统的陈 - 弗利斯级数实现、控制系统的等价性、嵌入或规范系统的存在性的先前结果。
英文摘要
It has been known since the seminal work of Guillemin and Sternberg that Lie subalgebras of finite codimension of an arbitrary real or complex Lie algebra can be realized as subalgebras of formal vector fields over formal power series. In this note, we characterize the Lie subalgebras which admit a convergent realization in the sense of locally analytic vector fields. We give generalizations of these properties for the problem of output realization. We give reformulations and applications of these algebraic results in the context of control theory. In particular, we recover and clarify previous results on the realization of Chen--Fliess series for control-affine systems, the equivalence of control systems, and the existence of embedded or canonical systems.
