AbstractFormal power series products appear in nonlinear control theory when systems modeled by Chen–Fliess series are interconnected to form new systems. In fields like adaptive control and learning systems, the coefficients of these formal power series are estimated sequentially with real-time data. The main goal is to prove the continuity and analyticity of such products with respect to several natural (locally convex) topologies on spaces of locally convergent formal power series in order to establish foundational properties behind these technologies. In addition, it is shown that a transformation group central to describing the output feedback connection is in fact an analytic Lie group in this setting with certain regularity properties.

中文翻译：

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非线性控制理论中形式幂级数积的连续性

摘要 当以 Chen-Fliess 级数建模的系统相互连接形成新系统时，非线性控制理论中出现形式化的幂级数积。在自适应控制和学习系统等领域，这些形式幂级数的系数是用实时数据顺序估计的。主要目标是证明此类产品相对于局部收敛形式幂级数空间上的几种自然（局部凸）拓扑的连续性和可分析性，以建立这些技术背后的基础特性。此外，它表明，一个描述输出反馈连接的核心变换群实际上是该设置中的一个解析李群，具有一定的规律性。